Towards Terahertz Dual-comb Spectroscopy Based
on
Quantum Cascade
Lasers
I
by
ARC_
M
Yang Yang
NOV 022015
B.Eng., Zhejiang University (2013)
LIBRARIES
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted
Signature.redacte
Author .................
Department of Electrical Engineering and Computer Science
August 20, 2015
Certified by.......Signature
redacted...........
Qing Hu
Professor
Thesis Supervisor
redacted
Accepted by...................Signature
/
_
MASSSHETTS0NSTUTE
1N
F HNO
g1alA. Kolodziejski
Chairman, Department Committee on Graduate Theses
Towards Terahertz Dual-comb Spectroscopy Based on
Quantum Cascade Lasers
by
Yang Yang
Submitted to the Department of Electrical Engineering and Computer Science
on August 20, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
In this thesis, terahertz (THz) laser frequency combs are improved and THz dualcomb spectroscopy method is demonstrated. To achieve better performance of THz
quantum cascade laser (QCL) frequency combs, several broadband homogeneous and
heterogeneous gain media are characterized, and corresponding dispersion compensators are designed. All THz QCL frequency combs are fabricated in Microsystems
Technology Laboratories at MIT using our group's standard process. By utilizing
the broad spectral coverage of THz QCL frequency combs and the multiheterodyne
detection method, a prototype of the THz dual-comb spectrometer is demonstrated.
This thesis work provides an important step towards realizing laser-based broadband
THz spectroscopy system for chemical identification and explosive detection.
Thesis Supervisor: Qing Hu
Title: Professor
3
Acknowledgments
I would like to express my sincere gratitude to my advisor Professor Qing Hu, for
providing the hard-core technology platform of terahertz quantum cascade laser and
giving me the opportunity to work on this project. His perseverance and dedication
have shaped me to be a better researcher and his research philosophy of pursuing
things, which really matter and last longer, will continue influencing me in the future.
Working in Qing's group, I have had the pleasure of working with many brilliant
minds. I would like to thank Dr. Ivan Chan and Xiaowei Cai for their time teaching
me how to do fabrication in the cleanroom. All of my fabrication skills come from their
patience and guidance. I am grateful to Dr. David Burghoff, my research mentor. I
thank David for initializing this project and offering me tremendous help when I was
a fledging. At the research aspect, David is still my role model, who stands on high
discipline, maintains the curiosity and the ambition, and is resourceful and handson. I would also like to thank Dr. Asaf Albo, Ali Khalatpour and Tianyi Zeng for
their support and accompany going through the financial dark period of the group
together.
Out side of research, I would like to thanks Prof. Terry Orlando for being my
academic advisor at MIT. We only meet twice a year, yet he makes each time counts.
Also, I feel so lucky to have a life mentor, Mr. John Redding. I would also thanks John
for spending his time and sharing his life-long experience with me. Those enlightening
conversations and fabulous off-campus activities really make my MIT life colorful and
memorable.
To all of my friends at or out of MIT, I am so grateful to know all of you in person.
My thanks go for the time we play basketball together, hang out together and play
drama together. I am not good at handle negative emotions and thank all of you for
keeping me sane and healthy. You are awesome!
To my family, for their consistent love and support through my life. Year 2015 is
the thirteenth year in my life being far from my family for better education. Looking
back to the first time when a young boy said goodbye to his family and left his
5
hometown alone, no one knew what the future would give to him. I can never get
to my current place without their sacrifice and understanding. I owe all, that I have
experienced and achieved, to you two, my mom and dad.
6
Contents
1
2
Introduction
17
1.1
Terahertz G ap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.2
Terahertz Quantum Cascade Lasers . . . . . . . . . . . . . . . . . . .
19
1.3
Terahertz Laser Frequency Combs . . . . . . . . . . . . . . . . . . . .
21
1.4
Terahertz Frequency Combs Based Spectroscopy . . . . . . . . . . . .
23
1.5
Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
Key Elements to Achieve Terahertz Laser Frequency Combs
25
2.1
Gain M edium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
. . . .
28
2.2
2.3
3
4
2.1.1
Homogeneous Gain Media- OW1194E-M4 and FL183s
2.1.2
Heterogeneous Gain Media- ETHOWI3E and ETHOWIE3-3
Dispersion Measurement
. . . . . . . . . . . . . . . . . . . . . . . . .
30
33
2.2.1
Introduction of THz-TDS
. . . . . . . . . . . . . . . . . . . .
34
2.2.2
Actual Dispersion Measurement . . . . . . . . . . . . . . . . .
36
. . .
38
Dispersion Compensator Design Implemented on ETHOWIE3-3
Fabrication of THz Laser Frequency Combs
43
3.1
General Fabrication Process
. . . . . . . . . . . . . . . . . . . . . . .
43
3.2
Lens M ounting
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Characterization of THz QCL frequency combs
51
4.1
Repetition rate beatnote measurement and beatnote stabilization
4.2
Coherence measurement of THz QCL frequency combs
7
.
. . . . . . . .
51
54
5
4.2.1
Mutual coherence of two lines . . . . . . . . . . . . . . . . . .
55
4.2.2
Mutual coherence of comb lines
. . . . . . . . . . . . . . . . .
58
4.2.3
Actual SWIFTS measurement . . . . . . . . . . . . . . . . . .
61
4.2.4
Coherence measurement in non-comb regions . . . . . . . . . .
64
4.2.5
Technical considerations for SWIFTS . . . . . . . . . . . . . .
67
Terahertz Dual-comb Spectroscopy Based on QCL Frequency Combs 71
5.1
Principle of the dual-comb sepctroscopy
5.2
Trial of THz dual-comb spectroscopy using QCL frequency combs
. . . . . . . . . . . . . . . .
.
71
76
A Fabrication Flow
85
B Lens Mounting Process
91
8
List of Figures
1-1
The "terahertz gap" in the electromagnetic spectrum.
1-2
Chemical structure of various explosives as well as the corresponding
terahertz absorption spectra (from Ref.[12j)
1-3
. . . . . . . . .
. . . . . . . . . . . . . .
18
19
Intersubband versus interband transitions. Unlike the interband transition energy(hw 2 ),which are essentially restricted to the bandgap of
the material, intersubband transition energy(hwi) can be engineered
via adjusting the growth thickness.
1-4
Schematic of QCL operation.
. . . . . . . . . . . . . . . . . . .
20
Theoretically speaking, one electron
emits one photon in each module before moving into the next one.
From Ref.16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-5
21
Illustration of a frequency comb. In the frequency domain, it consists
of large numbers of equally spaced modes separated by its repetition
rate frep together with a potential non-zero starting frequency fo, the
offset frequency; If all modes have the same phase, in the time domain,
it corresponds to a train of coherent pulses separated by the round trip
time, T =
I.
frep
Adjacent pulse shows a phase slippage, AO
=
2,T
fo
From R ef.[1j . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-6
Schematic of a basic photoconductive switch based on LT-GaAs. From
R ef.[41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-1
22
23
(a) Degenerate FWMs and non-degenerate FWMs. (b) In QCLs, FWM
generates sideband lasing frequencies, injection locking a multi-mode
laser to form a comb.Modified from Ref.[4]
9
. . . . . . . . . . . . . . .
26
2-2
(a) Band diagram of QCL at low bias and at high bias. (b) THz output
power versus the biasing current from one OW1194E-M4 device. (c)
Lasing spectrum due to resonant tunneling at low bias range. (d)Lasing
spectrum due to scattering assistant at high bias range. Inserts show
schemes of individual operating principle. . . . . . . . . . . . . . . . .
29
2-3
Band diagram of FL183s. . . . . . . . . . . . . . . . . . . . . . . . . .
30
2-4
Lasing spectrum of FL183s under design bias.
30
2-5
(a)Calculated gain cross-section g, . Blue curves: individual designs.
. . . . . . . . . . . . .
Green curve: total active region. Insert: arrangement of different active
region designs in the laser. (b)Octave-spanning spectrum of a device
under design bias. From Ref.[19] . . . . . . . . . . . . . . . . . . . . .
2-6
32
(a)Biasing voltage/current relationship versus operating temperature;
Output optical power at corresponding biasing. Same color line shows
data at same temperature. (b) Lasing spectrum at design bias(35K).
2-7
Typical terahertz time domain spectroscopy set-up and data requisition
scheme.From Ref.[4] . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-8
33
35
Detected terahertz pulse. The blue curve shows the pulse after one
round-trip, and the green curve shows the sample pulse after three
round-trips. From Ref. [4] . . . . . . . . . . . . . . . . . . . . . . . . .
2-9
37
Dispersion extrapolation for the time domain data. (a)Amplitude of
two adjacent pulses. one round-trip pulse is shown in blue and three
roun-trips one in green. (b) Phase of two adjacent pulses except their
linear components.
(c)Phase difference of the adjacent pulses.
Group velocity dispersion versus the laser biasing. From Ref.[4]
2-10 Dispersion compensator for low cavity dispersion.
versus frequency.
design .
(b) Reflectivity versus frequency.
(d)
. . .
(a) Group delay
(c) Corrugation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-11 Dispersion compensator for high cavity dispersion.
versus frequency.
(b) Reflectivity versus frequency.
40
(a) Group delay
(c) Corrugation
design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
38
41
3-1
Major steps in metal-metal waveguide THz QCL fabrication.
read from top to bottom, left to right.
3-2
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . .
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
49
. . . .
50
3-6
A new lens supporting scheme with adjacent supporting bars.
4-1
(a) Unstable beatnote from the bias tee. (b) Stabilized beatnote. (c)
Error signal from the PI controller.
. . . . . . . . . . . . . . . . . . .
52
Schematic illustration of the feedback loop to stabilize the repetition
frequency.
4-3
48
Examples of initial failure in lens mounting. (a) Crashed laser facet by
the spacer. (b) Spacer falling off.
4-2
47
Examples of initial failure in lens mounting. (a) Crashed laser facet by
the spacer. (b) Spacer falling off.
3-5
46
SEM pictures of the corrugation structure with defects. (a) Residues
of the passivation layer.(b) Low adhesion of top metal.
3-4
44
SEM pictures of the corrugation structure. (a) Longrange etching uniformity. (b) Vertical sidewall quality.
3-3
Steps
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
(a) Direct detection to characterize phase noise between two lines. (b)
A coherence detector scheme to measure the mutual coherence of two
lines with respect to a local oscillator. . . . . . . . . . . . . . . . . . .
4-4
56
Schematic illustration of SWIFTS. A coherence detector is placed at
the receiver port of the FTS. . . . . . . . . . . . . . . . . . . . . . . .
59
4-5
Actual SWIFTS measurement set-up. . . . . . . . . . . . . . . . . . .
61
4-6
SWIFTS results for a QCL comb. From top to bottom: (a). Raw interferograms of in-phase(I), quadrature phase(Q), and Normal(N) signals.
(b). Fourier transform of Si(t), SQ(t), and normal interferograms with
Hanning filter. (c). Power spectrum(N), (S (w))(P),and its conjugate
(S_(w))(M). (d). Magnitude of deconvolved coefficients . . . . . . . .
63
4-7
Pseudo-coherent QCL beatnotes.(a) Multi-beatnote. (b) Broad beatnote. 65
4-8
RF spectrum of multibeatnote regime. Spectra with and without RF
power injection are shown in parallel for comparison.
11
. . . . . . . . .
66
4-9
Self-reference SWIFTS results from the multi-beatnote regime. From
top to bottom: (a).
Raw interferograms of in-phase(I), quadrature
phase(Q), and Normal(N) signals.
(b).
Fourier transform of Si(t),
SQ(t), and normal interferograms with Hanning filter. (c). Power spectrum(N), (S+(w))(P),and its conjugate (S_ (w))(M). (d). Magnitude of
the deconvolved coefficients.
. . . . . . . . . . . . . . . . . . . . . . .
67
4-10 Self-reference SWIFTS results from the broad beatnote regime. From
top to bottom: (a).
Raw interferograms of in-phase(I), quadrature
phase(Q), and Normal(N) signals.
(b).
Fourier transform of SI(t),
SQ(t), and normal interferograms with Hanning window filter.
(c).
Power spectrum(N), (S+(w))(P),and its conjugate (S_(w))(M). (d).
Magnitude of the deconvolved coefficients.
. . . . . . . . . . . . . . .
68
4-11 Effect of transient feedback that destabilizes comb operation and causes
its output to become single-mode. Modified from Ref.[5]
. . . . . . .
69
4-12 Correlated averaging scheme. Nine power interferograms get aligned by
shifting to the points where their autocorrelation produces maximum
valu e.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
5-1
Schematic illustration of a dual-comb spectrometer. . . . . . . . . . .
71
5-2
Downconversion of the optical frequencies. Two frequency combs with
different repetition rates frep,i and frep,2 are combined and generate
a comb in the RF domain. Hence, the optical frequencies are downconverted to radio frequencies by a scaling factor a, a =
5-3
fep
frep,.
73
Schematic illustration of downconverted signal with different repetition
rate differences.
(a) The free spectral range is fully exploited and
the acquisition time is ideal for a given resolution. In this case, Av
is assumed to be frep/2.
M odified from Ref.t1I.
5-4
(b) Aliasing situation when 6 is too large.
. . . . . . . . . . . . . . . . . . . . . . . . . .
75
Experimental set-up for THz dual-comb spectroscopy. . . . . . . . . .
77
12
5-5
Lasing spetrum versus bias at 38K. (a) Current versus voltage and
current versus output power for one device. (b) Lasing spectra under
different biases. The different plotting color corresponds to the biasing
point in (a) and insets show the repetition beatnote collected from the
bias tee. The bias regime where detectable beatnotes exist is marked
with bold red line in (a). . . . . . . . . . . . . . . . . . . . . . . . . .
5-6
78
Repetition beatnotes and the multiheterodyne signal from a Schottky
mixer. (a) Repetition beatnotes from two devices center at around 9.1
GHz, each of which has a FWHM to be about 30 KHz and a SNR
higher than 15 dB. (b) Multiheterodyne signal at 2.4 GHz. . . . . . .
79
5-7
Repetition beatnotes from HEB. . . . . . . . . . . . . . . . . . . . . .
80
5-8
Multiheterodyne signal from HEB.
. . . . . . . . . . . . . . . . . . .
80
5-9
Downconverted multiheterodyne signal versus time, 1 us time slot. . .
82
5-10 Offset frequency's fluctuation versus time.
. . . . . . . . . . . . . . .
82
5-11 Downconverted repetition beatnotes versus time, 30 us time slot. . . .
83
13
14
List of Tables
15
16
Chapter 1
Introduction
Frequency combs have revolutionized the field of precision metrology and spectroscopy.
