High Field, High Efficiency Terahertz Pulse
Generation by Optical Rectification
by
Wenqian Ronny Huang
B.S., Cornell University (2009)
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science
O
at the
APR 10 2014
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
February 2014
© Massachusetts Institute of Technology 2014. All rights reserved.
Author...............................................
Department of E'lectrical Engineering and Computer Science
January 31, 2014
............................
Franz X. Kdrtner
Adjunct Professor of Electrical Engineering
C ertified by .
Thesis Supervisor
Certified by ..........
I h
NOGY
Erich P. Ippen
Professor of Electrical Engineering
Thesis Supervisor
Accepted by .........
Leslie A. Kolodziejski
Chairman, Department Committee on Graduate Theses
2
High Field, High Efficiency Terahertz Pulse Generation by
Optical Rectification
by
Wenqian Ronny Huang
Submitted to the Department of Electrical Engineering and Computer Science
on January 31, 2014, in partial fulfillment of the
requirements for the degree of
Master of Science
Abstract
The great difficulty of producing high intensity radiation in the terahertz (THz)
spectral region by conventional electronics has stimulated interest in development
of sources based on photonics. Optical rectification in lithium niobate is an attractive approach, because it supports high generation efficiencies, uses low cost, bulk LN
crystals, and is powered by common Yb-doped lasers at wavelengths of around 1 Pm.
In this work, a theoretical framework for THz generation by optical rectification is
developed. Several novel methods for optimizing the generation efficiency are shown,
including pump beam imaging, pump pulse optimization, cryogenic cooling, and THz
antirefiection coating. Finally, experimental results will be presented showing a THz
generation efficiency of 3.7%, which is 10x higher than current state-of-the-art. The
generated few-cycle THz pulses can be used for coherent control of electrons, setting
the stage for compact, table-top accelerators.
Thesis Supervisor: Franz X. Kdrtner
Title: Adjunct Professor of Electrical Engineering
Thesis Supervisor: Erich P. Ippen
Title: Professor of Electrical Engineering
3
4
Acknowledgments
First of all, I would like to thank my advisor Prof. Franz Kdrtner for supervising my
Masters work. His continual passion for science and unfailing optimism in the face of
setbacks have been a mainstay in my scientific development. I would also like thank
my co-advisor Prof. Erich Ippen for his words of wisdom and stable presence.
I would like to express my gratitude for to all those who helped and encouraged my
studies. I am obliged to Shu-Wei Huang and Eduardo Granados who initially helped
me to get up to speed on the terahertz project. I am grateful for the leadership and
guidance of experienced research scientists Kyunghan Hong, Luis Zapata, and Jeffrey
Moses. I am thankful for my ongoing colleagues on the terahertz project, Koustuban
Ravi and Emilio Nanni, for their constant collegiality and long, helpful discussions. I
acknowledge Hungwen Chen and Peter Krogen, who, though they were on separate
projects, sacrificed ample amounts of their time to help fix certain aspects of my
experiment. I am indebted to Donnie Keathley, Michael Swanwick, Richard Hobbs,
Billy Putnam, Hua Lin, Sergio Carbajo, and Jinkang Lim who have been generous
with their lab equipment and expertise. Finally, I am grateful for the other staff,
postdoctoral and graduate student colleagues-including Damian Schimpf, Liang Jie
Wong, Siddharth Bhardwaj, Hongyu Yang, Patrick Callahan, and Dorothy Fleischerwho have made my time at MIT intellectually stimulating and experientially fulfilling
in one way or the other.
Finally, I would like to thank my family and Calinda for their support through
my studies.
5
6
Contents
1
1.1
Intrapulse difference frequency generation
. . . . . . . . . . . . . . .
19
1.2
Mathematical description of broadband optical rectification . . . . . .
22
1.2.1
Undepleted pump derivation . . . . . . . . . . . . . . . . . . .
22
1.2.2
Cascaded optical rectification (depleted pump) . . . . . . . . .
23
1.2.3
Choice of nonlinear material: lithium niobate
. . . . . . . . .
24
Noncollinear phase matching . . . . . . . . . . . . . . . . . . . . . . .
25
1.3.1
Tilted pulse front pumping (TPFP) . . . . . . . . . . . . . . .
25
1.3.2
Angular dispersion picture of TPFP . . . . . . . . . . . . . . .
26
1.3.3
Phase-matching is limited by dispersive effects . . . . . . . . .
27
1.3
2
31
Optimization of THz Generation Efficiency
. . . . . . . . . . . . . . . . . . . .
31
2.1.1
Pulse front tilt is induced by diffraction from grating . . . . .
31
2.1.2
Relay-imaging of grating . . . . . . . . . . . . . . . . . . . . .
32
2.1.3
Design of a TPFP setup . . . . . . . . . . . . . . . . . . . . .
34
2.2
Optimization of pump pulse . . . . . . . . . . . . . . . . . . . . . . .
35
2.3
Cryogenic cooling of lithium niobate crystal
. . . . . . . . . . . . . .
37
2.4
THz antireflection coating . . . . . . . . . . . . . . . . . . . . . . . .
38
2.1
3
19
THz Generation by Optical Rectification
Tilted pulse front pumping setup
Experimental Demonstration of Efficient THz Generation
41
3.1
Experim ental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.2
Results and discussion
. . . . . . . . . . . . . . . . . . . . . . . . . .
44
7
8
List of Figures
1-1
(a) Energy level diagram of difference frequency generation. (b) Spectral diagram of intrapulse difference frequency generation (optical rectification).
(c) Optical rectification of a broadband IR pulse yields a
THz pulse with a spectrum spanning the few THz regime.
1-2
. . . . . .
20
(a) Energy level diagram of cascading. An IR photon at w generates
a THz photon at Q plus a downshifted IR photon at w - Q.
The
downshifted IR photon can be recycled to generate another THz photon
at Q plus a further downshifted photon at w - 2Q.
this process is
repeated as long as the IR and THz frequencies are phase-matched.
(b)-(f) Spectral picture of cascading. (b) Two frequency components
in the broadband IR spectrum generate a difference frequency that lies
in the THz regime. (c) The higher frequency component is downshifted.
(d) The downshifted frequency component mixes with an even lower
frequency component to generate another THz component.
(e) The
higher frequency IR component is downshifted once more. (f) In the
end, the output JR spectrum is redshifted and broadened.
1-3
21
(a) Tilted pulse front pumping scheme. (b) Angular dispersion picture
of phase-m atching.
1-4
. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Phasor diagram of intrapulse difference frequency generation with chirp.
The red arrows denote the integrand of Equation 1.2 and the blue arrow
denotes the total integral of Equation 1.2, or the sum of the red arrows,
in the case of (a) zero chirp (perfect phase match), (b) moderate chirp,
(c) severe chirp (perfect phase mismatch).
9
. . . . . . . . . . . . . . .
28
2-1
Schematic of pulse front tilting imaging setup. PFT, pulse front tilt;
OJ, incidence angle;
Od,
diffraction angle; f, focal length; n, refractive
index; ng, group index; A1 ,A2 ,A3 illustrate angular dispersion induced
by grating.
2-2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plot of required incidence angle as a function of groove density for
optimal phase matching.
