Tools for quantum optics: Pulsed
polarization-maintaining Er-doped fiber laser and
spatial mode manipulation in spontaneous parametric
downconversion
by
Dheera Venkatraman
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
at the Massachusetts Institute of Technology
May 2007
@ 2007 Massachusetts Institute of Technology
All rights reserved.
Signature of Author ......................... .... .......................
Department of Electrical Engineering and Computer Science
May 25, 2007
Certified by ..............
....................
Franco N. C. Wong
Thesis Supervisor
Accepted by................•
........•"
'••/
,
..
Arthur C. Smitlh
Professor of Electrical Engineering
Chairman, Department Committee on Graduate Theses
OFTECHNOLOGy
OCT 0 3 2007
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Tools for quantum optics: Pulsed
polarization-maintaining Er-doped fiber laser and
spatial mode manipulation in spontaneous parametric
downconversion
by
Dheera Venkatraman
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
May 2007
S
?co71j
ABSTRACT
Two separate projects were undertaken to improve technology for entangled photon sources,
useful for quantum optics. In one project, a pulsed, mode-locked erbium-doped fiber laser, designed to be used as a seed laser for a 390 nm source, was built using polarization-maintaining
components to address polarization drift. The fiber laser operated at a center wavelength of
1560.0 nm with an output power of 1 to 2.5 mW, and mode-locked with a repetition rate of
31.1 MHz. The laser also exhibited bandwidth tunability from 0.045 to 0.095 nm, as a function of the input pump power. A commercial 5 W erbium-doped fiber amplifier and a second
harmonic generation crystal were used to obtain pulses at 780 nm with an average power of
3 W. The next second harmonic generation stage, for generating the desired 390 nm output,
remains to be built. In the second project, we tried to optimize the coupling efficiency of
light generated from spontaneous parametric downconversion (SPDC) into single-mode optical fibers, which are useful for transporting entangled photons. Using a setup with a tunable
532 nm pump waist in a nonlinear crystal, we achieved an effective coupling efficiency of
48.8% of the 797 nm signal light into a single-mode fiber, higher than previously obtained in
the laboratory. Efficient single-mode operation of SPDC would enable the construction of a
high-flux fiber-coupled source of nondegenerate entangled photons at 797 nm and 1600 nm.
Thesis supervisor: Franco N. C. Wong
Title: Senior research scientist, Research Laboratory of Electronics at MIT
Contents
1 Introduction
1.1
Motivation .....................................
1.2
Organization
1.3
Basics of entangled states and their applications .
...................................
...............
2 Nonlinear Optics
2.1
Basic theory of nonlinear optics . . .
........................
2.2
Nonlinear optical processes .
2.3
Nonlinear crystals and quasi-phase-matching techinque
...............
3 Pulsed polarization-maintaining erbium-doped fiber laser
3.1
Motivation .
.................
. . . . . . . . . . . . . . .. . . .
13
3.2
Overall design ................
. . . . . . . . . . . . . . .. . . .
14
3.3
Seed laser design
. . . . . . . . . . . . . .. . . .
15
3.4
Use of polarization-maintaining fiber . . . . . . . . . . . . . . . . . . . . . .
17
3.5
Construction of the source . . . . . . ...
18
..............
...
. ...... .........
.
..... . . . . . . . . .. . . . 19
3.5.1
Pump diode set-up . . . . . . . ..
3.5.2
Gain fiber evaluation . . . . . . ..
. . . . . .
. . . . . . . 20
3.5.3
Continuous-wave laser construction
. . . . . . .
. . . . . . 21
3.5.4
From cw laser to pulsed seed laser .
. . . . .
3.5.5
Adjustment of the repetition rate .
.
. . . . .
. 22
3.6
3.5.6
Characterization of the seed laser . ..................
3.5.7
Testing the Erbium-doped fiber amplifier . ...............
3.5.8
Construction of the second harmonic generation stages .......
Summary
..........
.....
. .. ....
.
.
27
....
.
30
.......
31
4 Spatial mode manipulation in spontaneous parametric downconversion
4.1
Mode-matching and fiber optics . ..................
4.2
Optimizing the single-mode operation of SPDC
4.3
Experimental setup for optimizing coupling efficiency . ............
4.4
Optimization procedure
4.5
Coupling efficiency results . . . ...
4.6
Summary
...................
. .....
...