Conventionally, a THz frequency comb is generated by optical rectification or photoconduction, forming a THz pulse train in time domain. Despite its success in THz
spectroscopy, the generation and detection method involve bulky and expensive modelock lasers, restricted its usage in laboratory environment. Here, we demonstrate the
comb formation at terahertz regime in quantum cascade lasers. By measuring the lasing spectrum, fully characterizing the cavity dispersion and designing the dispersion
compensator, the performance of THz laser frequency combs is improved. Moreover,
we will explore the dual-comb spectroscopy at terahertz regime based on quantum
cascade laser frequency combs.
1.1
Terahertz Gap
Terahertz region, defined here as the frequency range spanning from 1 to 10 THz,
is technologically underdeveloped compared with other electromagnetic spectrum as
known today (shown in Figurel-1). The bottleneck for this underdevelopment mainly
results from the lack of powerful coherent light sources.
Two fundamental mechanisms of generating electromagnetic radiation can be
traced back to the modified Ampere's law(refer here as equation 1.1). J term is the
conduction current, corresponding to movable charges, and OP/Ot term is displace-
17
ment current produced by the locally oscillating charges. Radiation sources based on
these two terms have their own limits. On one hand, high speed electronic sources
are based on the
f
term. Their performance are harrowed by the transit time limit
and high frequency resistance-capacitance roll-off, leading their output power scale as
1/f' when the operating frequency reaches to above 100 GHz . On the other hand,
photonic sources depend on the UP/t term, and they suffer the low frequency limit
because of materials' bandgaps: the naturally occurring materials all have bandgaps
to be above 40meV (10 THz). For this reason, the challenge to generate radiation
between 1 to 10 THz (wavelength A between 30-300 pm, and photon energy hw between 4-40meV), and the lack of high quality coherent radiation sources result in the
so-called "terahertz gap".
v
x
H = (J
DP/Ot) + s 0 aE/at
(1.1)
Chart of the Elctramagnetfc Spectrum
A(M)
103
102
10
1
105
101
IM
10-
108
107
108
109
1n
I
104
10-5
1 Tz
I GIHz
1
1
(lz)
C
102
1f
waeIl
Im
101
101
1101
102
10-6
107
1Iz
10-8
10
1
10-IC
10"
10
1018
1 ZHz
10'
ad
102
102'
001unM
Rdo3X-ray
Broadaa
1012
EH,
VVW~wws
FaoAf&
X-ray
N4d X48ay
Figure 1-1: The "terahertz gap" in the electromagnetic spectrum.
At the meantime, terahertz technology is attractive for industrial applications.
Many materials that are opaque in visible or infrared regime still show transmission in
THz. This allows non-destructive inspections such as standoff personnel screening[7
and fabrication defects testing on printed circuit board[23].For fundamental research
concern, since the blackbody radiation of cool (30 Kelvin) interstellar medium peaks
at 3.1 THz, spectroscopy at terahertz regime gives information about star and galaxy
formation[161, which is of importance to astrophysics community. Moreover, for atmospheric research, monitoring the concentration of hydroxyl (OH) radicals, featuring
at
2THz, is crucial to understand the global warning and ozone destruction[17].
18
Actually, many molecules have strong "fingerprints" at THz regime due to their rotational and vibrational resonances [22][ 211. For example, Figure.1-2 shows the structure
of some explosives and their fingerprints in the terahertz. By conducting broadband
THz spectroscopy, one can elucidate those molecules and identify their concentration.
0.6
2A
4T
Frequency/THz
1.2
1.8
2.4
3.0
p.
"X
< =
HMX
PE
N
:IPETN,/
TNT
RDX
S
1*11WYO-40
Wavenumber/cm-1
16
Figure 1-2: Chemical structure of various explosives as well as the corresponding
terahertz absorption spectra (from Ref. [12J)
1.2
Terahertz Quantum Cascade Lasers
The quantum cascade laser is a strong and promising candidate to seal the "terahertz
gap"
QCLs are semiconductor lasers that generate optical gain via intersubband transitions. They are created by periodically growing alternating layers of different materials such as GaAs and AlGai_,As. Layers are grown using molecule beam epitaxy
(MBE) method, and because each layer is just several atomic layers thick, quantumsize effects dominate and create artificial energy levels at the band edge. As a result,
the energy gap between a lasing transition can be tailored by just changing the growth
thickness. This contrasts conventional semiconductor lasers, which operate based on
interband transition. Shown in Figurel-3, the interband transition energy(hw 2 ) is
fixed by the material gap, while energy of intersubband transition(hwi) varies with
19
the thickness of well using the same material. As a result, QCLs have no theoretical
upper bound on the wavelengths they can generate, giving them the versatility for
implementing long-wavelength oscillators. Cascade means once you design a module, the same structure can be repeatedly grown hundreds of times to form the gain
medium. When the entire structure is under electric biasing (Figure. 1-4), one electron
emits one photon in each module before tunneling to the next one, leading to high
internal quantum efficiency (theoretically about 10000% depending on the number of
modules).
hw
Figure 1-3: Intersubband versus interband transitions. Unlike the interband transition energy(hw 2 ),which are essentially restricted to the bandgap of the material, intersubband transition energy(hwi) can be engineered via adjusting the growth thickness.
Since its advent in 1994[9], QCLs have played a important role in generating long
wavelength radiation. High power and room temperature QCLs have been demonstrated in the mid-infrared region and are commercially available for practical applications. In 2002, the first QCL operating in the THz regime was developed[14.
Since then, continuous improvements of its maximum operating temperature, peak
gain/output power, far-field beam pattern and lasing spectrum coverage have been
pursued and is still an ongoing progress. Up to date, even though THz QCLs still
need to be operated under cryogenic temperature, a coin-size laser die mounted in20
1priod
Figure 1-4: Schematic of QCL operation. Theoretically speaking, one electron emits
one photon in each module before moving into the next one. From Ref.[6]
side an handhold thermal-electric cooler already can generate sufficient output power,
opening a door for practical applications outside laboratories.
1.3
Terahertz Laser Frequency Combs
Frequency combs are light sources whose lines are evenly-spaced and well-defined.
Shown in Figurel-5, the spectral lines of a frequency comb only need two parameters
to be fully characterized: an offset fo and a repetition rate frep. Historically speaking,
the concept of the frequency comb comes from the ultrafast optics community: due to
the Fourier transform duality, a pulse train in time domain corresponds to an impulse
train (a frequency comb) in frequency domain.
As such, the conventional way to
generate terahertz frequency combs relays on material's response of ultrashort optical
pulses. In fact, many materials will produce terahertz responding to ultrashort optical
pulses. For example, when an undoped semiconductor gets excited by a ultrashort
pulse, its electrons will be promoted from the valence band to the conduction band,
which will temporarily increase its conductivity. If this semiconductor piece is under
bias, a transient current will be generated. The far-field radiating electric field will
relate to the temporal derivative of the transient current, and so the resulting device
21
is named a photoconductive switch.
E (t) oc
(1.2)
at
Figure.1-6 shows one example of the photoconductive switch. Gold antenna is
patterned onto an low-temperature(LT) grown GaAs, which is chosen for its short
carrier lifetime(<0.4 ps) that leads to a broad terahertz response[11]. To efficiently
couple the THz radiation out, the antenna's shape is optimized to be the bowtie-type
and a silicon hyper-hemispherical lens is attached to improve the directionality of the
terahertz emission [181.
Time
-~
domain
VV
eFrequency
11 i
domain
f
Figure 1-5: Illustration of a frequency comb. In the frequency domain, it consists of
large numbers of equally spaced modes separated by its repetition rate frep together
with a potential non-zero starting frequency fo, the offset frequency; If all modes
have the same phase, in the time domain, it corresponds to a train of coherent pulses
Adjacent pulse shows a phase slippage,
separated by the round trip time, T = g.
AO =
2.
fo
From Ref.[1
Fo
Together with other generating methods, terahertz pulse sources have be used in
the terahertz spectroscopy and have led to a widely-adopted spectroscopy method
called terahertz time-domain spectroscopy (THz-TDS). However, pulse sources have
intrinsically low average power and need to be detected coherently. Moreover, their
generation inevitably involves mode-locked lasers. Thus, broadband THz frequency
22
....
....
....
Side view
Epitaxial view
GaAs substrate
LT-GaAs
pump pulse
pump pule
hyperhemispherical
Si lens
THz
Figure 1-6: Schematic of a basic photoconductive switch based on LT-GaAs. From
Ref. [41
combs generating by other methods are highly desired. Luckily, evidence shows that
if one can design a broadband gain medium and succeed to manage its dispersion,
THz QCLs can operate as frequency combs with several milliwatts output power[4].
By fully understanding the comb formation mechanism and optimizing its performance, terahertz laser frequency combs will revolutionize the broadband terahertz
spectroscopy and really push the frontier of terahertz technology.
1.4
Terahertz Frequency Combs Based Spectroscopy
One of the oldest and widespread techniques among spectroscopy is the absorption
spectroscopy, which compares the power of a light beam before and after its interaction
with a sample. Since absorption occurs only when the photon energy of the probing
light beam matches the energy difference between two states of the material, this
method can reveal the energy structure and the composition of matter. In the scope
of this thesis, focus will mainly tune to the molecule absorption spectroscopy method.
Frequency combs enable the first direct and phase coherent links between the measurable radio frequencies (RF) and quasi-optical/ optical frequencies (1012 to 1015 Hz),
offering a innovative way to conduct broadband absorption spectroscopy. Dual-comb
spectroscopy, which has first been proposed by Schiller in 2002[20], is such a example.
23
The key idea is that one can use two broadband frequency combs with slightly different repetition rates to naturally downconvert absorption features with a fast detector
from optical frequencies to the RF regime. This method shows at least two major
improvements compared with the conventional way like Fourier transform infrared
spectroscopy (FTIR). First, it abandons the moving component, which holds back
the resolution and requisition time. Second, after the signal is downconverted to RF
regime, mature signal amplification and digital data requisition/ analysis technologies
can help to boost its signal-to-noise ratio (SNR).
1.5
Thesis Overview
This thesis is dedicated to improve the performance of THz laser frequency combs
and explore the capability to conduct dual-comb spectroscopy based on THz QCL
frequency combs.
Chapter 2 reviews the key elements to achieve THz QCL fre-
quency combs including the choice of gain medium, cavity dispersion measurement
and the dispersion compensator design.
Chapter 3 details the fabrication flow of
THz QCL frequency combs. Special lens mounting technique will also be covered.
Chapter 4 discusses general characterizations and the coherence measurement for THz
QCL
frequency combs. A novel coherence measurement method called shifted wave
interference Fourier transform spectroscopy (SWIFTS) is introduced and analyzed.
Chapter 5 focuses on the development of dual-comb spectrometer based on THz QCL
frequency combs.
24
Chapter 2
Key Elements to Achieve Terahertz
Laser Frequency Combs
In contrast with traditional frequency combs generation methods based on mode-lock
lasers, Del'Haye et al.(Ref.181) in 2007 showed that the parametric gain via four-wave
mixing(FWM) can make it possible to generate a comb inside a microresonator spanning the frequency where the group velocity dispersion is low. Using this method, the
authors injected a continuous-wave pump laser into a high
Q microresonator,
achiev-
ing comb modes over a 500 nm wide span around 1550 nm. Figure2-1(a) sketches
how this micro-comb is formed. A high intensity single mode laser is first tuned and
coupled into one of the resonator's cavity modes. Initially, degenerate FWM causes
the pump laser to split into sidebands on either side of the pump frequency. Provided
energy conservation, the following non-degenrate FWM then allows more frequencies
to be generated.
Similar idea can apply to laser frequency combs. In mid-IR QCLs, recent work
by Hugi et al.[13J demonstrated that when the group velocity dispersion is made
sufficiently low, such devices can form a comb by FWM too. The main difference
here lies in the initialization step: in micro-combs, pump laser serves as a seeding
laser, while there is no such seed in QCLs. Laser modes which experience more gain
than loss lase, and due to spacial and spectrum hole burning, a laser can lase at lots
of frequencies. Moreover, in a QCL, parametric gain induced by FWM alone is not
25
- __
ONMEEEWa
1
cavity modes
(a)
w-w
T-
(
ENWIft __
(A
Degenerate
four-wave mixing
w+2Aw
w-Aw
Nondegenerate
four-wave mixing
Frequency
AW
mode spacing
Four-wave mixing generates
off-resonance sidebands
Multi-mode laser
cavity
(b)
modes
0
0
0.
0.
0
0
LL
1 1
Frequency
Frequency
Not evenly spaced!
Four-wavemixing plus injection locking
ensure mutural conherence
CL
0
VA
I
I
I I
I
IW~
6-.4
AW
I
II I
Frequency
Repetition rate
#mode
spacing
Figure 2-1: (a) Degenerate FWMs and non-degenerate FWMs. (b) In QCLs, FWM
generates sideband lasing frequencies, injection locking a multi-mode laser to form a
comb.Modified from Ref.[41
sufficient enough to overcome the loss. So instead, it acts as a sufficient pulling force
of injection locking.
Injection locking[2 describes a phenomenon that, under a strong power injection
near a natural lasing frequency, a laser will lase at the injecting frequency instead of
the original one. Think of a laser lase at wo, intracavity intensity 1i with laser cavity's
reflectivity, round-trip gain and loss are r, g, and a individually. At some point, a
field of intensity I at frequency w 5 wo is injected to cavity. For one round trip, it
26
experiences
Art(W)
eZn(2L) 2
=
=
(_O
2
(g-ca)( L)
2,L-00[egn(2L)
2 (g-a)(2L)
The bracket term is 1 because the laser originally lases at wO, which gives the transfer
function of A(w) to be
A(w)
=
1+ Art (W) + A t(W) + A t()
1
1
(2.3)
+...
(2.4)
1 - Art(W)
It can be approximately written as A(w) ~i
the free spectral range. When
IA(w)1
21
> Io or
_
2Lw-wo
=
<
27r w-w
, where
'AW = 2,
2nL
,Lfrequency w will
experience more gain than wo, and laser will lase at w instead of wo. Also, it suggests
that, in order to favor injection locking, the injecting power should be high and the
injecting frequency should be close to the original lasing frequency.
Figure.2-1(b) illustrates how this might happen inside the QCL. An multi-mode
(unevenly spaced) laser initially generates sidebands via FWM. These sidebands are
slightly off cavity modes and once they are strong enough, they will lock those cavity
modes to lase off-resonance.