A groove density of 1500 1/mm is chosen
because it has a required incidence angle close to the Littrow angle.
2-3
32
35
Simulation of the THz generation efficiency as a function of pump pulse
duration and temperature. The plot shows that the optimal efficiency
is achieved at a pump pulse duration of around 0.5 ps and at cryogenic
temperatures. Annotations show the results achieved by us (MIT) and
by Fulop [1]. Simulation adapted from [1].
2-4
37
..................................
Calculated power reflection coefficient of the lithium niobate to air
interface for various THz antireflection coatings.
3-1
36
THz absorption coefficient a(Q) as a function of temperature and frequency. ..........
2-5
. . . . . . . . . . . . . . .
. . . . . . . . . . .
39
Schematic of experiment. BS, 50:50 beam splitter; YDFA, Yb-doped
fiber amplifier; HWP, half-wave plate; LI, bestform lens with f = 20
cm; L2, concave cylindrical lens with f = 15 cm; HR, dielectric high
reflector mirror; L3, plano-convex lens with f = 23 cm; PBS, polarizing
beam splitter.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2
Schematic of the EO sampling setup.
. . . . . . . . . . . . . . . . . .
3-3
Pump energy sweep of THz generated from room temperature sLN
42
44
and cLN. The sLN fit shows a 1.97 power dependence and the cLN fit
. . . . . . . . . . . . . . . . . . . .
shows a 1.80 power dependence.
3-4
Power spectrum of IR beam after THz generation in cLN for various
conversion efficiencies at room temperature.
3-5
46
. . . . . . . . . . . . . .
46
IR-to-THz conversion efficiency enhancement as a function of temperature at constant 1.2 mJ pump energy.
10
. . . . . . . . . . . . . . . .
47
3-6
(a) Electric field of THz pulse as a function of time obtained by EO
sampling. (b) Power spectrum of THz pulse.
3-7
. . . . . . . . . . . . .
THz beam profile at the focus of an off axis parabola (EFL = 5 cm).
11
48
48
12
List of Tables
1.1
Properties and figure-of-merit of several candidate materials for THz
generation. ng(w) is given at 1.55 pum and n(Q) is given at 1 THz.
Data adapted from [2].
2.1
. . . . . . . . . . . . . . . . . . . . . . . . .
Free parameters and constraints for design of the tilted pulse front
pum ping setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
25
34
Parameters for design of AR coating optimized for 0.5 THz based on
several candidate materials, along with computed and experimental
results. n, refractive index at 0.5 THz; a, absorption coefficient at 0.5
THz; t, optimal thickness; R computed reflection at 0.5 THz;
To"t,
computed transmission divided by transmission without coating (efficiency enhancement);
Teopnenta,
experimental transmission divided
by transmission without coating (efficiency enhancement).
13
. . . . . .
38
14
Introduction
The recent generation of few-cycle, high peak electric field terahertz (THz) has led
to a variety of scientific applications. For example, in materials science, intense THz
pulses have enabled the study of the orientation and alignment of hydrogen bromide
molecules [3], nonlinear responses in carbon nanotubes [4], non perturbative interband
responses in indium antimonide (InSb) [5], electron-hole recollisions in semiconductor
quantum wells [6], and ultrafast carrier dynamics in GaAs [7]. In medicine, high energy THz pulses have been used for 3-dimensional (3D) imaging of a gelatin-soluble
medicine capsule by computed tomography [8], employed for label-free probing of
genes [9], and most recently, exploited to induce various DNA repair mechanisms
on human skin tissue [10].
In strong-field physics, intense THz pulses have been
investigated numerically for enhancement of high harmonic generation [11, 12] and
proposed for the manipulation of charged particles. Additionally, due to their relative
long wavelength THz pulses can accommodate large electron bunches and therefore
have been proposed for electron acceleration [13, 14], undulation [15], and bunch
compression [13, 15]. In light of the above applications, there is considerable interest
in developing highly efficient, scalable, relatively accessible, and compact THz pulse
generation schemes. Note that throughout this work, optical to THz conversion efficiency, or simply conversion efficiency, corresponds to the percentage of impinging
pump energy converted to detectable THz energy.
A conventional technique of generating short THz pulses is by exciting a biased
photoconductive switch with a femtosecond laser pulse. While this method enables
optical-to-THz efficiencies of up to 0.5% [16], it is not scalable to large pulse energies
due to saturation of the THz electric field amplitude [17].
15
Another technique of
broadband THz generation is by frequency mixing an ultrafast pulses fundamental
and second harmonic field in a gas, breaking symmetry of the AC field and generating
a directional electron current with simultaneous emission of THz radiation. THz
pulse energies of up 5 pJ have been reported by using this method [18]. High power
THz can also be generated in a free electron laser (FEL). In an FEL, relativistic
electron bunches are passed through an undulator which 'wiggles' them to produce
coherent emission via synchrotron radiation. THz pulses with pulse energies of 0.1
gJ at frequencies ranging from 0.05 to 5 THz with a repetition rate of 75 MHz
are reported by the Jefferson Lab FEL facility [19].
However, the requirement of
specialized facilities limits the accessibility of such approaches.
Another common technique for ultrashort THz pulse generation is by difference
frequency generation (DFG) in a nonlinear crystal. DFG has been demonstrated to
produce tunable THz pulses with peak electric fields of up to 108 MV/cm [20], but
the generated THz frequencies were limited to the >10 THz range.
On the other hand, optical rectification (OR) is a process where a series of DFG
processes occur between components of the same pulse. In this case, each JR photon
at angular frequency w, generates a THz photon at Q and another IR photon at w - Q
via DFG. Subsequently, the JR photon at w - Q, generates yet another THz photon at
Q and an IR photon at w - 2Q. This process of repeated down conversion continues
as long as phase matching is satisfied [21] and is known as cascading [22]. This can
potentially overcome the limit posed by DFG as an input JR photon can be completely
converted to several THz photons with >100% photon conversion efficiency. Zinc
telluride (ZnTe) and gallium phosphide (GaP) are some of the common materials
used to realize OR-based THz sources because phase matching can be achieved using
a collinear geometry for 800 nm and 1 pm, respectively. In [23], generation of 1.5
paJ THz pulses from a large-aperture ZnTe crystal was demonstrated. However, both
crystals exhibit large two-photon absorption of the IR due to their relatively small
band gap, which places an upper limit to the conversion efficiency. Organic crystals
can have very large nonlinearities, and THz generation efficiencies of up to 2.2%,
1.7%, and 0.8% have been demonstrated in DAST [24], OHi [25], and DSTMS [26],
16
respectively. However, the maximum THz energies achieved are limited to tens of pJ
due to the limited available aperture sizes of these crystals.
Lithium niobate (LN) is a good candidate for OR because it has low THz absorption, large bandgap, large damage threshold, and high nonlinearity
[2].
The
only drawback is that, since the THz index in LN is significantly mismatched to the
IR group index, alternative phase matching techniques are required. Quasi-phasematching by propagation through periodically poled (PP) material (e.g. PPLN) [21]
or by laser beam shaping [27, 28] has achieved efficiencies of up to 0.045%, but the
THz pulses produced are multiple cycle instead of single cycle, limiting the peak intensity. LN optical parametric oscillators (OPOs) can be used to generate THz pulses
[29], but the efficiency is still quite low (- 10-6).