.
42
..
.
33
36
................
...
33
. ...............
..............
26
...
. .
.
...
.
...
.....
.
.
44
.
45
46
5 Conclusions
47
6
49
Acknowledgements
List of Figures
1
Overall block diagram of the source ...............
. . . . . . . . . 15
2
Schematic of the seed laser.
. .... ....
3
Comparison of standard and polarization-maintaining fibers
. . . . . . . . . 17
4
Pulsed regim es
. . . . . . . . . 24
5
Spectrum of the seed laser ...................
6
Sample of bandwidth dependency on pump current . . . . . . . . . . . . . . 28
7
EDFA output power as a function of EDFA pump current
. . . . . . . . . 29
8
EDFA output spectrum .....................
. . . . . . . . . 30
9
SHG output power as a function of SHG input power . . . . . . . . . . . . . 31
10
Mode-matching example ....................
..................
.........................
16
. . . . . . . . . 27
. . . . . . . . . 35
1
Introduction
The field of quantum optics opens up new possibilities in how we may think about using
light. Taking advantage of nonclassical states of light and quantum optical devices has led
to potential innovations that implement quantum key distribution systems [1] and quantum
computing [2], attempt to increase imaging resolution [3], provide higher quality lithography
[4], and improve the capacity of communication channels [5]. The cornerstone of most of
these quantum optical designs, however, is a source of entangled states-a quantum state of
two or more particles-whose measurement outcomes are each probabilistic but correlated
beyond what classical physics allows [6]. While preliminary polarization-entangled sources
have been produced and used in various devices, much research remains to be done in making
these sources suitable for practical implementations. Some of the most lacking aspects of
current entangled sources include extremely low fluxes, inability to efficiently couple into
optical fibers, lack of portability, and high cost. Thus, we focus our research on developing
polarization-entangled sources and their components that address some of these issues.
1.1
Motivation
This research is broken down into two sub-projects, each of which is an essential component
for efficiently generating high-quality polarization-entangled photon states. First, we wish
to construct a compact 390 nm pulsed laser source (-100 ps pulses at a repetition rate of
31.1 MHz) from polarization-maintainng components, that is suitable for use in quantum
optics experiments including the generation of entangled pairs at 780 nm. Second, we aim
to create a high-flux nondegenerate fiber-coupled polarization-entangled pair source using a
phase-stable Sagnac geometry [7, 8], and in this project, investigate the efficiency of coupling
down-converted light into single-mode optical fibers.
1.2
Organization
To understand the goals of this research, we complete this introduction by presenting a basic
overview of entangled states, assuming a basic knowledge of quantum mechanics. A brief
background in nonlinear optics, the central concept around which these projects are based,
is then provided. We then discuss the pulsed fiber laser and the non-degenerate high-flux
source in two separate sections, and then conclude with a discussion of future work.
1.3
Basics of entangled states and their applications
As mentioned earlier, central to many quantum optical devices is the notion of an entangled
state. An entangled state is a joint quantum state between two or more particles which cannot
be expressed as a tensor product of individual particle pure states. In typical cases, the
measurement outcomes in a particular basis are highly correlated between the two particles
regardless of spatial separation. This correlation is greater than any correlation that can
classically exist.
The following illustrates a specific quantum feature of entangled states. If particle A is
in state (10) + 11))/xi2 and particle B is in state (10) + I1))/-2, their measurement outcomes
are probabilistic and independent of each other (that is, there is an equal chance of seeing
a 0 or 1 for A and an equal chance of seeing a 0 or 1 for B that is independent of A's
measurement), and these two particles are not entangled. In such a case, the joint state of
the two particles is simply their tensor product state:
(10) + I1>))/
(10) + 11))/v' = (10) I0)+ I0)11) + I1)I0)+ 11) 11))/2.