Eventually, modes spanning frequencies where FWM
is powerful will be phase-locked together to form a comb. As the injection locking
condition suggests, to achieve broadband frequency comb operation, a gain medium
which possesses broadband lasing capability is necessary. But what is of most importance is to manage the group velocity dispersion. A low group velocity dispersion
can promote the FWM by creating a easier phase matching condition and make cavity modes to be more evenly-spaced, both of which will boost the injection locking
process.
27
2.1
Gain Medium
Unlike traditional lasers utilizing electron transitions between naturally defined energy
gaps, all QCLs' gain media are artificial and based on transition between intersubband energy levels generating from quantum confinement effects. Starting from its
invention, gain medium design has been a essential research topic among the community. Up to now, three different design schemes[26], namely chirped superlattice,
bound-to-continuum, and resonant phonon, have been proposed and been pursued for
better performance. Merits to evaluate different designs focus on such parameters as
maximum lasing temperature(Tmax), peak gain and output power. But for frequency
comb usage, except merits mentioned above, the lasing spectrum coverage needs to
be considered. In particular, the creation of useful THz QCL frequency combs will
require a gain medium which possesses a uniform gain over a large frequency span.
Fortunately, because quantum cascade lasers have gain curves that can be designed
and engineered, they offer tremendous flexibility compared with traditional semiconductor lasers.
2.1.1
Homogeneous Gain Media- OWI194E-M4 and FL183s
Two gain media developed in our group have been investigated for their capability of
broadband lasing.
Design OWI194E-M4 is a modified version of former <2 THz Tmax record keeper[15].
It differs from other design by utilizing scattering assisted(SA) injection, in which
electrons are injected into the upper state by direct emission of an longitudinal optical(LO) phonon. Moreover, under low bias, this design also exhibits resonant tunneling(RT) type lasing at higher frequencies . Figure2-2(a) shows the band diagram
of OW1194E-M4.
The designed lasing happens between 5 -
4. Figure2-2(b) shows
the corresponding THz ouput power versus biasing current from one device. As the
biasing increases, collected electrons from preceding module resonantly tunnel from 2'
to 1', leading to population inversion between 1' -+ 5. RT type lasing happens first at
frequencies higher than 4 THz. If one keeps increasing the bias to let AE 1' 5 = hWLo,
28
level 1' gets depopulated via emitting a LO phonon and SA type lasing happens
between 5 -+ 4. Figure2-2(c) and (d) show corresponding lasing spectra.
#10-3THz power versus biasing current for OW1194E-M4 at 35K
(a)
(b)
C
1.5
-
/\
~
/~I
I
\
CLN
6
0.5
0
--
-0.5
0
---
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Baising current(A)
Spectrum
Spectrum
10
104
103
103
102
K
0
102
3-I
101
100
10-313.5
4.5
4
5
1.5
2.5
3
3.5
Freq [THz]
Freq [THz]
Figure 2-2: (a) Band diagram of QCL at low bias and at high bias. (b) THz output
power versus the biasing current from one OW1194E-M4 device. (c) Lasing spectrum
due to resonant tunneling at low bias range. (d)Lasing spectrum due to scattering
assistant at high bias range. Inserts show schemes of individual operating principle.
Even though design OWI194E-M4 shows a broadband lasing spetrum(2-2.9 THz
and 4.1-4.6 THz), its high power consumption(> 2000KA/cm2 ) and its lasing asynchrony disable it to be a candidate for the future comb usage.
A highly coherent resonant phonon design, FL183s, is analyzed.
This design
is one of the best-performing resonant-phonon QCLs in existence, producing high
optical power spanning at 3-4THz. Figure2-3 illustrates the band diagram of FL183s.
State 1' and 2' are the injector states, state 5 and 4 are the lasing upper and lower
state, and state 3 is the collector state. At design bias, the injector and upper laser
level anticross by 2.4meV, which gives a splitting of the gain spectrum by 580 GHz.
............
-
%=
11;= MIM1111
MNMMMM
.
29
Figure2-4 shows the lasing spectrum of FL183s, featuring with two lasing lumps.
FL183s is heavily used in the group for various projects and has been regrown multiple
times with consistent high performance. The first terahertz laser frequency comb is
also demonstrated with this gain medium, and experiment results in the following
chapter are largely from devices using this gain medium.
2
3
1'1
tl 2
Figure 2-3: Band diagram of FL183s.
103
101
2. 2
3
3.4
3
3.,
1.,
4
42
4.4
4
Fioq JTHzJ
Figure 2-4: Lasing spectrum of FL183s under design bias.
2.1.2
Heterogeneous Gain Media- ETHOWI3E and ETHOWLE33
Heterogeneous design is another natural trend to achieve broadband lasing coverage.
The idea is to have a laser system that consists of may independent segments whose
The final gain spectrum of such a
transition line-shapes are designed separately.
- -IM
-
-Imml
-
__
Immmoommmmvmpapa
1 -1
-
-
_
--
--
--
-
30
system would be the sum of the contributing gain spectra. The heterogeneous concept
was introduced already in the mid-infrared QCL community[10].
Key additional
requirement for the heterogeneous design compared with the homogeneous one is
that the laser threshold current density
Since
Jth
Jth
should be independent of wavelength.
can be written as:
ci (A) +
Jth(A) =
g(A)
(2.5)
am
The condition gets to
Jth =
0
(2.6)
aA
In other words, the modal gain needs to compensate for the modal loss over a very
wide spectrum range. Instead of designs trying to match the
which match the maximum current density[19j Jmax,
Jth,
following designs,
succeed lasing broadbandly too.
In our group, the heterogeneous gain medium design is still an ongoing process, so
several designs from Prof. Jerome Faist's group at Swiss Federal Institute of Technology in Zurich(ETH) are regrown at Sandia National Laboratories. The ETHOWI3E
is our first regrowth based on Ref.[241, containing three different designs (peak at
3THz, 2.7THz,and 2.3THz separately).
Our regrowth shows lower current density
compared with the established one and does not lase at 35K and above. The followed
second regrowth, ETHOWIE3-3, is modified based on Ref.[19], which consists same
modules with slightly changes of doping level and the arranging order. Figure2-5(a)
shows the calculated gain and inside arrangement.
A simple model is applied to
the calculation of the spectral gain cross-section for each substack i (blue curves in
Figure2-5(a)).
2wre2 z?
gi =
27ez
2
2
gonref LAj (E, - hw) + _y
(2.7)
nref is the refractive index, Ai is the wavelength of each relevant transition in each
stack i, y = 1meV is the level broadening, zi is the dipole matrix element for the two
states in each stack that contribute to the gain, e is the electron charge, and Ej is the
energy of the relevant transition in each stack i. The total spectral gain(green curve
31
in Figure2-5(a)) is calculated using
3
gtot
(2.8)
(N/Ntt)gi
=
i=1
Ti/Au contact
Contact
0.7
0.6a
layers
-
2.3 THz; 40x
0.6
0.5 -
B: 2.6 THz; SOx
C: 2.3 THz; 40x
A: 2.9 THz, 40x
0
.,
0.40.3
Octave
0.2
0.1
C
B
B
A
2.0
2.5
0.0
10
1.5
3.5
3.0
4.0
Frequency (THz)
b
10
E
10z
171AAAAA 4
Octave
10-4
6
18
20
2.2
I I Jill
26
24
28
30
32
Frequency (THz)
Figure 2-5: (a)Calculated gain cross-section g, . Blue curves: individual designs.
Green curve: total active region. Insert: arrangement of different active region designs
in the laser. (b)Octave-spanning spectrum of a device under design bias. From
Ref. [19]
Our second regrowth shows broadband lasing. Compared with results in Ref.[19],
our regrowth still has lower current density and shorter dynamic range, which may
be due to the energy level misalignment and the different doping calibration among
different MBE chambers. Our QCLs also show narrower lasing spectrum coverage.
Measurement results from a 150pm wide device are shown in Figure2-6 and lasing
covering 2 to 3THz is obtained under designed bias(Jmax). Provided a sufficient
cooling power, similar lasing spetrum coverage is expected in lower temperature.
One advantage of the lower current density is to allow us to continuous-wave(CW)
32
--
I..
_In-
-
_
__
___
,
_
-
-
-
-
-----------
bias multiple devices given our current cooling capability. This is crucial for following
dual-comb spectroscopy and in fact, our first dual-comb spectroscopy attempt is based
on devices using this gain medium.
(a)
15
ETH.OWIE-3-3-FPI Pulse measurement(O0urn)
[32K
10K
--
5
___
00
0
50
100
200
150
300
250
350
400
Current desity(A/cm2)
Spectrum
(b)
d
1.6
1.8
2
2.2
2.4
Freq [THz]
2.6
2.8
3
3.2
Figure 2-6: (a)Biasing voltage/current relationship versus operating temperature;
Output optical power at corresponding biasing. Same color line shows data at same
temperature. (b) Lasing spectrum at design bias(35K).
2.2
Dispersion Measurement
A broadband gain medium can not guarantee a broadband frequency comb generation.
A laser with such gain medium can lase in single mode if the total loss is high or in
multimodes due to spatial and spectrum hole burning. The main difference between
a broadband multimode laser and a frequency comb depends on how lasing modes
are spaced. To make a broadband frequency comb, dispersion management is one key
factor. Considering fundamental modes, the mode spacing for a laser cavity L is
AV =
C
2n(v )L
33
(2.9)
n(v) is gain medium's refractive index. For QCLs, its frequency dependence has two
main contributors. On one hand, the gain medium itself is dispersive, especially in
THz regime, where the photon energy is close to the lattice polariton's resonance.
The material dispersion for bulk GaAs has been calculated and well documented in
various references, but the unique challenge for QCL's gain medium is its artificial
transitions.
These subband transitions and absorptions introduce new dispersion,
and to make it even worse, the introduced dispersion has strong bias dependence.
On the other hand, the waveguide will introduce additional dispersion because each
mode has slightly different confinement. To fully acquire gain medium dispersion
information and its biasing dependence together with the waveguide dispersion, a
modified THz-TDS system is developed[31.
2.2.1
Introduction of THz-TDS
Figure.2-7 shows a typical terahertz time domain spectroscopy set-up together with
its data requisition scheme. It essentially is a pump-probe technique. A near-infrared
pulse generated by a mode-lock laser gets separated into two parts. One part of the
pulse shines on a terahertz emitter (shown in the figure is a photoconductive switch,
which is introduced in chapter 1 1.3), generating a terahertz pulse. Another part
of the same pulse goes through a delay stage and combines with the terahertz pulse
on a detection element (eletro-optical(EO) crystal in the figure). If the near-infrared
transmission property of the detection element varies with the terahertz intensity, the
terahertz field's intensity can be detected via measuring the modulated near-infrared
power. By changing the delay distance, one can fully scan the generated terahertz
pulse and the spectrum information of the terahertz pulse can be deduced using
standard Fourier transform.
Compared with other long-wave spectroscopy method like FTIR which records the
power spectrum, THz-TDS is sensitive to the terahertz field, preserving the intensity
and phase information at the same time. This is crucial for the dispersion measurement for QCL since dispersion is characterized by a nonlinear phase-frequency
relation. As all other methods, THz-TDS needs lots of practical considerations to
34
Delay stage
EO
crystal
Pulsed
laser
QWP
PPB
antenna
J
PBS
'PD
THz
THZ
Frequency domain
measurement
Time-domain
measurement
Optical signals
field NIR protb
E(t)
defay
(variable)
FT
*
*
measuremnent
I,,E
frequency
d
Figure 2-7: Typical terahertz time domain spectroscopy set-up and data requisition
scheme.From Ref.[41
achieve good performance, and for QCL dispersion measurement concerned, the entire system's resolution and frequency coverage are discussed.
9 Resolution:
THz-TDS utilizes a delay stage to sample the terahertz pulse
in time domain. From basic Fourier theory, the maximum delay in time domain determines the resolution in frequency domain. A delay stage with traveling distance L corresponds to c/2L frequency resolution. Thus, stages with
centimeters-long traveling distance give
-
10 GHz, the typical THz-TDS res-
olution. Meanwhile, the maximum time delay is limited by the period of the
mode-lock laser. Since after one period of the mode-lock laser, the second pump
pulse comes and the system starts to sample the new generated THz pulse, generating redundancy. Given the capability to reach this limit, lower repetition
35
rate mode-lock laser is preferred.
* Frequency coverage:
Unlike standard THz-TDS, the emitter in QCL dis-
persion characterization is a section of QCLs. Thus, the frequency coverage
ultimately depends on the detection element's terahertz response. In the scope
of this thesis, EO sampling is primarily used. Electro-optical effect is a second
order(X(2 )) nonlinear optical effect in crystal without inversion symmetry, describing the permittivity change of optical field(w) induced by electrical field(Q).
p(2 (W', W, Q)
=
X () (W', W,
Q) Ej (w) Ek(Q)
sinceQ < w
D
(2.10)
(2.11)
= eE(w) = coE(w) + [P(l) + p(2 ) +...]
(2.12)
X()E(Q) + .. .]}E(w)
(2.13)
=
co{l +
[(1) +
S= cO[1 + XM + X(2E(w)]
AC=
C
- E0 =
x
Ek(Q)
(2.14)
(2.15)
i,j is the crystal orientation. Phenomenally speaking, EO sampling is the polarization change of near-infrared pulse(w) by the terahertz pulse(Q) in EO crystal
like ZnTe or GaP. Since our gain media usually lase at 2- 4THz, ZnTe and GaP
crystal are used depending on the gain spectrum range.
2.2.2
Actual Dispersion Measurement
Leveraging from the measured phase information, dispersion measurement is performed on the FL183s gain medium using a self-reference scheme. In the measurement, a near-infrared pulse is shined on the rare facet of a QCL, generating a terahertz
pulse. The generated terahertz pulse then bonces around in the laser cavity and its
field intensity after one round-trip (shown in blue in Figure.2-8) and three round-trips
(shown in green in Figure.2-8) are recorded.
Figure.2-9 illustrate the data processing flow of dispersion extrapolation. Shown
36
Terahertz pulse
x 10-s
1
0.5 F
0
CD
i~
-0.5 F
-1
[
10
0
20
30
Time [ps]
Figure 2-8: Detected terahertz pulse. The blue curve shows the pulse after one
round-trip, and the green curve shows the sample pulse after three round-trips. From
Ref. [4]
in Figure.2-9(a) is the amplitude of individual pulses, where their difference indicates
the effect induced by the gain. Figure.2-9(b) shows their corresponded phases. Their
linear components are subtracted since they only refer to the group delay,
Tg(W) =
phase
aWh
(2.16)
The dispersion information can be calculated from their phase difference using the
polynomial fitting to any desired orders. Shown in 2-9(c) is the experiment data at one
biasing with second order fitting. The second-order group velocity dispersion(GVD),
named D 2 , is defined by
a
D 2 (w) = a
(2.17)
the measured GVD is 0.0752ps2 /mm and its biasing dependence is plotted in Figure.29(d). Their averaged value within the lasing bias range is used to design the dispersion
compensator.