The tilted-pulse-front-pumping (TPFP) technique, proposed by Hebling et al.
[30], is the predominant method of phase matching OR in LN. To date, it has been
reported that the highest THz pulse energy of 125 pJ at a conversion efficiency of
0.24% [1] was achieved using TPFP with a pump pulse duration of 1.3 ps in stoichiometric LN (sLN) at room temperature.
Recent simulations of OR in LN by TPFP [31] have shown that the conversion
efficiency can be further increased by optimizing the pump pulse duration and cryogenically cooling the LN crystal. These simulations show that a transform-limited
pulse duration of -500 fs is optimum because it maximizes the effective nonlinear
interaction length in the near-infrared. Furthermore, the simulations reveal that the
efficiency can be increased by up to a factor of 10 by cryogenic cooling because of
reduced THz absorption at lower temperatures [32, 33].
In our work, using near optimal pump pulse widths of 680 fs centered at 1030 nm,
1.15% of THz generation efficiency at room temperature and 3.7% in cryogenically
cooled cLN were demonstrated using OR in the TPFP scheme. In addition, we report
record THz generation efficiencies of 1.70% at room temperature using sLN. Results
characterizing the spatial and temporal nature of the THz radiation are also presented
which show good agreement with 1-D theoretical calculations. In Chapter 1, we lay
out a theoretical picture of THz generation by optical rectification. In Chapter 2,
17
we present several methods by which to optimize the THz generation efficiency. In
Chapter 3, we describe our experimental setup and present our results.
18
Chapter 1
THz Generation by Optical
Rectification
In this chapter, a basic theoretical description of the process of THz generation by
optical rectification is presented.
We will focus on providing a physical picture of
process as it occurs in our experiment described in Chapter 3, and therefore will focus
on the tilted-pulse-front (TFP) phase-matching geometry that was used. Other phasematching geometries for THz generation by optical rectification including Cherenkov,
Echelon, and periodically poled crystals are not within the scope of this thesis. Note
also that in this geometry the incident infrared and generated THz are polarized in
the same direction, so the following equations will be scalar.
1.1
Intrapulse difference frequency generation
Optical rectification is very similar to difference frequency generation (DFG). In DFG,
a single photon at a IR frequency w mixes with a photon at a lower IR frequency
w - Q to generate a photon at the difference frequency of Q, which lies in the THz
spectral range, and another photon at w - Q for energy conservation. Figure 1-1(a)
depicts an energy level diagram of this process. Assuming the initial infrared power
is predominantly at w, the maximum power efficiency achievable by DFG is Q/w, the
case in which 100% of the photons at w are converted to Q (100% photon efficiency).
19
b.
a.
W
W
A0
l
C.
E
E
A0
few THz
f
Figure 1-1: (a) Energy level diagram of difference frequency generation. (b) Spectral diagram of intrapulse difference frequency generation (optical rectification). (c)
Optical rectification of a broadband IR pulse yields a THz pulse with a spectrum
spanning the few THz regime.
This value is typically < 1% for THz frequencies.
Optical rectification can be seen as an intrapulse DFG process, where the DFG
occurs between different frequency components of the same broadband pulse. Figure
1-1(b)-(c) illustrates this process in the frequency domain. The high frequency rolloff of the generated spectrum is determined by the bandwidth of the pump IR pulse,
and the low frequency roll-off is due to the dipole antenna radiation effect (E oc Q).
The key difference in optical rectification is that a single IR photon at W can be
downconverted more than once (e.g. w
-4
w-Q -+ w -2Q
-+ ... ) to generate multiple
THz photons. This repeated downconversion phenomenon is called cascading and is
made possible because the frequency difference between the IR photons is so small
that phase-matching is satisfied for multiple cascading cycles. Figure 1-2(a) depicts
an energy level diagram of cascaded optical rectification, and Figure 1-2(b)-(f) depicts
a spectral diagram of the process. A readily observable indication of cascading is an
output IR pulse spectrum that is significantly redshifted and broadened (Figure 1-
2(f)). Photon efficiencies of > 100% are routinely observed in highly cascaded THz
generation experiments.
20
a.
w - 20
W-0
-30
w-2
w
IT
()
e.
b.
E
E
0
few THz
A0
O few THz
f
0
f
f.
C.
E
E
E
T
0 few THz
A0O
f
A0
few THz
d.
E
E
o few THzf
Figure 1-2: (a) Energy level diagram of cascading. An IR photon at w generates a THz
photon at Q plus a downshifted IR photon at w - Q. The downshifted JR photon can
be recycled to generate another THz photon at Q plus a further downshifted photon
at w - 2Q. this process is repeated as long as the IR and THz frequencies are phasematched. (b)-(f) Spectral picture of cascading. (b) Two frequency components in the
broadband JR spectrum generate a difference frequency that lies in the THz regime.
(c) The higher frequency component is downshifted. (d) The downshifted frequency
component mixes with an even lower frequency component to generate another THz
component. (e) The higher frequency JR component is downshifted once more. (f)
In the end, the output IR spectrum is redshifted and broadened.
21
1.2
Mathematical description of broadband optical rectification
1.2.1
Undepleted pump derivation
For a THz pulse centered at frequency Q, the one-dimensional frequency domain wave
equation in an arbitrary medium can be deduced from Maxwell's equations as
&2 E(Q z)
__2
+ k 2 (Q)E(Q, z)
a2
where k(Q) =
2n(Q)
=
2 PNL(QZ)
(1. 1)
is the wavenumber inside the medium. PNL is the nonlinear
polarization given by
PNL(Q,
PNLZ)
= COX(2)
Okff }A(w
fjsk
+ Q)A*(w)eijAkzdw
(1.2)
where X (2) is the 2nd order nonlinear coefficient, A(w) is the complex amplitude
of the IR electric field in the frequency domain, and Ak is the phase mismatch.
Equation 1.2 basically states that the driving nonlinear polarization is an aggregate
of all possible DFG processes between any two components A(w
+ Q) and A(w) of
the broadband IR pulse.
The equation governing the evolution of the THz field A(Q, z) can be obtained
from the Maxwell's equations under the slowly varying envelope approximation as
OA(Q, z) =
0Z
-
a(Q)A(Q, z) - JpOQc
OPNL (Qz)
2n(Q)
2
1
(1.3)
The first term on the right hand side of Equation 1.6 corresponds to the loss
from the linear material absorption coefficient oz(Q). The second term corresponds to
the gain from the nonlinear polarization. A good starting point for determining the
efficiency trends is to solve this equation for the case of an infinite plane wave, perfect
phase match, and negligible pump depletion. The efficiency in this case is equal to
[2]
22
r/ =
Here,
deff
2Q 2 d 2fL2
exp
eong(w) n(Q)c 3 e
f2
-- a()L
2
sinh2 [a(Q)L/4]
[a(Q)L/4]2 .