(1)
It is evident in this product basis that there is an equal chance of measuring the joint state
to be 10) 10) or 10) 11) or 11) 10) or I1)I1), as one would expect from considering the situation in terms of classical probability. However, if A and B are entangled, the joint state
cannot be written as a product of two individual states. An example of an entangled state
is (10) 10) + I1)I1))/IV. If both particles are each measured, it is evident that both must
measure to be 0 or both must measure to be 1, since there is zero probability amplitude
for the possibilities 10) 1) and 11) 10). Moreover, even if the state is mesaured in a different
basis set, such as (10) ± I1))/v. instead of 10) and I1), nonclassical correlation is still obtained. The entangled state can be distinguished from a mixture of unentangled states by
measurements in two incompatible bases (a Bell state measurement is one example of such
an entanglement test). The nonclassical correlation will hold true even if the particles are
separated by large distances before being measured; at first glance this may seem to imply
action at a distance that violates relativity; however, this does not provide a gateway to
superluminal communication of information [9], since the two sides have no way to influence
the measurement of the state at the other side. No methods of standard quantum mechanics
can permit superluminal communication using entanglement; thus, relativity is not violated
with it.
The concept of entanglement [10, 11] is immensely useful with the aid of classical communication. Entangled states can be used to create secure key distribution systems [1], to
perform linear optics quantum computing [2], transport quantum states from one system to
another [12], potentially increase channel capacities in communications lines [5], and image
at higher resolutions than possible with classical light [3], plus other proposed applications.
Given that such a vast set of potential applications exist for entanglement, we now focus
our attention on the problem of generating polarization-entangled photons in the laboratory.
The most common method to produce entangled photon pairs is by means of spontaneous
parametric down conversion (SPDC), a nonlinear optical process that converts single photons of a higher frequency into two lower-frequency photons [13] which can be entangled [14].
To understand this, we now present a brief background in nonlinear optics.
2
Nonlinear Optics
Nonlinear optics refers to a number of phenomena in a medium in which its polarization
responds nonlinearly to the electric field of the incident light. Typcially, new frequencies of
light are generated as a result of this, with greatly varying degrees of efficiency depending
on the type of process and the medium's nonlinearity. Nonlinear effects are highly materialdependent, and are useful for a wide variety of applications, including in our case, the generation of polarization-entangled photon states.
2.1
Basic theory of nonlinear optics
In conventional linear optics, the medium's induced polarization vector is linearly proportional to the electric field strength of the incident wave as described by the relation
P = cxE
(2)
where E is the permittivity of the medium and X is the susceptibility of the medium. In
nonlinear optics, however, the dependence on the electric field E is not necessarily linear.
Typical nonlinear dependence can be generalized to a power series, described by
P = EX(1)E' + eX(2)+ 2 +
X
+ ...
(3)
where X(n ) are the n-th order susceptibilities. Many crystal materials, such as lithium niobate,
have a large X(2) coefficient, thus, we take a particular interest in them for use in nonlinear
optics experiments. Nonlinear optical devices take advantage of the higher order terms above
to create input-output relations that do not necessarily preserve frequency composition, and
are responsible for a wide variety of applications. In this research, nonlinear optical devices
play a central role in the creation of entangled photon sources, both in desired forms, such as
the nonlinear process for creating outputs at the preferred frequencies, as well as undesired
forms, such as unwanted nonlinear effects that generate background light and noise. We now
present a brief overview of some important processes that result from the nonlinear relation
above.
2.2
Nonlinear optical processes
A number of nonlinear optical processes will be relevant to the experiments in this thesis. In
general, nonlinear optical processes permit a change in the frequency composition of light.
Most commonly described are perhaps the frequency-mixing processes, which include, among
others:
* Second Harmonic Generation (SHG), in which the input frequency is doubled (w
2w).
* Sum Frequency Generation (SFG), a more general case than SHG in which two light
frequencies are summed (wl, w2 -- w3 = W1 + w2 ).
* Difference Frequency Generation(DFG), in which the output frequency is the difference
between two input frequencies (W1,i
3
-
w2 = w3 - W1)
* Spontaneous Parametric Down Conversion (SPDC), of particular interest to us in
generating entangled photons. SPDC causes an input photon to split into two photons
whose frequencies sum to the input frequency. It is "stimulated" by vacuum fluctuations
and converts only a small fraction of the input pump light (w3 --* w, w2 with w1 +w 2 =
W3).
There are numerous other common nonlinear processes besides the frequency mixing processes. The Kerr effect, for instance, is of interest to us in that it is unwanted in our experiments. In the Kerr effect, the refractive index of a material responds to the electric field and
the change is proportional to the square of the electric field. The Kerr effect is responsible
10
for self phase modulation (SPM) [15], a X(3)-order effect most prominent when ultrashort
pulses travel through media such as single-mode optical fibers [16].