37
(a)
(b)
Amplitude of echos 1 and 2
10-6
Phase of echos 1 and 2
5
0
10
CL
-10
10
o)35
-40
1
0
1
3
2
Frequency
4
5
(C)
4
3
2
1
6
5
Frequency [THzJ
[THzJ
3
(d
Phase difference and quadratic fit
-40
-10
6
-12 -0.200
.5-IV
and GVDs
0.07
-432GD=5.72p2m
(
0.23
-430
0.06
-M
0.25
-440072p
W-445-
-450
-455
0
1
2
3
4
5
6
E.0
.1
0.03
0.1
0.05
0.02
0.01
5
10
15
20
Voltage [V]
Frequency [THz
Figure 2-9: Dispersion extrapolation for the time domain data. (a)Amplitude of two
adjacent pulses. one round-trip pulse is shown in blue and three roun-trips one in
green. (b) Phase of two adjacent pulses except their linear components. (c)Phase difference of the adjacent pulses. (d) Group velocity dispersion versus the laser biasing.
From Ref.[14]
2.3
Dispersion Compensator Design Implemented on
ETHOWIE3-3
The success of former THz laser frequency combs heavily relies on the preceding in-situ
cavity dispersion measurement and the following integrated dispersion compensator
design.
Actually, dispersion management is a well-known issue in ultrafast optics
community. In order to achieve shorter and sharper output, dispersion compensators
such as prism pairs or double-chirped mirrors are often in use externally to shape
the output pulse coming from the mode lock laser. Integrated with
QCLs, the basic
idea of compensator design mimics the double-chirped mirrors. By etching part of the
laser ridge, a chirped distributed Bragg reflector is defined at one end of the laser bar,
tailoring from short period to long period with a increasing corrugation amplitudes.
38
-...........
-
.......
......................
. ..
...
....
......
. . ... .. ....................
. ...
........
.. ..
......
....
........
....
...............
In this way, the longer wavelength light with higher velocity gets reflected at the
end of the reflector, while the shorter wavelength light gets reflected earlier, thus
compensating the cavity dispersion. The increasing corrugating amplitude is to avoid
interference by abrupt impedance change, creating a smooth linear compensanting
range. The start and stop period of the corrugation structure need to be determined
based on the targeting frequency range. Depending on the length of laser cavity, the
length of dispersion compensator is accordingly adjusted.
In the previous demonstration of frequency combs, dispersion compensator is designed based on the measured cavity dispersion. But since the real cavity dispersion
is not available for the ETHOWIE3-3, only the one dimension simulation is implemented here. More accurate three dimensions full-wave simulation will be performed
once the cavity dispersion data are available. In reality, the ID simulation is still sufficient to capture the general idea of the design and set a good starting point for the
future simulation. The main assumption here is that all light is highly confined in the
waveguide with width w, thickness t, and index n. Basic transfer matrix formalism
gives its impedance to be
Z = riw
(2.18)
qo is the vacuum impedance and Zi, wi represent discrete slices using in the finite
element simulation. Follow this way, the reflectivity as a function of frequency, 1'(w),
can be found and its phase, same as the phase in the preceding dispersion measurement, can be used to determine the group delay and GVD to any desired orders. The
goal here is to construct a structure with the exact opposite dispersion relation as
from the dispersion measurement.
Figure.2-10 and Figure.2-11 show two dispersion compensator designs for ETHOWIE33, with targeting frequency spanning form 2-3 THz. It features a general sinusoidal
shape with a chirped period and amplitude. The major difference in these two designs
is the intended compensation amount. As shown in figures, even though the designed
amount varies by an order of magnitude, this scheme still maintains a linear compensation in the targeting frequency range. In fact, any type of distributed feedback
39
..
.......................
- ....
...............
..
..
..........
......
(b)
Group delay vs frequency
Reflectivity vs frequency, rf, .. J=0.9
0.8
0.8
0.7
0.6
v
0.6
0.4
-
(a)
0
a-
0.2
0.5
2
(C)
50
2.8
2.6
2.4
Frequency [THz]
2.2
'
0
0.4
1
3
1.5
2
2.5
3
3.5
4
Frequency [THz]
Corrugation design
L = 48 7m
, = 0.7
Narrowest width = 1 7m
Waveguide width = 25 7m
Start period = 10 7m
Stop period = 28 7m
End phase = 0:
0-
GDD over design range=-0.458 ps2
-50
-2 0
0
20
40
60
Positiom [7m]
Figure 2-10: Dispersion compensator for low cavity dispersion. (a) Group delay versus
frequency. (b) Reflectivity versus frequency. (c) Corrugation design.
system can be utilized and by combining with standard generic optimization, original
dispersion in any arbitrary shape can be compensated, making it feasible for future
implementation of octave spanning QCL frequency combs.
40
Group delay vs frequency
'
5
(b)
'
(a)
Reflectivity vs frequency, rfact=0
9
1
4.5
3.
0.95
4
.
3.5
0
30
3
(D
0.9
CL
2.5
0.85
2
2
2.6
2.4
2.2
2.8
1
3
Frequency [THz]
(c)
50
1.5
3
2.5
2
Frequency [THz]
3.5
4
Corrugation design
L = 280 7m
, = 0.8
Narrowest width = 1 7m
Waveguide width = 25 7m
Start period = 10 7m
Stop period = 28 7m
End phase = 0:
0
GOD over design range=-2.4 ps
2
-~f
-100
0
100
200
300
Positiom [7m]
Figure 2-11: Dispersion compensator for high cavity dispersion. (a) Group delay
versus frequency. (b) Reflectivity versus frequency. (c) Corrugation design.
41
42
Chapter 3
Fabrication of THz Laser Frequency
Combs
3.1
General Fabrication Process
The general fabrication process of THz laser frequency combs is based on the standard
dry etching recipe for metal-metal waveguide THz QCLs. By utilizing the modified
dry etching method, the preceding designed corrugation structure can be fabricated
as desired. Main parts of the fabrication are done in the cleanroom at Microsystem
Technology Laboratories, and detailed process is attached to the Appendix. Figure.31 sketches some major steps.
Depending on the mask size, samples sizing - 1.5 x ~ 2 cm2 are cleaved from
the received MBE wafers, together with slightly lager n+ doped substrates. The n+
doped substrate is called "receptor", as the MBE growth will be transfer to it in the
following process.
Both the MBE sample and the receptor are first coated by electron-beam metal
deposition. Multiple choices of metal combination can be used such as Ta/Au/Ta/Cu
(150/1500/150/3500A), Ti/Au(150/2500A), or Ta/Au(150/2500A). Previous experience suggests low depostition rate (~
1A/sec) to achieve high quality metal-metal
bond. After this metal deposition, the MBE sample is then flipped and placed on
top of the receptor. Delicate adjustment is required to align both crystal lines for
43
(a)
(C)
metal layer
(d)
thermocompression
(b)
(e)
Figure 3-1: Major steps in metal-metal waveguide THz QCL fabrication. Steps read
from top to bottom, left to right.
future cleaving purpose. The thermal-compression bonding is then performed under
vacuum at 300'C and 4 MPa for 60 minutes. To release the induced stress between
metal stacks in the thermal compression, bonded samples then undergo a 60 minutes
annealing at 300 C in nitrogen environment. If one needs to process multiple samples
in one fabrication run, it is highly recommended to process one sample at a time in
the thermal compression step since the compression tool needs to be adjusted according to sample's height, while the annealing can be done for all samples given enough
holder space.
Followed the wafer bonding, the bonded sample is taken out from the cleanroom
for mechanical lapping, leaving the native MBE substrate to be ~ 100pm. Chemical
etching is then applied for entire substrate removal.
Volume ratio 3:1 solution of
citric acid, 20% hydrogen peroxide(H 2 02 ) is mixed to selectively etch away GaAs
substrate and stop at AlGaAs stop layer. During the chemical etching process, the
receptor side needs to be protected with a thick layer of photoresist. To maintain an
uniform etching and a reasonable etching rate(~ 0.25pm/min), the etchant should
be under constant agitation and be replaced every 60-90 minutes. The thin etching
stop layer(400 nm) can be removed using a quick hydrofluoric acid(HF) dip, letting
the fist layer of real gain medium exposed to the air.
44
Top metal is then defined by image reversal photolithography and the following
metal deposition (Ta/Au or Ti/Au 150/2500A) together with lift-off process. Mesa
definition is then processed through dry etching in 0.5/3/16 sccm(standard cubic
centimeters per minutes) C12 : SiCl 4 : Ar, for which the top metal will act as a
self-aligned mask.
This dry etch recipe achieves smooth and vertical sidewalls by
forming a silicon-rich passivation layer along the etching direction. This passivation
layer finally needs to be removed using hexafluoride(SF) plasma (Plasma Quest,
ECR Power: 500W, Pressure: 70 mtorr, and SF flow rate: 100 sccm).
Figure.3-2 shows SEM pictures of the corrugation structure with high sidewall
quality, while Figure.3-3 shows the mesa definition with some defects like low adhesion of top metal and laser ridges wrapped by passivation layer. These defects may
result from non-uniformity in the Plasmaquest tool ( high etching rate in the center and low etching rate along edges) and can be eliminated by preconditioning the
etching environment and adjusting the sample positioning scheme. If one needs to
process multiple samples, dividing samples into small process group and monitoring
the passivation layer removal quality under SEM will be a good attempt.
Finally, the receptor substrate is lapped down to
150 pm and deposited with a
Ti/Au(150/2500A) layer for backside contact. The device is then cleaved into small
laser die, In/Au bonded to a copper carrier and gold-wire/In-ribbon bonded, ready
for future measurement.
3.2
Lens Mounting
One drawback of the metal-metal waveguide structure is its low out coupling efficiency. In the growth direction, the subwavelength(10 pm) confinement achieved by
sandwiching gain medium into two metal plates results in a divergent beam pattern
exceeding 1800, and the enhanced reflectivity(R ~~0.7 - 0.9). This enhancement is
due to the mode mismatch between the confined surface plasmon modes and the nearfield modes, resulting low output power. A hyper hemispherical silicon lens coupling
scheme is proposed to improve the collecting efficiency, thus increasing the output
45
Figure 3-2: SEM pictures of the corrugation structure. (a) Longrange etching uniformity. (b) Vertical sidewall quality.
power[251.
Any detection element has a collecting aperture limited by its physical size. Collecting efficiency is determined by detector's collecting aperture and the distance
46
(a)
(b)
Figure 3-3: SEM pictures of the corrugation structure with defects. (a) Residues of
the passivation layer. (b) Low adhesion of top metal.
between the source and the detector. Showing in Figure.3-4, for a power meter with
29-mm diameter, the collecting angle a is
15.26' for a bare laser facet, while for a
lens-coupled facet, the collecting angle in the same distance is a = sin-1 (r*sin(b)/sb),
47
Figure 3-4: Examples of initial failure in lens mounting. (a) Crashed laser facet by
the spacer. (b) Spacer falling off.
sb : set back. r is the radius of the lens (2 mm), b is limited by the critical angle
at the lens/air boundary (bma,
=
sinrV
1
nsilicon
26.1'), and the set back determined
by spacer's thickness and hyper hemispherical lens's design, rounding up to 870ptm.
This gives the calculated collecting angle to be 89.7 '.
In order to mount a lens to one laser facet, the laser die is aligned to be parallel with
one edge of a copper mount and then indium soldered with a overhanging distance of
~ 50pm. A double-side polished high-resistance silicon(500pm thick, >1OKQ - cm.)
spacer is then pressed against the facet and glued down to the copper mount. The
fixed spacer provides a mating surface for the silicon lens, preventing damages to the
facet in the lens alignment. The lens is then positioned against the spacer, temporally
holding by a homemade clip on a 3D micro-manipulating stage.
optimized coupling, the laser is 10% pulse biased to ~ 1KW/cm
2
To guarantee a
power dissipation
and the lens is delicately adjusted to achieve a clean thermal image of the heated
ridge on a monitoring infrared thermal camera. Once the lens is in good position, it
first gets glued to the spacer on edges of their contacting facet and then stycasted
together.
Using a suitable amount of stycast is the most tricky part in the lens mounting
process.
Several initial tests fail when the devices get cooled down to cryogenic
temperature. Because of the difference of thermal expansion coefficients between the
copper carrier and the stycast, the shear force induced in the cooling has the potential
to tilt the lens upward, pulling the spacer/lens to crash the laser die. Figure.3-5(a)
shows a resulting crashed laser facet.
Actually, if one uses too much stycast, the
induced shear force can be strong enough to crash the entire laser die. Another typical
48
type of failure is the lens falling-off, showing in Figure.3-5(b).
This is because all
ordinary room temperature glues fail at cryogenic temperature and too little stycast
can not hold the heavy lens system.
Figure 3-5: Examples of initial failure in lens mounting. (a) Crashed laser facet by
the spacer. (b) Spacer falling off.
In order to overcome this problem, the author comes up with a new lens supporting
scheme, showing in Figure.3-6. Instead of gluing and stycasting the spacer/lens to
the underneath copper mount, Two supporting bars are first glued and stycasted
next to the laser die and the entire spacer/lens combination is then fixed to these two
supporting bars. Since supporting bars are at the same height level as the laser die,
the induced force is approximately perpendicular to the laser facet, avoiding the tilting
potential. Moreover, more stycast can be applied to join points between supporting
bars and the spacer/lens system, making the entire lens-coupled system more robust
at low temperature.
This new scheme achieves higher yield and the details of lens
mounting is in the appendix.
49
Copper mount
Supporting bar
Laser die
Spacer
Silicon lens
Figure 3-6: A new lens supporting scheme with adjacent supporting bars.
50
Chapter 4
Characterization of THz QCL
frequency combs
4.1
Repetition rate beatnote measurement and beatnote stabilization
Initial measurement are focused on 3-mm-long frequency comb devices using FL183s
gain medium.
Considering the uncertainties in dispersion measurement and fabri-
cation process, frequency comb devices with compensators, which compensated the
measured D 2 adjusted by 0%, +6.6%,
13.3% and
20% are fabricated in the same
batch.