(1.4)
is the effective nonlinear coefficient, L is the length of the nonlinear
interaction, ng(w) is the group index of the IR, and I is the intensity of the pump
beam. One can observe that there is a sweet spot for the interaction length L that
maximizes the efficiency. This occurs near the point where
()
= 1. In this case
the efficiency can be written as
8Q 2 d2 I
f
.(1.5)
r oc con(2
()n(Q)C3a(Q)29on
From this equation, we see that the efficiency of optical rectification is, in general, proportional to the intensity of the pump pulse I, the square of the nonlinear
coefficient deff, the square of the THz frequency Q, the inverse square of the THz
absorption coefficient a(Q), the inverse square of the IR group index ng(w), and the
inverse of the THz index n(Q).
This relation is useful in the determination of a
suitable nonlinear material, to be discussed in Section 1.2.3.
1.2.2
Cascaded optical rectification (depleted pump)
The derivation for efficiency in Section 1.2.1 assumed that the pump pulse is unchanged (non-depleted pump approximation). As described in Section 1.1, cascading
involves the depletion of higher IR frequency components in the pump pulse and creation of downshifted frequency components. Thus, to include the effects of cascading,
the evolution of the pump pulse must be incorporated mathematically.
The evolution of both the THz field A(Q, z) and the IR field A(w, z/ cos 'y) can
be written as a system of equations, using again the slowly varying envelope approximation. (Note that the change of coordinate in the JR field (z -z/
cos y) is due to
a noncollinear geometry which will be described in the upcoming Section 1.3.1.)
23
A(Q,z)
a()A(
2
-Z
&A(w,z/ cosy)
)-
1
a-(w)A(w, z/cos)
=z/cos-y
jpuowc o
_
(1.6)
2 Cos YPNL(WZ)
2n(w)
(1-7)
+ Q, z/ cos y)A*(w, z/cosl)ejkzdw
(1.8)
-
a2/ Cos Y
oQCPNL(QZ)
2n(Q)
-
2
The nonlinear polarizations are given as
PNL(Q,Z) =
coX0
PNL (W, Z = C(
f
A(
A(w ± Q, z/ cos -y)A*(Q, z)ejAkzdQ
(1.9)
One can write a simulation to solve this first order system of integro-differential
equation to obtain a variety of results. In the remainder of this thesis, all simulations
will be performed by the code of Ravi [34] unless otherwise noted.
1.2.3
Choice of nonlinear material: lithium niobate
From Equation 1.5, one can derive a figure-of-merit (FOM) parameter for a given
crystal's ability to generate THz efficiently. Keeping only material parameters in
Equation 1.5, we obtain a FOM equal to
FOM =
4d 2
e
n(W)2n(Q)a(Q)2
(1.10)
Table 1.1 gives the properties and FOM for several candidate nonlinear materials
for THz generation. The best two materials are DAST 1 and stoichiometric lithium
niobate (sLiNbO 3 , or sLN). DAST is a rare and expensive organic material that has
limited aperture sizes due to fabrication difficulties, whereas lithium niobate is a
common material used in the telecommunications industry and can readily be grown
to large apertures. Furthermore, lithium niobate has a large bandgap and high optical
damage threshold, reducing two-photon absorption effects and making it scalable to
14-N,N-dimethylamino-4'-N'-methyl stilbazolium tosylate, an organic salt nonlinear crystal
24
Material
ZnTe
CdTe
GaAs
DAST
sLiNbO 3 293 K
sLiNbO 3 100 K
deff (pm/V)
68.5
81.8
65.6
615
168
-
a(Q) (cm- 1 )
ng(w)
1.3
4.8
0.5
50
17
4.8
2.81
2.81
3.56
2.25
2.18
-
n(Q)
3.17
3.24
3.59
2.58
4.96
-
FOM (pm 2 cm 2 V- 2 )
7.27
11.0
4.21
41.5
18.2
48.6
Table 1.1: Properties and figure-of-merit of several candidate materials for THz generation. ng(w) is given at 1.55 um and n(Q) is given at 1 THz. Data adapted from
[2].
high intensity pumping. Because of these benefits, lithium niobate is our material of
choice for THz generation by optical rectification.
1.3
Noncollinear phase matching
A key challenge to producing high nonlinear conversion is phase matching. In lithium
niobate, phase matching is an especially critical problem because the pump and THz
velocities are severly mismatched. This section discusses the use of a clever phase
matching technique called tilted pulse front pumping (TPFP) to solve this problem.
1.3.1
Tilted pulse front pumping (TPFP)
The driving nonlinear polarization is largest when the phase mismatch Ak is minimized. We can write Ak as
Ak(Q) = k(Q) + k(w) - k(w + Q)
dk
dwwo
=
- ng(wo)
-[n(Q)
C
(1.11)
Here, the approximation is made under the assumption that Q < wo, where wo is
the center frequency of the IR pulse. Equation 1.11 states that the phase mismatch
25
is proportional to the difference between the phase index of THz and group index of
IR. In lithium niobate however, the difference between these two parameters is large,
causing prohibitively short coherence length.
For example, for 0.5 THz radiation
generated by a pump pulse centered at 1030 nm, n(Q) = 4.95 and ng(wo) = 2.25,
leading to a coherence length of Lc0h
=
7r/Ak = 0.7 mm.
To minimize the phase mismatch, a noncollinear phase-matching geometry must
be employed.
One remarkably effective noncollinear geometry is the tilted pulse
front pumping (TPFP) geometry, shown in Figure 1-3(a). In TPFP, an incident IR
beam propagating in the z'-direction has a pulsefront that is tilted with respect to its
propagation direction by an angle of -y, given by
cos y =
ng (wo)
n(Q)
(1.12)
The generated THz propagates in the z-direction, normal to the tilted pulse front.
The coordinate transform between the z'- and z-direction is
(1.13)
z' = z/ cos Y
A physical explanation of this is that the IR pulse propagation distance is 1/ cos -y
larger than the THz propagation distance. With this modification, the phase mismatch becomes
Ak
c
[n(1) -
Cosy _Y
0
(1.14)
or in other words, the process is phase matched. A physical explanation of this
scheme is that the velocity of the pump projected in the direction of its pulse front is
matched to the velocity of the THz wave.
1.3.2
Angular dispersion picture of TPFP
A tilted pulse front is created by inducing angular dispersion into the JR beam.
Hebling [30] showed that the pulse front tilt angle -y induced by an angular dispersion
26
a.
b.
polarization
polarization
ZZ
----k(
z'--
z) '
Bulk Lithium Niobate
Bulk Lithium NIobate
Figure 1-3: (a) Tilted pulse front pumping scheme. (b) Angular dispersion picture of
phase-matching.
d
is given by
tan -y=n(w) A dO
?lg(w) dA
(1.15)
Equation 1.15 infers that a pulse front tilt is synonymous with angular dispersion,
which begs for an alternative picture of the TPFP phase-matching scheme based
on angular dispersion.
Figure 1-3(b) shows the wavevectors k(wo), k(wo + Q) of
two incident JR frequency components and the wavevector k(Q) of the generated
THz. The two IR wavevectors are angularly separated by an angle of
0Q ([
is the
angular dispersion), and the THz wavevector k(Q) is angularly separated from the IR
wavevector wo by the pulse front tilt -y. It can be intuitively seen by vector addition
that Ak(Q) = k(Q) + k(wo) - k(wo
+ Q) is zero. Hence, the angular dispersion picture
of phase-matching is consistent with the tilted pulse front picture given in Section
1.3.1.