2.3
Nonlinear crystals and quasi-phase-matching techinque
Lithium niobate (LiNbO 3 ) is a particularly useful crystal for optical experiments. It has
electro-optical, piezoelectric, nonlinear, and birefringent properties, among others, but we
employ it for its large X(2) coefficient, making it useful for second-order three-wave mixing
processes, and in particular, SPDC. Efficient frequency mixing can occur only when the
nonlinear process is phased matched at the three wavelengths. For example, SPDC will only
occur in a crystal in cases where the relation
S- - = 0
(4)
is satisfied (where kp is the pump k-vector, and k, and ki are the k-vectors of the so-called
signal and idler frequencies generated by SPDC).
In many cases, it is not often possible to precisely tune the input frequency, and in
many cases, some tunability of the output frequency combination is desired. This can be
done by employing quasi-phase matching (QPM). QPM, first proposed by Armstrong et. al.
[17] and further explained by Byer, et. al. [18], employs a periodically-poled crystal, such
as periodically-poled lithium niobate (PPLN) or periodically-poled potassium titanyl phosphate (PPKTP), where the crystal is composed of a large number of domains, evenly-spaced
along the direction of light propagation, alternating in ferroelectric domain orientation. The
flipping of alternate domains is accomplished by applying a large electric field near its breakdown value at alternate spacing intervals. The resulting flips in the domain polarizability
enables efficient nonlinear mixing that is about 40% of a perfectly phase-matched interaction.
More importantly, this technique permits the use of the largest nonlinear coefficient (d33 )
of LiNbO 3 , which is not available for birefringently phase-matched interactions, resulting
in an overall efficiency that is significantly higher than in the non-QPM case. In addition,
the phase-matching condition required for quasi-phase matching is dependent on the poling
period A:
kpkski
27r
A
(5)
By poling a crystal with a user-defined period A and fine-tuning the period by placing the
crystal in a temperature-controlled oven, one can phase-match at any desirable operating
wavelengths over the crystal's transparency window, making QPM a powerful tool in nonlinear optics.
3
Pulsed polarization-maintaining erbium-doped fiber
laser
Our goal is to construct a pulsed ultraviolet source at 390 nm, intended for use as a pump
for entangled photon generation at 780 nm. Our pulsed source is composed of a low-power
pulsed seed laser at 1560 nm, an erbium-doped fiber amplifier, and two stages of second
harmonic generation (SHG) using nonlinear crystals that convert the infrared pulses to the
desired 390 nm wavelength. In this section, we describe the motivation for this source, our
overall setup, the mechanisms for generating pulses in lasers, how we plan to build the seed
laser source, and the basic design principle. We will discuss the laser characterization and
experimental results.
3.1
Motivation
The 390 nm source we plan to build is a pulsed, mode-locked, low-power seed laser at 1560
nm which is then amplified and passed through two stages of second harmonic generation to
obtain the desired 390 nm. A previous such seed laser was built in our laboratory by Onur
Kuzucu [19], using standard non-polarization maintaining (non-PM) single-mode fibers and
components. This yielded an uncertain polarization at the output of the system, which had
to be corrected using a triple paddle system before feeding into an amplifier and second harmonic stages. The input to the PM amplifier requires a fixed, well-defined linear polarization
from the seed laser. Similarly the two SHG stages also require a fixed linearly polarized
input. For the non-PM laser, the polarization may drift over long periods of time or under
13
perturbations. Given these issues, we primarily concentrate our research on creating a PM
version of this seed laser, using mostly PM fibers and components to ensure that the output
polarization is well-defined and stable. Following this construction, we aim to characterize
the seed laser and incorporate it into the amplification and SHG stages to achieve a 390 nm
pulsed source that is compact, portable, and reliable.
3.2
Overall design
The UV source is composed of several stages that were built in sequence, as shown in the
block diagram in Fig. 1. A 980 nm fiber-coupled laser diode pumps a fiber-based seed laser,
which operates in a mode-locking regime to generate short pulses (v100 ps) at a repetition
rate of 31.1 MHz at 1560.0 nm. The output of the seed laser is fed into a commerciallyobtained PM erbium-doped fiber amplifier (EDFA), which amplifies the pulsed output to an
average of approixmately 5 W. The output of the EDFA, still at 1560.0 nm but amplified
in power, is output-coupled to a collimator, and, in free space, fed through two stages of
second harmonic generation (SHG) using nonlinear crystals, resulting in the final desired
390 nm wavelength. Although an earlier version of this source was built by Onur Kuzucu
at MIT [19], in this research, we investigate the use of polarization-maintaining fibers and
components in the seed laser to improve its stability and characteristics, and aim to produce
a more compact version of the entire source. We now turn to the problem of designing the
seed laser, the main component this source and this research.