Opposite to the previous results from 5mm devices[4j, all
+6.6%, +13.3% and
+20% device lase broadbandly under designed bias. And different batches are tested
with reproducible results, suggesting that shorter devices are less sensitive to dispersion compensation. This agrees with the injection locking mechanism. Since the
total cavity dispersion is lower in the shorter device (the group velocity dispersion is
a function of laser length), original cavity modes are not far off to be evenly-spaced,
allowing a larger dynamic range for compensators to adjust and still maintain the
injection locking conditions.
A interesting side-effect of the broadband terahertz radiation is that it generates
51
-
. -
-
-
_.
__: _
__
-
-
__
-
-
-
-
-
I -
.1 ;-
-
-_:.
- -
a strong radio frequency(RF) beatnote at its round-trip frequency when device is
under CW biased. This RF signal can be detected from laser's biasing line using a
bias tee, from an adjacent laser ridge, and from a high-speed detector, implying that
the beatnote generated from all the pairs in the spectrum are adding up coherently.
The repetition rate beatnote from the 3-mm device is around 11GHz. As the biasing circuits inside the cryocooler and even the normal SMA cable both have strong
attenuation in high RF regime, it is hard to estimate the absolute RF power inside
laser's metal-metal waveguide. Figure.4-1(a) shows a beatnote from the bias line of
QCL using a bias tee. It features with FWHM of about 500KHz and a low-frequency
If all modes are evenly-spaced and add up coherently to form a RF
modulation.
beatnote, where does this low-frequency modulation come from?
-4S1
-45
-8-50
-55
-55-
-60i
-60-
E -65r
-6S-
70
-70
7
-75
-8-8-90
10.9802 10.9804 10.9806 10.9808
10.981
10.9812
10.9802
10.9814 10.9816
G~z
10.9804
10.9806
GHz
10.9808
10.981
10.9812
Noise floor
10-
-
17as
1Cr16 --
10
0.2
O.4
0.6
0.8
M
1Ffeun
z
1.2
Figure 4-1: (a) Unstable beatnote from the bias tee.
Error signal from the PI controller.
1.4
1.6
18
2
(b) Stabilized beatnote.
(c)
The answer is that the beatnote gets broaden by environmental factors. Because
the device is mounted on the cold head of a pulse-tube cryocooler, mechanical vibrations cause a position sensitive optical feedback, which introduces low frequency
52
- . .. , - .. , , , - - -.........
.
-
............................
---- II-- ......
.............
..........
..
...............
"I'l ", ..
....
....
_ _ _ _ -1
"I'll,
fluctuation to the beatnote. Fortunately, standard feedback control system can be
used to apply a sub mA modulated current adding to the QCL's bias line, which
can remove most of the phase noise and stabilize the RF beatnote. Figure.4-2 shows
the beatnote stabilization system. The original beatnote from the bias tee first gets
amplified and mixed with a local oscillator. The local oscillator's frequency is deliberately chosen to be ~ 10MHz away from the beatnote frequency, giving the mixed
output centering at 10MHz. This output is then mixed again with a 10MHz local
oscillator, downconverted to a quasi-DC signal. The quasi-DC signal is used as the
error signal to a PI controller and the PI controller's output then is fed into the
QCL's bias line by a 1KQ resistor. Note that this feedback control system is not
doing injection locking, as the injecting current is only sub-mA with a low frequency
up to only about 100KHz.
Figure.4-1(b) shows the stabilized beatnote after adding the feedback current,
featuring the FWHM less than the resolution of the frequency analyzer. Also, error
signals are recorded using a fast oscilloscope to compare the difference before and
after the stabilization. Figure.4-1(c) shows the power spectrum of error signals after
Fourier transform. The phase noise lump centering at 400KHz is clearly removed.
bias tee
~-11GHz
7
11
GHZ
: .....
C1KC
10
MHZ
X
PiLoop
..
QCL
bias
t
Figure 4-2: Schematic illustration of the feedback loop to stabilize the repetition
frequency.
To be noted, the same device does not always act as a frequency comb when it
53
is lasing. The laser dynamics is so rich when it lases in multimode. In the RF domain, except pre-described narrow repetition rate beatnote, its multi-mode lasing can
feature without detectable beatnote, with multi-beatnote, and with broad beatnote
depending on laser's bias. This is a strong evidence of the bias-dependent dispersion relation even when the gain is clapped. Other intersubband transitions are still
heavily affected by the biasing voltage (their energy alignment). Also, the repetition
beatnote alone can not prove the frequency comb operation, as it can be generated
by a strong pair or couple of pairs of lasing modes, leaving a large portion of the
radiation still not being phase-locked together. To rule out this possibility, further
coherence measurement is needed to show that this device is truly a comb.
4.2
Coherence measurement of THz QCL frequency
combs
Coherence separates lasers from all earlier light sources. It specifies the phase difference between two wave sources. Temporal coherence, which describes the average
correlation between one wave and its time delayed copy, and spatial coherence, which
characterizes cross-correlation between two points in a wave for all times, are good
examples. For a frequency comb, as it only needs two parameters to be fully characterized, there are two types of coherence to be discussed. The first one is the absolute
coherence, which shows the global phase stability of all lines. It is highly related to
frequency comb's offset frequency fluctuation. The second one is called the mutual
coherence, rendering the relative phase stability between any two lasing lines in the
comb. This essentially checks how uniformly these lines are spaced. To attain good
absolute coherence, techniques like lf-2f locking scheme is well-established in the ultrafast optics community, which can be applied to the QCL provided the comb spans
a octave spectrum range of lasing. As for mutual coherence, adjacent modes separate by several GHz in a normal few mm-long QCL, which is 10 to 100 times higher
than typical repetition rate of mode-lock lasers(- 100MHz). This relatively high
54
repetition rate in QCL frequency comb brings challenges to characterize the mutual
coherence.
4.2.1
Mutual coherence of two lines
Toy model to describe mutual coherence will give better idea of its definition. The
simplest task will be the characterization of mutual coherence between two lines in
an oscillator. Any field can be written in the form E(t) = Re[A(t)eiwt+(t], in which
A(t) is the time variant amplitude, w is the oscillating frequency, and
#(t)
is the time
variant phase fluctuation. If we assume the amplitude is time invariant (it is a good
assumption for a established laser), the oscillation's broadening in frequency domain
will all result from its phase fluctuation.
The quantity we care about is the mutual coherence, the relative phase stability
between two lines 021 =
02 -
01 .
When 021 is constant in time, it means that these
two lines are fully coherent with each other. When 02 1 (t) varies with time, we can
quantify this variation by defining the power spectrum of the phase fluctuation per
unit bandwidth:
S
21
(4.1)
( = T-I 0j#21(t)ewtdt12
(w)
f
The most straightforward way to get access to this quantity is to shine these two
lines on a fast photodetector simultaneously, shown in figure.4-3(a). The detected
power will be
P(t) = 1/2(E1 1 2 + IE212 +
E*E2 ei(W2-1)+21
+ E1E2i(*
1 -2)+4")
(4.2)
In frequency domain, the first two terms on the right-hand side are DC component and
are phase insensitive. The last two terms center at W2 1
broadening by the phase fluctuation S
21
= W2 -
W 1 with a introduced
(w).
Next, a local oscillator(LO) with a well-defined amplitude(1) and phase(#o) is
tuned to the frequency close to W2 1 , so the low-pass filtered result would have a
55
A
V2
(a)
_
xL
0
Vi
V2
AV
VThZ
VRF
VAudio
mixer product
X
V2
V1
VVVV/NJOP-
J\NVV\
RF LO
SQ
0
s0
0*90*
RF LO
I/Q demodulator
Figure 4-3: (a) Direct detection to characterize phase noise between two lines. (b) A
coherence detector scheme to measure the mutual coherence of two lines with respect
to a local oscillator.
component:
(4.3)
S(t) = 1/2Re[E1E2* e'G0-W21)t+(00-02d())
=
EjE 2 cos((wo - W 2 1 )t + (0o - #
2 1 (t)))
(4.4)
One can utilize the feedback control to make wo = W2 1 and set LO's phase to be
#o
= 7r/2. In this way, S(t) = E1E 2 sin(0 21 (t))
EE1 E 24 2 1 (t), which can be recorded
and Fourier transformed to get the power spectrum of the phase noise.
56
Actually, to fully capture the phase noise, one may rather construct a coherence
detector, recording both quadratures of S(t).
This can be done by phase shifting
the LO by 7r/2, and record the second downconverted signal as before. Figure.4-3(b)
shows the scheme of a coherence detector and its two outputs can be written as:
S1 (t)
=
Re[EE*e oWO-21)t+(00-021](t))
(4.5)
SQ(t)
=
Im[E1E2*e(Wo-21)t+(o-21(0)]
(4.6)
S1 (t) stands for the in-phase signal, while SQ(t) is the signal in quadrature phase.
Since these two signals are taken at the same time, one can use one quantity to
describe them as
S+(t)
(4.7)
SI(t) - iS(t)
=
E 1 E2* e(WoW21)t+(o0-21
(t))
The S+(t) is always measured at a laboratory time scale average (~
ferred by angle bracket (S+(t)).
(4.8)
second), re-
This long time averaging brings an effective way
to evaluate the phase noise in the millisecond or second time scale. We can define
the absolute value of S+(t) to be
IS+(t)I = IElIE2 1. If the phase difference between
two lines are completely stable, the time average value will be the same as the instantaneous value. The time average value decreases as the phase noise rises. Once
the phase difference between these two lines varies a lot within the laboratory time,
(S+(t)) will decrease to 0. With this picture in mind, the mutual coherence between
two lines can be mathematically written as
g+(P21) =_
((E*E2ei(W21-WO)t+21)
1
v/(IE1 (t)1 2 ) (IE 2 (t)
(4-9)
2)
On the right-hand side of Equation.4.9, the numerator comes from the (S+(t)),
which can be caculated with coherence detector's result, while the denominator is
the ordinary power measurement, thus making this definition convenient to use. Actually, the same definition of mutual coherence is applied by many groups studying
57
microresonator combs. Note that the value of numerator depends on the choice of
LO's frequency wo. Once wo
4.2.2
7
W2 1 , the coherence measurement will result in 0.
Mutual coherence of comb lines
To generalize the mutual coherence definition from two lines to multiple lines in a
comb is straightforward. One can follow the former formula and define the mutual
coherence between line i and
j
in a comb to be
g+ (wj)
I(ElEseos-wi+i
,l(lEi (t) )(lEj (t)
I
(4.10)
2)
Challenging thing here is how to physically measure all g+(wji) for each pairs in a
comb. Aside from an requirement of N(N-1) measurements for a comb with N different
lines, this measurement needs a tunable LO covering the comb's entire spectrum span
(usually few hundreds GHz or even 1 THz) and a corresponding fast detector. Instead,
we mainly focus on the coherence of adjacent lines and modify mutual coherence to
be
g (Pwo)
(E*(w)E(w wo))(
wo)2)
V'( E(w)12)(IE(w
Nevertheless, there are still a N-fold degeneracy in this mutual coherence and one
needs some kind of frequency discriminator to resolve individual pairs. In the technique we named as Shifted Wave Interference FTS (SWIFTS), as its name implies,
we present a FTS system as our frequency discriminator. The schematic set-up is
shown in Figure.4-4. We position a coherence detector at the output of FTS, and use
the beatnote signal coming from the detector side as our local oscillator. Unlike the
ordinary FTS that measures the autocorrelation of the field So(T)
=
(E(t)E(t - r)),
SWIFTS measures the crosscorrelation of the field with a well-defined frequencyshifted version of itself. Though the LO frequency is chosen to be the repetition
frequency in this mutual coherence measurement, it can be repetition rate's higher
order harmonics, giving the capability to assess mutual coherence between next nearest lasing modes.
58
delay
t
source
E(t)
I/Q demodulato r
- SQ(t)
Figure 4-4: Schematic illustration of SWIFTS. A coherence detector is placed at the
receiver port of the FTS.
As in conventional FTS, the Fourier transform of the field's autocorrelation function supposes to give the power spectrum of the field.
So(w)
dTA(r)
=
J dtK(t)E(t)E(t -
T)e--iWr
(4.12)
Here, A(T) presents the apodization function from FTS's finite traveling distance and
K(t) is the integration time for the data acquisition process. Solving this convolution,
So(w)
=
dtK(t)E(t)
dTE(t - T)ejw t
A(w) *
So(w)
=
(4.13)
(4.14)
t - Tr
'
So(w)
A(w) *
dtK(t)E(t)
dt'E(t')ewt'
A(w) * [E*(w) - (E * K)(w)]
(4.15)
(4.16)
~ A(w) * E(w)12
(4.17)
Note as the data acquisition averaging is always chosen to be millisecond or subsecond, K(w) (- Hz to KHz level) is very narrow compared to other measuring
quantities, and can be treated as 6(w), while A(w), the delay stage's apodization
function which applied when the measurement finishes, is GHz wide.
In SWIFTS, the raw signal collected from two ports of the coherence detector are
SI(T)
=
(E(t)E(t - T)cos(Awt)) and SQ() = (E(t)E(t 59
T)sin(Awt)).
The Fourier
transform of SI(r) can be written as
Si(w)
=
d()A(r)(E(t)E(t - r)cos(Awt))e-wr
(4.18)
J dtK(t)E(t)E(t -
(4.19)
= A(w) *
dr
= A(w) *
dtK(t) E(t)(ejwt + e-wt)
A(w) *
=
7)cos(AWt)e-jw
dtK(t)E(t)(e(L
J
dTE(t - T)d-iW'
"L)t
+ e-j(W+Aw)t)
(4.20)
dt'E(t')eWt'(4.21)
1
2
= A(w) * [(E * K)(w - Aw) + (E * K)(w + Aw)]E*(w)
(4.22)
Similar calculation also gives
1
* K)(w - Aw) - (E * K)(w + Aw)]E*(w)
SQ(w) = A(w) * -[(E
2j
(4.23)
S, - jSQ
Combing these two into the former defined S+
S+(w) = A() * [E*(w) (E * K)(w + Aw)]
(4.24)
S+(w)
(4.25)
~
A(w) * [E*(w) E(w + Aw)]
The fact that the apodization applies when the measurement finishes (the moving
stage does not know when to stop) preserves the coherence information, making
the coherence evaluation independent of FTS's resolution. Actually, the accuracy of
SWIFTS is determined by K(t),the averaging time in data acquisition which is few
milliseconds or a second, ensuring the SWIFTS can measure mutual coherence to the
Hz level. Think about a field with phase variation
#(t)
time integration in SWIFTS (E(t)E(t - r)cos((wt))
J
dtk(t)cos(Awt + q(t))E(t)E(t -
T)
between adjacent lines, the
can be written as
Oc
Jdtk(t)coso(t)
(4.26)
Unless, 0(t) is stable within the integration time, Equation.4.26 will vanish to be 0.