1.3.3
Phase-matching is limited by dispersive effects
There are two factors that limit the interaction length of the phase-matching: material
dispersion and angular dispersion. Both have the effect of causing the IR pulse to
accumulate chirp as it propagates. For THz generation in lithium niobate, the chirp
caused by angular dispersion is the predominant limitation of interaction length,
because the angular dispersion must be significantly large in order to meet the phase
matching condition.
27
a.
/
b.
/
C.
/
It
kff
-v
Figure 1-4: Phasor diagram of intrapulse difference frequency generation with chirp.
The red arrows denote the integrand of Equation 1.2 and the blue arrow denotes
the total integral of Equation 1.2, or the sum of the red arrows, in the case of (a)
zero chirp (perfect phase match), (b) moderate chirp, (c) severe chirp (perfect phase
mismatch).
We recall the expression for the nonlinear polarization from Equation 1.2:
PNL(, Z) =
OX ( fj
A(w + Q)A*(w)ejAkzdw
In the case of perfect phase match Ak = 0, the integrand in Equation 1.2 can be
rewritten as
JA(w + Q) jA*(w) ej[k(wQ)-k(w)]z =
IA(w + Q)
|A*(w)je
= JA(w + Q)I A*(w)le
diw+(w±Q)-Idw(w)]z
d
= JA(w + Q) IA*(w)lejAkc(wQ)z
+
+
(1.16)
where Akc(w, Q) is the phase mismatch between the two IR components w + Q
and w due to chirp:
d2k Q 2 + d k3
+-dw3 W
(1.17)
A physical picture of the effect of dispersion on the THz generation efficiency can
be seen in the phasor diagram of Figure 1-4. The red phasors represent the normalized
integrand (Equation 1.16) at various frequencies w within the integral, and the blue
28
phasor represents the sum of the red phasors, or the nonlinear polarization (Equation
1.2).
Figure 1-4(a) shows the phasor diagram without any dispersive effects. The
red phasors are lined up leading to a long blue phasor (large nonlinear polarization).
On the contrary, Figure 1-4(b) shows the phasor diagram in the event of dispersive
effects. The red phasors are misaligned because there is a frequency dependent phase
Akc(w, Q). As a result, the blue phasor is shortened and the nonlinear polarization
is reduced. As the propagation distance z increases, the frequency dependent phase
mismatch is accentuated, causing the angle between the red arrows to increase. At
some length LD, the blue arrow will go to zero as shown in Figure 1-4(c). For pulses
dominated by second order dispersion, LD C
-2
, where r is the transform-limited
pump pulse duration. This is the physical picture of the limitation in coherence length
caused by dispersive effects.
29
30
Chapter 2
Optimization of THz Generation
Efficiency
In strong field applications such as electron acceleration, high THz energy pulses
(millijoule-scale) are needed. One way to accomplish this is to pump with higher
energy lasers, which would require scaling of size and cost.
A more elegant and
economical way is to investigate methods to optimize the efficiency of the THz generation process. In Chapter 1, we gave a theoretical framework of optical rectification.
In this chapter, we will utilize this knowledge to explore several techniques for efficiency optimization. These will include (1)
optimization of the pulse front tilting
setup, (2) optimization of the pump pulse parameters, (3) cryogenic cooling of the
lithium niobate crystal, and (4) implementation of a THz antireflection coating for
the lithium-niobate-to-air interface.
2.1
2.1.1
Tilted pulse front pumping setup
Pulse front tilt is induced by diffraction from grating
To experimentally realize a pulse front tilt with angle -y, the IR beam must have
angular dispersion. In [30], Hebling derived the relation between pulse front tilt y
and angular dispersion
to be
31
I
si
s2
THz
630Y
l~~ens, fn,
0
g
46
Figure 2-1: Schematic of pulse front tilting imaging setup. PFT, pulse front tilt; Oi,
incidence angle; Od, diffraction angle; f, focal length; n, refractive index; ng, group
index; AiA 2 ,A3 illustrate angular dispersion induced by grating.
n
tany = -A
?lg
An angular dispersion !
dO
dA
(2.1)
in the pump beam can be realized by mth-order diffrac-
tion from a grating with groove density g. Using the grating equation sin 0% + sin 0 d =
mgA, we derive the angular dispersion to be
d~d
d
dA
mg
-
co
COS Od
(2.2)
Putting Equations 2.1 and 2.2 together, we arrive at the expression for the pulse
front tilt in from a grating
tan 7 =
2.1.2
nAmg
.
cos Od(23
(2.3)
Relay-imaging of grating
The diffracted beam experiences undesired chirp and spatial walkoff as it moves away
from the grating. Even if the THz generation crystal were placed directly behind the
grating at some small distance, the beam would have already experienced significant
group velocity mismatch, leading to poor conversion efficiency. Ideally, the crystal
would be superimposed at the location of the impinged beam on the grating; however,
this is physically impossible. One solution is to image relay the beam diffracted from
32
the grating onto the crystal, placed some distance away, such that the beam on the
crystal is an image of the diffracted beam from the grating. A single-lens image relay
scheme is shown in Figure 2-1.
Proper imaging of the grating requires that the tilted pulse front coincide with the
image of the grating, or in other words, that the angle of the grating image 0 must
match the angle of the pulse front tilt -y.
If these two angles are mismatched, only
the center (the point intersecting the optical axis) of the pulse front will be properly
imaged and generate THz efficiently. Points in the pulse front away from the center
will be offset from the image plane and become 'blurry'. From the phase matching
point of view, points that are not on the image plane will have group delay mismatch
leading to poor conversion efficiency. A more detailed analysis of these effects can be
found in [35].
To derive the angle of the grating image, we first observe in Figure 2-1 that the
angle of the grating object is
Od.
The grating image has the shape of the original
grating scaled transversely by magnification factor Mt (from the imaging setup) and
by index n (from refraction into the crystal). Consequently, the angle of the grating
image 0 inside the crystal is
tan 0 = nMt tan Od.
(2.4)
To derive the angle of the pulse front inside the crystal, we begin with the expression for pulse front tilt angle before image relay given by Equation 2.1. A smaller
transverse magnification factor causes a larger angular dispersion, and refraction into
a crystal reduces the angular dispersion. Therefore, Equation 2.1 should be inversely
scaled by Mt and n. The expression for pulse front tilt inside the crystal becomes
tan y =
Ao
(2.5)
ng Mt COS Od
Note that we have now set the diffraction order m to 1 since a majority of commercial gratings are designed for this order.
33
Free parameters
g, groove density
Mt, transverse magnification
Od, diffraction angle
Constraints
-/ = 0 = 63'
Od should be close to littrow angle sinolitt = 2-
Table 2.1: Free parameters and constraints for design of the tilted pulse front pumping
setup.
2.1.3
Design of a TPFP setup
We are now presented with a design problem. In order to image properly, we must
match 9 and 'y. Furthermore, in order to achieve phase matching, we must set y =
cos 1
ng(wo)
=
cos-
1
2-
630, as discussed in Section 1.3.1.
(2.6)
-y = 9 = 63'.