Pump
Er-doped pulsed laser """"
980nm
1560nm
EDFA
"""t
1560nm
HG
390nm
SHG .....
780nm
Figure 1: Overall block diagram of the source.
3.3
Seed laser design
While pulsed lasers can be built in free-space, using a fiber medium as the laser cavity for
the seed laser provides a number of advantages, including durability, resistance to vibrations,
smaller physical footprint, and absence of intricate alignment requirements. Fibers can be
doped, and all the necessary components to pump a fiber gain medium and output-couple
light are available commercially. Our seed laser design, shown in Fig. 2, is composed of several
components arranged in a ring geometry. A pump diode at 980 nm, suitable for pumping
erbium, is coupled into the ring using a wavelength division multiplexer (WDM). The 980
nm light is pumped counter to the intended direction of lasing. An optimized length of Erdoped fiber is spliced to the WDM and serves as the gain medium for the laser cavity. Two
circulators are spliced into the cavity, each of which permits light to flow directionally only
from its labelled port 1 to port 2, and port 2 to port 3. These circulators permit reflective
components to be included in the cavity. Attached to port 2 of one circulator is a Bragg
grating at 1560.0 nm which fixes the laser wavelength; to the other circulator is a saturable
absorber setup which mode-locks the laser and preferentially amplifies high-intensity pulses,
causing the laser to output short pulses. The saturable absorber preferentially amplifies highintensity pulses in the cavity, and with proper alignment, can be used to achieve a modelocking state, in which the cavity modes have a fixed phase relationship with each other,
constructively interfering to yield short and high-intensity pulses. The final component in
the laser cavity is an output coupler, which diverts 10 percent of the circulating power to
the laser output at each round trip. The total length of the laser cavity will be adjusted to
permit a 31.1 MHz pulse repetition rate, and the desired average output power is 1 to 5 mW.
While a very similar seed laser was previously built, our objective is to build the entire seed
laser out of polarization-maintaining components, to alleviate polarization instability issues,
which are undesirable when connecting the seed laser to the amplifier in the next stage of
the overall design.
01
mator
ieric f=3mm
Figure 2: Schematic of the seed laser.
3.4
Use of polarization-maintaining fiber
In the overall design, it is important that a fixed and well-defined polarization be maintained
at the input of a polarization-maintaining EDFA and also for second harmonic generation.
As mentioned before, another student constructed a similar but non-PM source; however,
this source required polarization corrections at its output and is susceptible to polarization drifts over time. This instability is a result of a lack of polarization selectivity in the
construction of the laser. However, in this work, we improve upon the design by building it
almost entirely out of polarization-maintaining components (with the exception of the Bragg
grating, which was not commercially available in a PM version at the time). Polarization
maintaining fibers contain embedded rods that induce mechanical stresses in the fiber, which
in turn induces optical birefringence in the material. The difference in index allows light of a
fixed polarization along one axis to more easily remain polarized in that axis. Since the fibers
now have a specific orientation, it is important to note that they cannot be spliced using a
standard splicer; a special polarization-maintaining splicer (such as those manufactured by
Ericcson or Fujikura) must be used which inspects both cleaved fiber ends for their stress
rod orientation and aligns the axes of birefringence before performing the splice.
Cladding
Core
e
Stress rods
Standard SM fiber
Panda PM fiber
Figure 3: Comparison of standard and polarization-maintaining fibers. Stress rods in the
cladding of polarization-maintaining fibers maintain the polarization orientation.
3.5
Construction of the source
Since the polarization-maintaining EDFA is a commercial product and the second harmonic
generation stages are relatively standard configurations, we omit a detailed description of
their design. We now consider the process of building the entire UV source, which will be
accomplished in several stages. First, we set up the pump diode and test its characteristics.