60
4.2.3
Actual SWIFTS measurement
Normal
FS HEB -- + Hlock-in
bias
amplifier
~6.8 GHz
6.8
GHZ
amplifier
~X
3kOX
RF I
lock-in
10
--
CLMHZ
bias l Loo
X
~
amplifier:
Demodulator --RF Q
lock-in
amplifier
---
SWIFT
interferograms
repetition rate
stabilization
Figure 4-5: Actual SWIFTS measurement set-up.
Figure.4-5 shows how to conduct the actual SWIFTS measurement. Light from
the lens-coupled THz QCL frequency comb first gets collimated and mechanically
chopped, sends through a FTS system, and then shines on a hot electron bolometer(HEB) at FTS's output. To avoid water absorption, the collimation system and
the FTS system are both boxed and purged with dry nitrogen gas. As for the electrical circuit concerned, a feedback system stabilizes QCL's biasing to achieve a clear
repetition beatnote. The stabilized beatnote collected from HEB's RF port and the
bias tee side both get amplified and feed into the I/Q demodulator. Figure.4-5 contains two downcoversion steps (one with a ~6.8 GHz LO and another one with a 10
MHz LO), which is due to the I/Q demodulator's operation bandwidth. By utilizing
a high frequency I/Q demodulator, the stabilization and demodulation step can be
61
simplified.
To collect data, as the delay stage in the FTS is moving, the DC sig-
nal from the HEB's DC monitor line, the in-phase signal SI(t), and the quadrature
phase signal SQ(t) from the I/Q demodulator are collected simultaneously using three
lock-in amplifiers.
In order to get access to the repetition beatnote, the detector used in SWIFTS
needs to be able to measure THz radiation with a 10 GHz bandwidth. We previously used a HEB detector from collaborators at TU Delft and at SRON. HEB detects
light via the resistivity change between superconductor's superconducting phase and
normal phase, giving a high sensitivity (NEP ~ 10-14 W/v Hz). This HEB differs
from other HEB by delicately coupling light to a superconducting bridge so that the
detection element has a very low heat capacity. Because only the bridge superconductor is heating up above the critical temperature, the electron-phonon interaction
can efficiently cool down the electron system, and a very short thermal response time
(sub-ns) can be realized. This special design endows the HEB with a excellent combination of both sensitivity and speed, leaving the trade-off of its robustness.
The
sub-micron width makes the HEB extremely static-sensitive. Moreover, as any superconducting device, it requires cooling to the liquid helium temperature, limiting
its function time to be
~ 8 hours given the holding volume of its dewar.
An alternative option is a horn-coupled Schottky mixer from Virginia Diodes Inc.
Despite its relatively low sensitivity (1000 times lower than the HEB), it operates at
room temperature. Benefiting from a long time average, Schottky mixer even posses
the possibility to resolve coherence information from some low SNR regions like multibeatnote region or broad beatnote region. All SWIFTS results shown in this thesis
come from the same device in Ref.[4] using the VDI schottky mixer as the detector
with a overnight averaging.
Figure.4-6(a) shows SWIFTS interferograms measured from device[4], along with
a normal interferogram recorded at the same time. Unlike normal power spectrum
without phase information, SWIFTS interferograms have non-zero phase, making
them asymmetric about the zero path difference. Figure.4-6(b)(c) show intermediate
plots of Si(w)(SQ(w)) and post-combined S+(w)( and its conjugate S_(w)) together
62
De-meaned
2
I
I
I
50
100
150
IQN
Data
FUl
C
T) 0
-2
-2
200
250
350
300
400
550
500
450
Time (ps)
FT of IQN (Hanning-windowed)
.
102
10
3.4
3.3
3 .2
3.6
3.5
3.7
3.9
3.8
Frequency (THz)
FT of PMN (Hanning-windowed)
P
- -- M
N
102
C
10
3.6
3.5
3.4
3.3
3 .2
3.7
3.8
3.9
Frequency (THz)
Deconvolved coefficients
-C0
10-4
3.2
3.3
3.4
3.6
3.5
3.7
3.8
3.9
4
Frequency (THz)
Figure 4-6: SWIFTS results for a QCL comb. From top to bottom: (a). Raw interferograms of in-phase(I), quadrature phase(Q), and Normal(N) signals. (b). Fourier
transform of Si(t), SQ(t), and normal interferograms with Hanning filter. (c). Power
spectrum(N), (S+(w))(P),and its conjugate (S_(w))(M). (d). Magnitude of deconvolved coefficients.
with normal power spectrum as a comparison. Once the normal spectrum So(w) and
the SWIFTS spectrum S+(w) have been measured. Further data processing can be
applied to numerically evaluate mutual coherence. Because all spectra were broadened
by the apodization function, decovolution needs to be done to resolve these real
spectra. To fulfill this requirement, discrete lasing frequencies {wi} are determined
63
.....
.........
......
....
"'W
by zero-padding the power spectrum and lest-square fitted the interferogram to a
discrete summation of exponentials:
So(T)
=
S+(T)
=
Zce
e
(4.27)
c (eiwiT
(4.28)
Phasors {c'} and {c'} are equivalent Fourier coefficients for each measurement. Once
these corresponding phasors have been found, the degree of coherence can be expressed at a particular frequency wi by simply calculating the ratio
= Sgi)
(4.29)
+
c 0(i) c0(i+1)
Figure.4-6(d) shows the numerator and denominator extracted from above data. Despite the fact that they are quite different measurements, their excellent agreement
implies that almost all of lasing modes contribute to the beatnote and that this is
indeed a frequency comb covering its entire lasing spectrum range (3.25 to 3.45 THz
and 3.7 to 3.9 THz). At two portions of the gain spectrum where the laser output is
the largest, the degree of coherence is close to unity. However, the coherence spectrum
falls off faster than the power spectrum along the lasing spectrum edges. This can
be understood as a consequence of the FWM: lasing modes along the spectrum edges
only can be locked with adjacent weak modes, reducing its coherence. This behavior
also makes sense since the coherence should not exceed unity, Ig(w)
4.2.4
; 1.
Coherence measurement in non-comb regions
The most crucial aspect of SWIFTS is the choice of the reference local oscillator.
In the preceding measurement, this is achieved by phase locking comb's repetition
rate to a synthesizer.
Extensive RF circuits are involved in the stabilization part.
And as a consequence of this stabilization, SWIFTS gets restricted to characterize
the comb operation with a clean narrow beatnote.
64
As mentioned before, instead
of comb operation, some pseudo-coherent regimes featuring multi-beatnote or broad
beatnote are of interests to understand the laser dynamics and have the potential to
improve future dispersion compasentor design. The choice of reference local oscillator
actually should be treated as a degree of freedom. Excluding the stabilization circuits
altogether, one can use the unstable beatnote from the QCL itself as the reference
oscillator. Provided the beatnote is still stable over short time scale, this self-reference
SWIFTS can extend its versatility to analyze the multi-beatnote and broad beatnote
regimes.
(b)
.
(a)
+0
+~KHz
o
-5
+^+,MHz
-10-15
-20
incoherent
-30
-20
shoulders
-25
-30-30
-35-
-50
-60
-40-
-70
6.805
-456.3
6.81
6.815
6.82
6.825
6.83
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
Figure 4-7: Pseudo-coherent QCL beatnotes.(a) Multi-beatnote. (b) Broad beatnote.
Figure.4-7 shows some beatnote examples of the same QCL operating at pseudocoherent regimes. Shown in Figure.4-7(a) is the multi-beatnote regime. At around
repetition rate frequency, differing from former clean narrow beatnote, it highlights
a strong narrow beatnote with two lower shoulders.
Actually, if one injects high
RF power at their difference frequency, these lower shoulders will converge to clearer
peaks and peaks with same frequency difference can start cascading, spanning -1
GHz range. Figure.4-8 illustrates one such example. Meanwhile, Figure.4-7(b) shows
the broad beatnote regime featuring with the beatnote FWHM greater than 1 MHz.
Both these unstable beatnotes are taken out from detector's RF port and bias tee
attached to the device, get amplified and are injected into the I/Q demodulator to
conduct the self-reference SWIFTS. Note that the beatnote from the bias tee is served
as I/Q demodulator's local oscillator, while the one from detector side is input RF
signal.
65
10
0
-10
-20
no injection
50
-60
-
~-40strog50 MHz injection
Mz spacing)
-70 -(25
Frequency (GHz)
-
-3U
-r4RF
-35
1.5
106
10 7
oft7power at 541 MHz 3
in comb regime, driven with116 dBm 111
1.
11.2
10.5
0.
11.
11.5
-40
~45
~ 50
o
-55
-60
,ii
-70 -~ll~i
10.5
10.6
d-
-..
-75~tiiI~A
10.7
10.8
11.1
11
10.9
Frequency (GHz)
11.2
11.3
5MHz
5
injection
11.4
11.5
Figure 4-8: RF spectrum of multibeatnote regime. Spectra with and without RF
power injection are shown in parallel for comparison.
Figure.4-9 and Figure.4-10 show these self-reference SWIFTS results from the
multi-beatnote and the broad beatnote regime individually, both of which accent
their unique features. Shown in Figure.4-9, QCL at the multi-beatnote regime lases
even broader than in the comb regime. But, the lasing is too weak that FWM fails
to inject-lock these lasing modes to be evenly-spaced, letting the power spectrum
have four side lumps which do not show up in the coherence measurement. In the
broad beatnote case, the coherence degrades in the entire lasing spectrum, featuring
sharp decreasing shoulders in the coherence measurement. More data and analysis
are needed to fully understand laser's behavior in these regimes and the self-reference
SWIFTS can be served as an critical analyzing tool.
66
De-meaned IQN Data
2
C7
Cl
P,
0
La
C0
N
300
Time (ps)
200
100
0
600
500
400
FT of IQN (Hanning-windowed)
=
m
a) 1dD
C
3.2
3.6
3.5
3.4
3.3
3.9
3.8
3.7
Frequency (THz)
FT of PMN (Hanning-windowed)
C
a)
C
3.6
3.5
3.4
3.3
3.2
3.9
3.8
3.7
Frequency (THz)
Deconvolved coefficients
-0-
Incoherent light
+0131/2
C
C
10
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
Frequency (THz)
Figure 4-9: Self-reference SWIFTS results from the multi-beatnote regime. From
top to bottom: (a). Raw interferograms of in-phase(I), quadrature phase(Q), and
Normal(N) signals. (b). Fourier transform of S 1 (t), SQ(t), and normal interferograms with Hanning filter. (c). Power spectrum(N), (S+(w))(P),and its conjugate
(S_(w))(M). (d). Magnitude of the deconvolved coefficients.
4.2.5
Technical considerations for SWIFTS
Minimization of optical feedback
One key feature shared by all types of frequency combs is that their operation is
extremely susceptible to optical feedback. Unlike in other well-developed frequen-
67
-
e - __
- :1 4
De-meaned IQN Data
CY
-2
100
400
300
200
600
500
Time (ps)
FT of IQN (Hanning-windowed)
Q
C
C
1id
3.2
3.1
3.3
3.4
3.6
3.5
3.9
3.8
3.7
Frequency (THz)
FT of PMN (Hanning-windowed)
N
(A
C
3.2
3.3
3.4
3.6
3.5
3.7
3.8
3.9
Frequency (THz)
Deconvolved coefficients
-
C
C0
+T/102
U,
C
a)
C
10-4
3 .1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Frequency (THz)
Figure 4-10: Self-reference SWIFTS results from the broad beatnote regime. From
top to bottom: (a). Raw interferograms of in-phase(I), quadrature phase(Q), and
Normal(N) signals. (b). Fourier transform of SI(t), SQ(t), and normal interferograms
with Hanning window filter. (c). Power spectrum(N), (S+(w))(P),and its conjugate
(S-(w))(M). (d). Magnitude of the deconvolved coefficients.
cies, there is no low-loss optical isolator at THz and the lens-coupled scheme makes
the QCL combs even more environmentally sensitive. In the worst case, transient
feedback can even switch QCL's operation mode and totally destroy the comb oper-
68
ation. Figure.4-11 illustrates one transient event that changes QCL from the comb
operation to single mode lasing, vanishing the SWIFTS signal. Clearly, minimizing
the impact of feedback is of great importance to establish the coherence of a comb.
One of major sources of feedback is the presence of FTS, in which retroreflection
from build-in optics send a large portion of the light back to the emitting source. To
make it even worse, the moving stage makes this feedback become delay-dependent,
so that frequency comb that is stable at a particular FTS delay may not be stable at
another. In the homemade FTS system, this feedback is largely removed by utilizing
roof-type mirrors instead of flat mirrors. It helps to spacially offset the retroreflection
to the input beam path, making it easy to be blocked. Similar optics like cube-corner
retroreflectors can serve the same purpose as well.
Effect of cat-strophic feedback on comb
nor mal
=
--
6-
RFI
RF
3
Q
AL
3.2
3.4
3.6
Frequency (THz)
3.8
4
3
3.2
3.4
3.6
3.8
Frequency (THz)
4
Figure 4-11: Effect of transient feedback that destabilizes comb operation and causes
its output to become single-mode. Modified from Ref.[5]
Correlated averaging scheme
In order to achieve a better SNR and resolve subtle features, SWITFS measurement
under the same condition always has been conducted repeatedly and all results then
get averaged, letting the entire experiment last for a day. Long term drifting of the experiment environment gradually shifts the interferogram and makes them misaligned
with each other a little bit. Brute-force averaging in this circumstance is problematic and by acting as a low-pass filter, this averaging will vanish all high frequency
information and lead to some unreal decoherence result. Thus, correlated averaging
69
scheme is essential to achieve good SNR while preserving all information. Given all
results come from the same condition, correlated averaging scheme calculates the autocorrelation between each measured interferogram and averages all interferograms
after shifting them to points where their autocorrelation produces maximum value.
Shown in Figure.4-12 are nine interferograms aligned in their maximum likelihood
positions.
12
lop
8
6
-|
4
2
MS~0
I
-2
0
0.5
1
1.5
2
2.5
-J
3
# 104
Figure 4-12: Correlated averaging scheme. Nine power interferograms get aligned by
shifting to the points where their autocorrelation produces maximum value.
70
Chapter 5
Terahertz Dual-comb Spectroscopy
Based on QCL Frequency Combs
5.1
Principle of the dual-comb sepctroscopy
As its name implies, a dual-comb spectrometer combines two frequency combs in an
interferometric way to conduct fast and high resolution spectroscopy with a broad
spectral bandwidth. It has been first proposed by Schiller in 2002[201, and compared
with traditional Fourier transform spectroscopy, this method circumvents the scanning components for the spectral resolution and handles the frequency discrimination
in a static manner.