A final constraint is that the diffraction angle
Od
should be close to the Littrow
angle 0litt = sin-' 2A in order to maintain high diffraction efficiency from the grating:
d ~
(2.7)
1itt.
To achieve these objectives, we have control over three free variables: grating
groove density g, transverse magnification Mt, and diffraction angle
Od.
Table 2.1
summarizes the free parameters and constraints. One approach to this design problem is to first decide on a groove density g and then back-calculate Mt and
Od.
Ma-
nipulating Equations 2.5 and 2.4 and setting tan -y = tan 9 gives
9=
2g cos 6dtan '
.gCSOda
nA tand(
(2.8)
Since incidence angle is experimentally easier to measure, we can apply sin O =
gA - sin d to convert from diffraction angle to incidence angle. Figure 2-2 shows a
plot of the required incidence angle as a function of groove density based on Equation
2.8. It is seen that a groove density of 1500 1/mm is near optimal because its required
incidence angle closely matches the Littrow angle. Having fixed a groove density g, the
incidence angle and transverse magnification can be back-calculated from Equations
34
incidence angle required for 63* PFT
80
----
littrowangle
8)
S60
8 40
- -
-
-
Groove density: 1500 I/mm
incidence angle: 46*
Magnification: 0.6218
-
U20
.E 2
100
1100
1200
1400
1500
1300
groove density (1/mm)
1600
1700
Figure 2-2: Plot of required incidence angle as a function of groove density for optimal
phase matching. A groove density of 1500 1/mm is chosen because it has a required
incidence angle close to the Littrow angle.
2.5 and 2.4 to be 460 and 0.6218, respectively.
Finally, a transverse magnification Mt is realized physically by setting the object
and image distances, s, and S2, such that
A
=-2
(2.9)
Si
where S2 and si are subject to the lensmaker equation - +
=
It is beneficial
to use long focal lengths (f > 200 mm) in order to reduce imaging aberrations.
2.2
Optimization of pump pulse
The pump pulse that impinges onto the crystal can be characterized spatially and
temporally. A full investigation of the spatial properties optimal for THz generation
is out of the scope of this thesis. However, because the theoretical analysis in Section
1.2.1 assumed plane waves, spatial properties are of secondary importance so long as
the pump pulse is of large enough spatial extent and good enough beam quality that
the plane wave approximation can be applied.
The dependence of the THz generation efficiency as a function of temporal properties is of greater interest.
In Section 1.1, optical rectification was treated as an
intrapulse DFG process in the frequency domain.
35
Thus, the optimization of the
1Too
short
Tolow intensity
dispersion length
-- J- 300 K
-0-- 100 K
610 K
10 --
0
0
0
0.69 ps
3.7% MIT cLN 77K
1.7% MIT sLN 300K
0'-22%
0.0
1.0 J. Fulop sLN
0.5
pump pulse duration [ps]
1.5
Figure 2-3: Simulation of the THz generation efficiency as a function of pump pulse
duration and temperature. The plot shows that the optimal efficiency is achieved at
a pump pulse duration of around 0.5 ps and at cryogenic temperatures. Annotations
show the results achieved by us (MIT) and by Fulop [1]. Simulation adapted from
[1].
pump pulse should be treated in the frequency domain as well. The pump pulse can
be characterized by two parameters: bandwidth and chirp. We know intuitively from
phasor diagrams in Figure 1-4 that the optimal chirp condition is to have no chirp at
all, or in other words, to have a transform-limited (TL) pulse.
We proceed to determination of the optimal pump bandwidth. Having fixed the
chirp condition to transform-limited pulses, we can directly correlate the pump bandwidth to its time-domain pulse duration (assuming a Gaussian profile). Figure 2-3
shows a simulation of the THz generation efficiency as a function of transform-limited
pump pulse duration at full-width-half-maximum (FWHM). It is seen that there exists a maximum at around 500 fs. The reason for having a sweet spot in the pump
pulse duration (assumed to be transform-limited from here on) can be seen by looking at the two extremes. When the pulse duration is short, its bandwidth is large,
36
W
I
iF
40
a ~4
c20
T= 10K
.0
-SLN(68%)
*
CLN(61%)
S10
= 300 K
0T
-SLN(048%)
a w 20
CLN(&.%)
Frequency (Cfff)
1 THz
Figure 2-4: THz absorption coefficient a(Q) as a function of temperature and frequency.
causing dispersive effects to dominate. This in turn reduces the interaction length of
the nonlinear process which ultimately limits the conversion efficiency. On the other
hand, when the pulse duration is long, its intensity is low, reducing the nonlinear yield
(see Equation 1.4). It turns out that a transform-limited pump pulse with duration
around 0.5 ps balances the trade-off between these two effects. Therefore, the optimal
pump is a transform-limited pulse with pulse duration of 0.5 ps.
2.3
Cryogenic cooling of lithium niobate crystal
A major obstacle of THz generation in lithium niobate is the large absorption coefficient of room-temperature lithium niobate. The absorption can be dramatically
reduced at cryogenic temperatures. Figure 2-4 shows that the absorption coefficient
at 1 THz in lithium niobate drops dramatically from -20 cmto ~4 cm-
1
1
at room temperature
at cryogenic temperatures. Based on the figure of merit described in 1.10
and the simulation in Figure 2-3, the THz generation efficiency can be increased by
a factor of 3 through cooling to 100 K.
37
a (cm- 1 ) t (pm)
R
'xperiment
Coating
Source
n
None
Ideal
-
-
2.23
0
67.4
0.44
0
1
1.79
1
-
Z-cut quartz
Fused silica
Kapton
Parylene
[36]
[36]
[37]
[38]
2.21
1.95
1.86
1.62
0.03
0.3
10
11
67.87
76.84
80.65
92.59
0.0011
0.017
0.032
0.095
1.78
1.76
1.729
1.62
1.5
1.3
1.3
1.2
omputed
TO
TO
Table 2.2: Parameters for design of AR coating optimized for 0.5 THz based on several candidate materials, along with computed and experimental results. n, refractive
index at 0.5 THz; a, absorption coefficient at 0.5 THz; t, optimal thickness; R compute refectin at0.5
~z;Teompu±ed
To ", computed transmission divided by transmission
at 0.5 THz;
puted reflection
without coating (efficiency enhancement);
Texperi"enta,
experimental transmission di-
vided by transmission without coating (efficiency enhancement).
2.4
THz antireflection coating
The large THz index mismatch between lithium niobate and air causes a 44% loss of
efficiency due to Fresnel reflection. This problem can be solved by using an antireflection (AR) coating optimized for THz. While, AR coatings for optical wavelengths
have well-established materials and fabrication processes, AR coatings for THz wavelengths are still in their infant stages. In this section, we present our investigation of
several candidate THz AR coatings for lithium niobate.
The optimal thickness for an AR coating is
, where nAR is the index of the
A
coating material. Under this condition the normal incidence reflection coefficient is
(from [39])
2
R =
2
n ~nR
-""I
non1 + nA
Equation 2.10 goes to zero when nAR
=
rHoni.
(2.10)
For the lithium-niobate-to-air in-
terface (where ni = 4.96 and no = 1), the optimal AR coating index is
/4.96 = 2.23.