Frequency comb 2
f O,2 frp,2
Frequency comb 1-
D
-
Gas Cell/
-/
Figure 5-1: Schematic illustration of a dual-comb spectrometer.
Shown in Figure.5-1 is the schematic illustration of a dual-comb spectrometer.
It involves two frequency combs with slightly different repetition frequencies. One
71
-
_M_ -
- 1-1 1
__-_
_1MMMMMMW_-R_
_.
-
__
-
' -
-
-- nn
of these two combs probes the sample and is combined with another comb via a
beam splitter. The combined light then shines onto a fast detector. The output from
the detector is a interferogram, attaining the time variation of the combined light
signal and by applying Fourier transform to this signal, one can obtain its spectral
information. Given a sufficient response time of the detector, this spectrum should be
a RF domain frequency comb, individual tooth of which has definitive correspondence
to the frequency difference between two lasing modes in the original combs. Figure.52 illustrates the frequency domain picture for this downconversion. The two utilized
combs posses slightly different repetition rates, frep,i
frep,2.
Thus modes for each
frequency comb can be expressed as fn,k = fo,k + nfrep,k, in which k = [1, 2] represents
either the first or the second comb. Assuming that
frep,2 > frep,i
for simplicity, the
relationship between these two repetition rates can be written as
frep,2 = frep,I
(5.1)
+ 6
Actually, all lasing modes of both frequency combs generate beating signals and
Figure.5-2 only shows the beating signal between the tooth of the same order n from
each individual comb. The frequency of
Afn
11a
beating signal can be written as
(5.2)
fn,i
=
fn,2 -
=
[fO,2+ nfrep,2 ] -
=
1f0,2 -
=
[fo,2 - fo,1 ] + n6
[fo,i + nfrep,i]
fo,i] + n[frep,2
-
(5.3)
(5.4)
frep,1]
(5.5)
The difference in repetition rates 3 turns out to be the repetition rate for the beating
signal, which is low enough to restrict all beating signals {fn,2
-
fn,1} into the RF
domain so that one can get access to it through the RF port of a high-speed detector.
72
The downconversion coefficient can be described using a scaling factor:
a
frep,2 - frep,1
(5.6)
frep,2
6
(5.7)
frep,2
measured
spectrum
transmission
spectrum
(D)
pair i
AV
VRF
Figure 5-2: Downconversion of the optical frequencies. Two frequency combs with
different repetition rates frep,i and frep,2 are combined and generate a comb in the
RF domain. Hence, the optical frequencies are down-converted to radio frequencies
by a scaling factor a, a = frep,2-.rep,
frep,2
One can also describe the spectroscopic process in the time domain. The electric field of a frequency comb can be written as Ek(t) = E,
An,ke-i( 2 7rfn,k)t
+ c.c.,
where A,,k is the amplitude of the n-th mode of the comb k and c.c. is the abbreviation of the conjugate complex. Frequency comb 1 shines through a gas cell and
the light-molecule interaction will introduce additional attenuation and phase shifting to comb modes. Following the Beer-Lambert law, one can write this interaction
as e-(a(f)++(f)), where a(f) is the amplitude attenuation and the 0p(f) is the phase
shifting at frequency
El(t) = E
f.
The electric filed of comb 1 after the gas cell is therefore:
2
An,ie-(an, +in,l)e-( rfn,)t
+ c.c..
Similar analysis can apply to the comb 2 and after these two combs get combined,
the electric field shining on the detector sum up to be:
Ei(t) + E2 (t) =
E[An,1e- (an+i+n,1e-irn,)t
+
An, 2 e(
2
7fn"2)t]
+ c.c.
(5.8)
n
+
Since the detector only responses to the power instead of the field, S(t) oc [F1 (t)
73
E2 (t)] - [E1 (t) + E 2 (t)]*. If we only consider the beating between the same order mode
coming from two combs, this beating signal can be written as:
Sn,n(t)
=
Z[En,1(t) + En,2 (t)] - [En,1(t) + En,2 (t)]*
(5.9)
n
=
Z(A ie-
2
an1 + A, 2 )
(5.10)
n
+
Z(2An,1An, 2 e~n'1 cos[27r(n6 + fo,2
n
-
fo,)t - 0(n, 1)])
(5.11)
Only the last term on the right-hand side is of interest since it discernibly preserves
all the spectral information of the probed gas sample. Special attention needs to
be paid to the oscillating frequencies of this term. As shown in the mathematical
formula, all the attenuation and phase shifting featuring at optical frequencies now
are clustered to the RF domain by the scaling factor a (Equation5.7). The first term
contains attenuation information too, but attenuation from all frequencies collapses
into the DC component and can not be discriminated.
Actually, it is not only the same order modes that can generate beating, one can
write down the beating signal between the n-th order mode of comb 1 and (n+1)-th
mode of comb 2 to be
A
Sn_1,3(t)
_1 1 e-2anj + A ,2
(5.12)
n
+
2An_1,1An, 2 e'nj1
cos[27r(n6 + fo,2 - fo,i + frep,2 )t + On_1,1](5.13)
Here, Sn_1,n is almost equal to Sn,n and the main difference is that all downconverted frequencies get grouped to around frep,2. Same calculation can be continued
for the next term or even higher orders. Given the bandwidth limit of any physical
detector, we focus on the S,,, which has all the absorption information we want and
its spectrum is at a relative low RF frequency.
For an optical bandwidth Af where two combs have overlapping, one wishes to
acquire, it is possible to deduce an optimum repetition rate difference between two
combs[1], 6opt, with which no aliasing of the beating signal occurs and only the beating
74
from the same order modes contributes to the interferogram. From Nyquist-Shannon
sampling condition, it requires Av = Af - a, Av <
f-P,
saying that the bandwidth
of the downconverted signals should not exceed half of the repetition rate of the
original comb, where Av is the downconverted signal bandwidth and a is the predefined scaling factor. Since, When 6 increases, the downconverted RF bandwidth
(Av
=
Af - a = Af - 6
grows.
And by the time it surpasses
fr
it starts to
overlap with itself on the low frequency end and beatings from higher orders on
the high frequency end. Figure.5-3(b) illustrates the aliasing situation, in which the
spectral information on two ends becomes ambiguous. A too low value of 6 means
that detector's bandwidth is not fully exploited and the data acquisition time tM also
suffers since tM oc 6-'[1]. All these constrains lead to the optimal scaling factor to be
aaPt =
-2A,,vin
in repetition rate to be:
, giving the
ifrnert
h ideal difference
60t -
(5.14)
2a'1
2Av
Shown in Figure.5-3(a) is the frequency domain picture under the optimum situation.
(a)
0
frep 1/2
01
frep,0/2fI
I
frep,
f
(b)
~rep,
I
f
Figure 5-3: Schematic illustration of downconverted signal with different repetition
rate differences. (a) The free spectral range is fully exploited and the acquisition time
2
is ideal for a given resolution. In this case, Av is assumed to be frep/ . (b) Aliasing
situation when 6 is too large. Modified from Ref.[1.
75
Unlike the traditional Fourier transform spectroscopy, the resolution of which is
determined by the maximum path difference between two interferometer arms, dualcomb spectrometer abandons the moving stage, letting its interferogram becomes just
a function of time. In this way, its resolution is ultimately determined by the linewidth
of individual tooth in the frequency comb, since the gas is probed by comb's individual
mode with a defined linewidth. Experimentally speaking, the limiting factor can be
the fluctuation of the comb parameters fo and frep during the acquisition time. And
for THz dual-comb spectroscopy based on QCL frequency combs, stabilizing comb
parameters for the acquisition time is of the most challenge task.
When the bandwidth of downconverted signal does not exceed
freP
2
and the sam-
pling frequency at detector's output fulfills Nyquist sampling theorem (assume to be
frep
in the following discussion), the total sample amount reaches tM - frep for an
acquisition time tM, giving the resolution in RF domain to be:
frep/2
tM , frep
A
2
1
tM
(5.15)
Here the time-frequency uncertainty is retrieved, which is generally true for any physical system. In the optical domain, the spectral resolution is calculated to be
1
6VuA
2
tM
a
aopt
tM - frep
(5.16)
As a consequence, in order to achieve a higher resolution for a given bandwidth, one
needs to conduct experiment with longer acquisition time using higher repetition rate
frequency combs.
5.2
Trial of THz dual-comb spectroscopy using QCL
frequency combs
Figure.5-4 shows the actual experimental set-up for our THz dual-comb spectroscopy.
Two 4mm-long comb devices using gain medium ETHOWIE3-3 are lens-coupled and
76
get mounted into a pulse-tube cooler, shining to the opposite direction.
This gain
medium is chosen because of its low power consumption and its capability of broadband lasing. Figure.5-5(b) shows the lasing spectrum from one device under CW bias
at 38K. The different color corresponds to the same color-marked biasing point in
Figure.5-5(a). To be noted, repetition beatnote was detected in the entire multimode
lasing regime. But after the device is lens-coupled and undergoes several cooling cycles, the regime featuring with detectable beatnote get shrunk (marked with bold red
line in Figure.5-5(a)) and the lasing spectral coverage shrinks to be about 200 GHz.
This may result from the lens degradation and oil contamination from the mechanical
pump, which change the loss and introduce additional adverse feedback.
These two devices are biased to the regime where they both generate narrow
beatnotes, get collimated via OAPs and combined using a silicon beam splitter, and
then are focused together on a fast detector. Water absorption is reduced by purging
the entire set-up with dry nitrogen gas.
Detector
S |
~~~-~--- -------------
-
------
Gas cell
~~
~ ~
Beam
splitter
Figure 5-4: Experimental set-up for THz dual-comb spectroscopy.
Figure.5-6 shows the result from the RF port of a Schottky mixer.
The de-
tected repetition beatnotes from the two devices centered around 9.1 GHz (shown in
Figure.5-6(a)), each of which has a FWHM to be about 30 KHz and SNR higher than
15 dB. The difference between repetition beatnotes is about 33 MHz. At the same
77
.
.............
....
........
*to'
IVL at 38K CW biased
11.
(a)
112;
2
0.
10.81
0
1 5
210
205
200
020
215
225
230
235
240
Current density(A/hn
(b)
Spectrum
Spectrum
102
10
101
2.4
2.5
2.6
2.8
2.7
2.9
2.4
3.2
3.1
3
2.5
2.6
2.7
2.6
2.7
2.8
2.9
2.4
3.2
3.1
3
2.5
2.6
2.7
2.4
2.5
2.7
2.6
2.9
2.8
Freq [THz]
3
2.4
3.2
3.1
2.5
2.6
2.7
I
29
3
3.1
32
2.9
2.8
Freq [THz]
3
3.1
3.2
3
3.1
3.2
2.8
Spectrum
Spectrum
L
3.2
Freq [THz]
Freq [THz]
Spectrum
102
3.1
3
-rg
-1
r
10
2.5
2.9
Spectrum
Spectrum
2.4
2.8
U1 -- --
==
r-----
I
____________lol-_
id_______________id"__________________
2.4
2.5
2.6
2.7
2.9
2.8
Freq [THz]
3
3.2
3.1
2.4
2.5
2.6
2.7
2.9
2.8
Freq [THz]
Figure 5-5: Lasing spetrum versus bias at 38K. (a) Current versus voltage and current
versus output power for one device. (b) Lasing spectra under different biases. The
different plotting color corresponds to the biasing point in (a) and insets show the
repetition beatnote collected from the bias tee. The bias regime where detectable
beatnotes exist is marked with bold red line in (a).
time, we can measure the downconverted heterodyne RF signal at around 2.4GHz
with 400 MHz spectrum coverage. Based on previous calculation, this means that
the two combs offset frequency fo,2
-
fo, = 2.4 GHz. Also using the scaling factor a
78
.. . ........
this RF spectrum coverage corresponds to a 120 GHz spectrum overlapping in two FCs' lasing spectrum. Under 20 ms acquisition time, the single tooth
(a
= 3Hz),
of the heterodyne signal shows 8MHz linewidth, which is broader than the theoretical
convolution of two lasing modes. This broadening is mainly due to the fluctuation
of comb parameters, fo and frep, within this requisition time. One can minimize the
feedback to stabilize the frep, but without a stabilization method for fo, the entire
spectrum of a frequency comb can still wobbles as one entity: in this case, a 12 GHz
fluctuation in THz frequency can lead to a 4 MHz broadening in the RF domain,
giving the convolution to be 8 MHz.
(a)
-30KHz
91
9.11
912
9142
9.16
9,15
9.14
9.13
Frequency(G~z)
9.1425
9143 9.1435
GHz
9.144
9.144
(b)
-20
1.9
I
2
21
22
2.3
24
Frsquetcy(G~z)
2.5
26
27
2.8
2.9
Figure 5-6: Repetition beatnotes and the multiheterodyne signal from a Schottky
mixer. (a) Repetition beatnotes from two devices center at around 9.1 GHz, each
of which has a FWHM to be about 30 KHz and a SNR higher than 15 dB. (b)
Multiheterodyne signal at 2.4 GHz.
To be noted, one can get better SNR signal by using the HEB. Figure.5-7 and
Figure.5-8 show the repetition beatnotes and the multiheterodyne signal from the
HEB. Even though the SNR is boosted up to be above 20 dB but the multiheterodyne
signal still gets messed up to be indistinguishable. A proposed attempt is to trace
the time domain interferogram with a shorter acquisition time, estimate a fluctuation
kernel and apply a time domain filter to the entire interferogram. The key challenge
here is how to estimate the fluctuation kernel. One can downconvert the repetition
beatnotes to the quasi-DC regime and record them with the multiheterodyne signal
79
Since the optical feedback introduced by the environment which
simultaneously.
will affect the repetition beatnote, the fluctuation kernel can be estimated using the
repetition beatnotes' inteferogram.
Repetition rate beatnotes
-:
on the HEB
on the bias tee
-45-
-50-
-55C
-60-
-65
I
9.08
9.09
9.1
9.11
9.12
9.13
9.15
9.14
9.16
Frequency(GHz)
Figure 5-7: Repetition beatnotes from HEB.
Multi-heterodyne signal
-14
-16
-18
-20"
E
CO -22
-e24
S-26
-28
-
-30
-32
-34
1.4
1.6
1.8
2
2.2
2.4
Frequency(GHz)
Figure 5-8: Multiheterodyne signal from HEB.