Table 2.2 shows the parameters and for several candidate THz AR coating materials. The efficiency enhancement was computed and experimentally tested for each
material with our broadband THz source (Section 3.2). Z-cut crystal quartz showed
the best performance with an efficiency enhancement of 1.5, compared to a computed
enhancement of 1.78. The discrepancy is mainly due to the broad bandwidth of the
38
U.
2-
-
-
-25
-z-cut
.25---fused
-
-30
-35
0
0.2
coating
ideal coating
-no
-
0.4
0.6
Frequency (THz)
crystal quartz
silica
kapton
parylene
0.8
Figure 2-5: Calculated power reflection coefficient of the lithium niobate to air interface for various THz antireflection coatings.
THz covering regions away from the design frequency. Since this AR coating is single
layer, the reflection increases quickly at frequencies away from the design frequency.
This is shown in the power reflection spectra in Figure 2-5.
39
40
Chapter 3
Experimental Demonstration of
Efficient THz Generation
In this chapter, we discuss in detail the experiment leading to THz generation with
a record 3.7% conversion efficiency.
3.1
Experimental setup
The experimental setup consists of a sub-ps pump source and a THz generation
component, as depicted as Figure 1. The pump source is a Yb:KYW chirped pulse
regenerative amplifier (RGA) producing 2 mJ pulses with 1 kHz repetition rate at
a center wavelength of 1030 nm and bandwidth of 2.6 nm. The dielectric grating
compressor following the RGA compresses the pulses to 680 fs, which is -15% longer
than the transform-limited pulse duration assuming a Gaussian profile. The seed for
the RGA was a mode-locked Yb-doped fiber oscillator emitting 70 fs, 0.2 nJ pulses at
80 MHz [40] amplified to 1.6 nJ by a Yb-doped fiber amplifier. After losses through
the optical elements in the setup, the impinging pump energy into the LN crystal was
1.2 mJ.
The TPFP scheme was achieved using a grating and a lens for image relay. as
shown in Figure 3-1. The laser beam is incident at 46 degrees to the normal of a 1500
line/mm gold grating and is then imaged onto the LN crystal by a single 230 mm
41
Grating
HWP
Yb dop.
fiber osc.
.- '.a
Compressor
f
U
L1
BS
HWP
dwrL2
Regen.
amplifier
-Fiber
stretcher
cl-N
QWP
Grating
Photodiode
PB
L3
stretcher
ZnTe
HR
YDFA
Boxcar
integrator
Oscilloscope
Figure 3-1: Schematic of experiment. BS, 50:50 beam splitter; YDFA, Yb-doped
fiber amplifier; HWP, half-wave plate; L1, bestform lens with f = 20 cm; L2, concave
cylindrical lens with f = 15 cm; HR, dielectric high reflector mirror; L3, plano-convex
lens with f = 23 cm; PBS, polarizing beam splitter.
bestform lens (Li). The grating-to-lens distance was 584 mm and the lens-to-crystal
distance was 379 mm, implying a demagnification of 1.54. A half-wave plate was
used to rotate the polarization of the pump to be parallel to the optic axis of the
crystal. A cylindrical lens was used to reshape the 1/e
2
pump diameter to 3.0 mm
in the horizontal and 3.0 mm in the vertical directions, which corresponds to a pump
fluence of 17 mJ/cm2
The LN crystals have been doped with MgO at 6.0% in cLN and 1% in sLN
to reduce photorefractive losses [41]. The crystals were z-cut and shaped into an
isosceles prism with a vertex angle of 56 degrees and base angles of 62 degrees to
minimize the Fresnel reflection loss at the uncoated THz output face (perpendicular
to propagation direction). This geometry is necessary to circumvent the small THz
critical angle of ~11 degrees due to large THz refractive index in LN. The infrared (IR)
beam experiences total internal reflection at the THz output face and is transmitted
through the adjacent surface. The entry and exit surfaces for the IR beam are anti42
reflection (AR) coated for 1030 nm.
The predominant motivation for cryogenic cooling is to result in high conversion
efficiencies which can then be exploited to scale to large THz energies by scaling the
pump energy. Since it is relatively difficult to grow sLN to large dimensions beyond 1
cm, we opted to use cryo-cooled cLN despite its relatively higher absorption [33] and
lower effective second order nonlinear coefficient deff [42]. The crystal was indium
soldered to a nickel heat sink whose thermal expansion is well-matched to that of
LN, the heat sink was screw-mounted to a commercial liquid nitrogen dewar, and a
silicon diode temperature monitor was adhered to the bottom face of the crystal by
thermally-conductive glue.
The THz power was measured by focusing the output onto a pyroelectric detector
(Microtech Instruments) by a single off-axis parabolic mirror with an effective focal
length of 25.4 mm. In order to match to the voltage relaxation time of the pyroelectric crystal, the repetition rate of the laser was reduced to 10 Hz. The THz pulse
energy was then calculated from the voltage modulation using the factory-calibrated
responsivity of 3.4 ± 0.4 V/mW.
The THz waveform was measured by means of a conventional electro-optic (EO)
sampling technique [43], shown in Figure 3-2. An 80 MHz, 70 fs IR pulse train from
the mode-locked fiber oscillator, which is the seed laser for the RGA (ensuring optical synchronization), were spatio-temporally overlapped with the THz pulses and
focused onto a 200 pm thick, 110-cut ZnTe crystal. The JR pulses sample the THz
field-induced birefringence as a function of delay, which is swept at a constant rate
(1.2 mm/sec) using a calibrated motorized translation stage. A quarter-wave plate
followed by a polarizer converts the field-induced birefringence to an intensity modulation, and the intensity modulation is recorded by a fast photodiode. Because of
the much higher repetition rate of the IR pulse train, a boxcar integrator (Stanford
Research SR250) is used to electronically gate out all other pulses except the one
whose intensity is modulated by the THz. The integrated signal is then recorded by
an oscilloscope.
Spatial characterization of the THz beam was performed using a microbolometer
43
177 mm
f/2.5
70 fs
IR
probe
110-cut ZnTe
200 pm
k
QWP
200 mm
200
I GHz APD
Dielectric
Mirror
(40% THz tx)
I GHz APD
180*1 RF power d
THz
5-1000 MHz
Ider
50 mm
f/1
Boxcar
integrator
unit
Output
DAC
Figure 3-2: Schematic of the EO sampling setup.
imaging camera (NEC IRVT0831) at 30 Hz with continuous averaging of 8 frames.
The camera has a pixel format of 320 x 240 and a spectral response that rolls off below
1 THz [44]. Thus the beam characteristic measured is heavily weighted towards the
high frequency components.