To get access to the shorter acquisition time data, a LO with frequency of ~9.3
GHz and another LO with frequency of ~2.6 GHz are chosen to downconvert repetition beatnotes and multiheterodyne singal to the RF regime at the same time, both
80
of which are then recorded with a fast oscilloscope (RF bandwith> 500 MHz with
sampling rate > 1.25 GS/s). Figure.5-11 shows the downconverted repetition beatnotes with 30 us acquisition time at various laboratory time moment. One can see
that repetition beatnotes maintain narrow and stable within 30 us and there is no significant time drifting at laboratory time scale (270 us in this case). On the contrary,
Figure.5-9 shows some examples of downconverted multiheterodyne signals with an
acquisition time of 1 us at different laboratory time moment. The downconverted
multiheterodyne signal has a strong time-variant movement as one entity (shown
with dash lines in Figure.5-9), which corresponds to the offset frequency fluctuation.
The offset frequency's fluctuation is so strong that it can smear the downconverted
multiheterodyne signal with milliseconds acquisition time, resulting Figure.5-8 to be
indistinguishable.
Figure.5-10 illustrates the offset frequency's fluctuation.
At the
meantime, differing from previous Figure.5-8, one can see more than 20 distinguishable multiheterodyne peaks within 1 us acquisition time, all of which have 33 MHz
frequency spacing with their neighbor. This 33 MHz spacing matches the repetition
beatnote's difference between the two devices, implying that there are more than 20
modes in each comb which contribute to this downconverted multiheteridyne signal,
and two combs' overlapping spectral range is more than 182 GHz (9.1 GHzx 20).
Also, it posts a new issue: in order to achieve higher resolution, how can we stabilize
the fast variation of the offset frequency's fluctuation?
81
Downconverted multiheterodyne singals vs time, 1 us time slot
1035
10=3029
t--=1840 ps
5
400
200
10-50
Offset
freuency
010
(MHz)
20
Figure 5-9: Downconverted mnultiheterodyne signal versus time, 1 us time slot.
Offset frequenCy fluCtuat|ons
80
0-
10
20-
-60
-90
0
5
1=0
15
20
Time (us)
Figure 5-10: Offset frequency's fluctuation versus time.
82
25
Downconverted repetition beatnote vs time, 30 us time slot
t=270 Ps
10 25
t=240 ps
t=210 ps
o20
1
t=150 ps
W0 ps
t=60 ps
105
t=30 PS
=0 ps
10-5
220
230
240
Offset frequency (MHz)
250
260
270
Figure 5-11: Downconverted repetition beatnotes versus time, 30 us time slot.
83
84
Appendix A
Fabrication Flow
85
THz lasers in double-metal waveguides
Description: Hu group standard process for fabrication of terahertz quantum cascade lasers in metal
waveguides using thermocompression. Process is red throughout. This is a revised version of
metalwavebonder copper originally submitted by Benjamin Williams, but updated to reflect all
changes accumulated over the years since Ben graduated.
Facilities used: TRL, Qing Hu laboratory for lapping.
Starting materials:
1. GaAs wafers with MBE grown AlGaAs GaAs MBE heterostructures from Sandia National
Laboratories).
2. Bare 3" n+ GaAs wafers (thermocompression receptor wafers) from AXT.
Part 1. Thermocompression bonding
Step Description
1.
Cleave and name MBE
Lab
Machine
Comments
TRL
Sample size -Ix2cm. Gently scribe MBE wafer
name onto one edge (for identification
following ebeam deposition).
samples
2.
Cleave 3" n+ GaAs wafers
into halves
TRL
Cleave into halves for ebeam loading.
3.
Predeposition oxide strip
TRL acid-hood
4.
Deposit thermocompression
metal
TRL ebeamAu
30s dip in 1:1 HCl:H20, or IOs dip in BOE
Ta/Au 100 A/2500 A, deposited at I A/s
5.
Cleave scribed edges off
MBE samples
TRL
6.
Cleave 3" n+ GaAs halves
into smaller pieces
TRL
7.
Thermocompression
TRL EV501
Scribed edges will not be flat, so must be
removed prior to thermocompression.
Pieces should be moderately larger than MBE
samples.
Replace quartz pressure plate with steel plate.
On 4" wafer chuck, align edges of MBE
samples and receptor dies, face to face (use
glass slide).
Place 4" steel electrode (no bow) on top of
wafer stack with graphite spacers.
Bond for 60 min at -300 C and -4 MPa
pressure, in vacuum. (EV501 recipe:
bwilliamcu300.aba)
8.
Name bonded sample
TRL
Scribe MBE wafer number on exposed receptor
wafer around the edges of bonded sample, This
is for identification following anneal step.
9.
Anneal
TRL EV501
Place all bonded pieces in EV501. Place
graphite spacers on top of pieces, and top with
4" steel electrode.
Anneal for 45min at 300C, in N2 ambient
(EV501 recipe: bwilliamanneal300.aba)
10.
MBE sidewall/receptor
backside protective
dielectric deposition
TRL STS-CVD
Deposit 4000A LFSIO2 on front and back of
bonded samples.
Part 2. Substrate lapping and removal
Step Description
11.
MBE substrate lapping
Lab
Machine
Hu
Lab
Comments
Affix bonded sample to steel chuck using
Crystal Bond wax. Lap MBE substrate using
400 grit sandpaper until -00um substrate
remains.
Dissolve wax in acetone, remove sample.
Soak in clean acetone for -h to remove wax
residues.
Rinse in clean acetone, MeOH, then IPA.
12.
Ultrasound clean
TRL Ultrasound Ultrasound samples for I Os in acetone, then
MeOH, then IPA.
13.
Backside photoresist
coating (optional)
TRL Coater
(Optional step, generally used only use if STSCVD is down).
Manually swab Shipleye 1813 photoresist onto
receptor backside. Postbake 30min.
14.
Wet etch removal of
remaining substrate
TRL acid-hood
Selective etch of GaAs MBE receptor stopping
on AlGaAs etch stop. Put all samples in citric
acid:H202 3:1 solution (- 500mL).
Etching solution is strongly diffusion limited
and must be kept agitated to achieve reasonable
etch rates. Use a stir bar and magnetic stirrer to
avoid prolonged standing at the acid-hood.
Etch speed and selectivity degrades with time.
Change solution every -1 h.
15.
Receptor photoresist
removal
TRL photo-wet If backside photoresist was used earlier, strip
this off in acetone, followed by MeOH and IPA
clean.
16.
Etch stop removal
TRL
17.
Top contact removal
(optional)
TRL acid-hood
For high pulsed temperature performance,
remove the doping layer for the top contact.
Etch away in 1:1:25 H3PO4:H202:H20
(0.25um/min; typically a minute is enough).
Step Description
Lab
Comments
18.
TRL Coater
acid-hood HF, -15-30 s, or until clear. AlGaAs etch
appears as a pretty rainbow colored layer; GaAs
is a dull gray. Removal is visually obvious.
Part 3. Top metal definition
Image reversal resist
coating
Machine
Use 3 solvent clean immediately before coating.
AZ5214E photoresist
Dispense/Spread/Spin for 6/8/30s at
0.5/0.75/3.95 krpm
Follow with 20min prebake (95 C).
Note 1: Do not do lithographyimmediately
after previous wet-etching steps. Adhesion
becomes extremely poor, for reasons not well
understood. Let the samples "rest" for a few
hours, or overnight.
Note 2: we have in-house verified that HMDS
is totally useless for GaAs. Don't bother.
19.
Photoresist exposure
TRL MA-6
7s low vacuum exposure.
20.
Image reversal bake
TRL hot-plate
1,2 or 3
120 C bake for 1 min. Bake on top of a silicon
dummy, monitor temperature using contact
thermometer (don't use in-built hotplate
thermometers).
21.
Flood exposure
TRL MA-6
Flood expose all samples for 135s.
22.
Development
TRL photo-wet
AZ422MIF for 2:30. Follow by two rinses in DI
water for 1 minute each.
23.
Post development clean
TRL Asher
Ash for 5 min to remove possible photoresist
residues
24.
Predeposition oxide strip
TRL acid-hood
30 s dip in 1:1 HCl:H20 or lOs dip in BOE
25.
Top metal deposition
TRL ebeamAu
Ta/Au 1 OOA/3000A deposited at IA/s
26.
Lift-off
TRL ebeamAu
Soak all pieces for -2 h in acetone (or
overnight, exact time is unimportant). Clean
samples in MeOH and IPA afterwards.
Part 4a. Mesa definition by dry etch
Machine
Step Description
Lab
27.
Post liftoff clean
TRL Asher
Ash for 30min
28.
Mesa dry etch
TRL SAMCO
Run standard Cl clean, then precondition
chamber using GaAs dummies for 30 minutes
using recipe 7 (ICP120W, RF 40W, 0.5/3/16
sccm C12/SiC14/Ar, I Pa)
Comments
Leaving dummies inside, etch samples using
recipe 7 for 65min (for 1 Oum MBE layer). Top
metallization (gold) acts as self-aligned mask,
thermocompression layer (bottom gold) acts as
etch-stop.
Chamber needs to be chlorine cleaned and
reconditioned every -3-4 runs, else stuff starts
to deposit on the samples and dummies causing
etch roughness.
29.
Sidewall passivation
removal (wet etch)
TRL acid-hood
Dip samples in BOE for 4min. If passivation is
not removed, lasers ridges will shatter later
during cleaving, instead of breaking cleanly.
30.
Sidewall passivation
removal (dry etch)
TRL plasmaquest If sample is not BOE safe, use dry removal in
plasmaquest, recipe: SF6_WK2.rcp 600sec
70 mtorr /100 sccm SF6/ ECR500W/RF OW
Part 4b. Mesa definition by wet etch
Step Description
31.
Positive resist coating
Lab
Machine
TRL Asher
Comments
Use 3 solvent clean immediately before coating.
Shipley 1813
Dispense/Spread/Spin for 6/8/30s at
0.5/0.75/3.90 krpm
Follow with 30min prebake (95C).
32.
Photoresist exposure
TRL MA-6
75s low vacuum exposure. Take great care in
aligning photoresist mask to top-metal mask,
else ridges will suffer from lateral etch damage
later.
33.
Development
TRL photo-wet
MIF319 for 45 s. Follow by two rinses in DI
water for 1 minute each.
Follow by 30 min post-bake (120 C).
Note: MTL's MIF319 developer is expired by
~5-6 years, but it's okay to use still...
34.
Wet etch
TRL acid-hood
Etch mesas in 1:1:25 H3PO4:H202:H20
(~0.25um/min). For lOum MBE layer, starting
monitoring the etch progress under the photoroom microscope after ~30min, to avoid overetching.
Do not agitate the solution. The etch is reaction
limited and requires no stirring. Stirring may
damage the photoresist, particularly once the
etch becomes deep.
Part 5. Backside metallization
Step Description
35.
Backside metal deposition
Lab
Machine
Comments
TRL
ebeamAu
Deposit Ti/Au 300A/2000A at IA/s.
Samples need to be device-side down.To avoid
scratching devices, samples should be placed on
top of unscratched GaAs (or Si) dummies.
36.
Celebrate/Weep
Done! But you've probably lost at least a month
of your life, probably two.
Appendix B
Lens Mounting Process
91
1. Preparation
Clip: clip is made from a thin copper mount and is cut to a suitable height for lens holding during
the whole process.
Spacer: to adjust the relative position of lens and device, a spacer is placed between the facet and
the lens. Spacer is made of high resistant silicon (cleaving from the HR silicon wafer), which is the
same material as silicon lens. The spacer should be make wider than the device and slightly longer
for easy holding purpose.
Lens: Silicon lens.
Optical glue, copper wire, stycast, SMA connector, Omni mount.
Note:
o
o
2.
Several things should be done before lens mounting.
i. The biasing part (wire bonding/indium bonding).
ii. Chip carrier.
If lens should be mount on both facet, the copper mount should be milled to the same
length as the device so that each facet are reachable. If lens is needed for one facet, make
sure that that facet faces the edge of copper mount and the copper mount edge is sharp.
The device should be mounted slightly overhanging in the front facet in order to secure the
contact with the spacer.
Spacer mounting
Mount the whole copper mount to the side facet of the omnimount, and then mount the whole
sturcture to the side of the die bonder aluminum mount.
a. Use the razor blade (can break it into small pieces) to make the wafer as flat as possible.
b. Clean the spacer and the facet with blue tape.
c. Put the blue tape on one side of the spacer and use the die bond machine to put it on the
facet of the device.
d. Stick the spacer to the copper mount (not the laser chip) using optical glue.
i. The idea here is just to hold the spacer, bottom and side first and make sure the glue is
fully cured before move to the next step.
Note:
The die bound stage may move during the holding time, and the tip may vibrate when the stage
posits at its left end. It is better to turn on the gas and move the stage to its right end.
3. Lens mounting
The set-up for lens mounting needs a FLIR camera (infrared camera), optical microscope, and a 3-D
micromanipulator.
Note:
0
Know the moving direction of the micromanipulator before doing anything.
*
a.
Before lens mountir
toxrv;r
-
solder a SMA connector for biasii
b.
c.
d.
e.
f.
Use the output from FLIR camera as a trigger signal for function generator to generate a signal
with 1/3 frequency (usually the output from camera is a around 30Hz, 100ns pulse, so the output
from the generator is around 10 Hz and set the duty cycle close to 1/3).
Use the signal from the synthesizer as a GATE signal for the AV-tech power source(usually 10KHz,
10%? Can be arbitrary). In this configuration, the software can get three image in one period, one
with laser on, two with laser off(to cool down the laser & get clearer thermal image).
Run software "camera collection GUl" to get a clear thermal image and run "THz-image David".
The differential images are (laser on-laser off(1),laser off(1)-laser off(2) and laser off(2)-laser
on),which can give a clear thermal image.
Bias the device with Avtech, and from the thermal image we can see that the only place to be
heated up is the biasing device.
Focus is about 23 turns (14.375 mm)
back from device location
Downsampled by 4, 60 s averaging
60
20 um device, 625 W/cm 2 applied to ON
frame
100
120
20
g.
40
60
80
100
120
140
160
After contacting the lens with the spacer, the focus plane is move back by about 7 mm (Rn=2
mm*3.4). So change the distance between camera and its focusing lens to make sure that it
focuses on the device. Then, use the 3D micro manipulator to adjust the position of the lens to
make sure the lens and the device are concentric.
h.
Use optical glue to fill the gap between the lens and the copper mount (optical glue should not
touch the device and the spacer since it is lossy @ THz). Use the copper wire to put optical glue on
both side of the lens and use the UV light to cure it.
.
After UV curing the optical glue, put stycast around the optical glue but do not touch the device.
96
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