3.2
Results and discussion
Figure 3-3 depicts the THz energy as a function of the pump energy at room temperature for both sLN and cLN crystals. The THz energy increases with a power
dependence of 1.80 for cLN and 1.97 for sLN without any sign of roll-off from freecarrier absorption. The maximum THz energy achieved with the sLN crystal was
21.8 pJ at 1.28 mJ of pump energy, corresponding to an efficiency of 1.7%. Likewise, the maximum achieved THz energy in the cLN crystal was 13.7 pJ at 1.18 mJ
of pump energy, corresponding to an efficiency of 1.16%. The conversion efficiency
in sLN is greater than that in cLN by a factor of 1.47; this is expected with the
-20%
increase in deff (of sLN over cLN) [42] since the efficiency is proportional to
the square of deff The experimental results of efficiency show good agreement with
simulations based on the 1-D models described in [31] for the previously described
experimental parameters. A def f=168 pm/V and effective interaction length of 4 mm
was assumed. Since the precise dispersion in the frequency range of 0 to 0.9 THz was
44
not known, a constant absorption coefficient of 5 cm-
was assumed as an adjustable
parameter. After accounting for a THz reflection of ~44% at the air-crystal interface,
the calculated efficiency is 1.33% for cLN which closely matches the experimental result of 1.15%. Note that the use of adjustable parameters can be justified since the
THz waveform, spectrum and efficiency calculations, all triangulate with the same
parameters. Hence the 1-D model in [31] is of reasonable predictive value. To further
verify the high efficiency conversion, the spectrum of the IR beam after THz generation was measured as shown in Figure 3-4. The large red shift and broadening of the
IR spectrum is a consequence of the repeated frequency down-conversion of the IR
pulse leading to repeated THz generation. This 'cascading' has been suggested as the
reason for large conversion efficiencies [21, 45, 46]. A calculation of the center-of-mass
optical frequency shift of the IR spectrum at full efficiency divided by the THz center
frequency (0.45 THz) reveals roughly 5.5 cascading cycles, or 550% photon conversion
efficiency. To verify that the broadening and the red shift of the output IR spectrum
can indeed be explained by the concept of cascading, one can use an effective 1-D
system of coupled equations similar to [47, 48] which predict an extent of broadening
qualitatively consistent with experiments for similar parameters.
Further efficiency enhancement was achieved by cryogenically cooling the cLN
crystal. Figure 3-5 shows the efficiency enhancement as a function of temperature at a
fixed pump energy of 1.2 mJ. It is observed that the efficiency enhancement increases
monotonically from 300 K to about 150 K. It then peaks at 150 K and slightly
decreases as the temperature goes below 150 K. A maximum efficiency enhancement
of 3.2 was achieved at 140 K, corresponding to an estimated conversion efficiency of
3.7 ± 0.4%. The saturation of the efficiency below 150 K is suspected to be due to
thermally-induced refractive index changes causing phase mismatch as no realignment
of the pulse front tilt was performed in the middle of the temperature sweep. Other
potential reasons could be a change in the nonlinear properties at lower temperatures.
Temporal characterization of the THz pulse generated from sLN at room temperature was performed by EO sampling. The results for cLN are expected to be
qualitatively similar. Figure 3-6(a) depicts the measured single-cycle THz waveform
45
30
o
sLN
sLN fit
20
1.70% eff.
(sLN)
-110
7
5
e
1.160 %eff.
(cL N)
A
.
-/--
2
1
cLN
cLN fit
''
0.2
I I i I I I I I II
1 1.2
0.3 0.4 0.5 0.7
Pump energy (mJ)
Figure 3-3: Pump energy sweep of THz generated from room temperature sLN and
cLN. The sLN fit shows a 1.97 power dependence and the cLN fit shows a 1.80 power
dependence.
Before conversion
After conversion
(U
0
C,
WU
282
284
286 288 290 292
Optical frequency (THz)
294
296
Figure 3-4: Power spectrum of IR beam after THz generation in cLN for various
conversion efficiencies at room temperature.
46
.. 3.5
3.7% eff.
44 pJ THz
a 3.02.5 .
0
-4.0
3.5
-
2.00
0
i
-
1.0 50
Z.
2.5 a
2.0 ra) 1.5 -
3.0
Pump energy = 1.2 mJ
-1.5
,1.0
100
150
200
Temperature (K)
250
300
Figure 3-5: IR-to-THz conversion efficiency enhancement as a function of temperature
at constant 1.2 mJ pump energy.
with a cycle period of -2.2 ps. The theoretical calculation of the temporal electric
field waveform is overlaid with the experimental measurement in Figure 3-6(a) and
resembles the basic feature of the experimental result. The temporal waveform is
sensitive to the tilt angle of the pulse front, the input amplitude, as well as phase
spectrum of the IR pulse which can explain the discrepancy between theory and experiment. The corresponding experimental and calculated spectra are presented in
Figure 3-6(b). It is seen that the THz pulse has a center frequency of 0.45 THz and
a full-width-half-maximum (FWHM) bandwidth of 0.4 THz with a tail extending
beyond 1 THz, showing good match with the simulations based on the model in [31].
The echo pulse at -3.5 ps is a common artifact caused by multiple reflections of the
IR probe pulses off the EO crystal and can be disregarded. Due to the echo pulse, a
time window was applied prior to the Fourier transform; therefore, the typical absorption lines of water are not observed because of the limited frequency resolution. The
temporal shape of the THz pulses from cryogenic LN is expected to be similar to that
at room temperature except for a slightly shifted spectrum towards high frequency
due to reduced losses.
Figure 3-7 depicts the beam at the focus of an off-axis parabola with 50 mm of
effective focal length. The actual focused beam diameter is believed to be wider by
47
THz Spectrum
Temporal Electric Field Waveform
-Experiment
(a)
Experiment
--Theory
(b)
---Theory
6 0.8
0.6
0
/
\
0.4
0.2
-1
-4
-2
4
0
2
Time [ps]
0
0
6
0.5
1.5
1
Frequency [THz]
2
Figure 3-6: (a) Electric field of THz pulse as a function of time obtained by EO
sampling. (b) Power spectrum of THz pulse.
r_ 9I
E1
S2
(/3
04
>5
1
6
5
4
3
2
Horizontal distance [mm]
7
Figure 3-7: THz beam profile at the focus of an off axis parabola (EFL = 5 cm).
a factor of 2 or 3 considering the high-pass spectral response of the camera with a
cutoff at 1 THz and our pulse center frequency of 0.45 THz. Nevertheless, the focused
beam diameter of 1 mm shows a near diffraction-limited beam quality at the -1 THz
portion of our pulse.
48
2.5
Conclusion
In this thesis, we have laid a theoretical background for THz generation by optical rectification and presented several methods for optimization of the conversion efficiency,
culminating in an experimental demonstration. We experimentally demonstrated a
peak efficiency of 3.7% in cryogenic cLN and 1.7% in room temperature sLN using a
near-optimum pump pulse duration of 680 fs. Both efficiency results are several factors above the current state-of-the-art. The THz pulses were characterized temporally
by EO sampling and spatially by a microbolometer camera. Further enhancement of
the efficiency is possible by depositing an AR coating on the THz output surface [38]
and reducing imaging aberrations by a more optimized TPFP setup, such as the double lens or contact grating schemes [35]. Another possibility is the use of cryogenically
cooled sLN instead of cLN. Scaling the crystal size may be possible through diffusion
bonding several smaller pieces together, but the enhancement of sLN at cryogenic
temperature needs first to be investigated. Through these upgrades, optical to THz
conversion efficiency of 10% are potentially achievable enabling the production of
multi-millijoule THz pulses upon development of a 100 mJ pump source. Such a THz
source can be used to drive a compact next-generation linear accelerator and free
electron laser for various applications.
49
50
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