Second, we test various commercial Er-doped gain fibers and select one that is suitable for
our purposes. We then splice together a continuous-wave (cw) laser by including only the
pump, WDM, gain fiber, Bragg grating (using one circulator), and output coupler. After
testing this setup, we break a splice to insert the second circulator attached to the saturable
absorber setup to convert it into a mode-locked pulsed laser. After testing its characteristics
and ensuring that it mode-locks reliably, we adjust the repetition rate of the pulses to the
desired value of 31.1 MHz by cutting unnecessary segments of undoped fiber inside the
laser cavity. This value of 31.1 MHz matches a similar but non-PM version of the seed
source previously built by Onur Kuzucu. This completes the construction of the seed laser.
If its characteristics are satisfactory at this point, the output is then connectorized and
attached to an IPG Photonics erbium-doped fiber amplifier (EDFA) in an original equipment
manufacturer (OEM) configuration that allows us to customize the setup. The EDFA is tested
and tuned, after which the second harmonic generation stages can be built to complete the
construction of the UV source. We now examine the actual execution of these individual
construction steps in detail.
3.5.1
Pump diode set-up
Since we plan to operate at 1560.0 nm, we use erbium-doped fibers with optical pumping at
980 nm. We obtained a 980 nm, 500 mW JDS Uniphase diode (29-8052-500) with a built-in
thermoelectric (TE) cooler, designed to fit into a 14-pin butterfly mount and with a bare
fiber output. The diode was mounted onto a Thorlabs butterfly mount, designed to support
both of the two commonly-used pin specifications. This diode had a Type 1 specification,
which was acommodated simply by fitting the appropriate board supplied with the butterfly
mount. A Thorlabs ITC 100 OEM driver was used to control the diode and TE cooler, and
required adjustment of the PID controller to properly and quickly reach a set operating
temperature throughout the experiment (approximately 16-18 0 C). As it did not come with
a power supply and required +12 to +15, 0, and -12 to -15 volt inputs, we initially used
known clean power sources such as two HP power units in series. We then tested a Lambda
Electronics OEM switching power supply unit (SCD601515), which provides all 3 necessary
inputs with a rated maximum of 1 percent peak-to-peak ripple. One important concern with
using switching power supplies is that significant components of the high switching frequency
(and even 60 Hz line frequency in some cases) may leak into the diode driving current and
cause an unwanted modulation in the light output. However, testing this particular power
unit and using a high-speed photodiode and oscilloscope to look for frequency artifacts
showed no noticable oscillations or difference when compared to the use of a linear power
unit. We believe that the input power filtering mechanism in the ITC 100 driver was good
enough for us to use the switching supply, which is a much less expensive and compact power
solution. An acrylic housing was made to hold both the ITC 100 and the SCD601515 units
and forced-air cooled with four fans.
3.5.2
Gain fiber evaluation
An ideal gain fiber for use in the seed laser would have a high gain over a short distance,
allowing for maximum freedom in adjusting undoped fiber lengths to achieve the desired
repetition rate. Three commercially-available erbium-doped polarization maintaining fibers
were tested for their suitability: Nufern PM-ESF-7/125, Fibercore DHB1500, and CorActive
EDF-Er-25-05-PM. Each fiber was spliced in turn to the output of a custom-made Senko
polarization-maintaining wavelength-division multiplexer (WDM), with one input connected
to the 980 nm pump diode and the other input connected to a 1560 nm source of known
average power of 1.5 mW. For each gain fiber, we began with at least 3 meters spliced to the
WDM, and ran the JDS Uniphase diode at a fixed current level of about 560 mA, providing
approximately 250 mW of pump power. The output power at the loose end of the gain fiber
(after proper cleaving) was measured to determine the gain provided by the fiber at 1560
nm. At excessively long lengths, the Er-doped fiber attenuated the output, and at excessively
short lengths, the pump power barely depleted; we looked for an optimal length with the
maximum gain. This optimal length was determined by continually monitoring the output
power while progressively cutting back and cleaving the Er-doped fiber in small intervals
until it reached a maximum and just began to drop again. It is helpful that Er-doped fibers,
under pumping, fluoresce in visible green as well, providing a hint of the extent of the length
of the fiber that the pump light was being absorbed.
We found that the lightly-doped Fibercore and medium-doped Nufern fibers required
long lengths to provide significant gain, and as briefly mentioned before, this would make it
difficult to control the repetition rate of the laser later since there would have to be much
less undoped fiber in the cavity to maintain the same total cavity length, thus requiring tight
splices to be made. The highly-doped CorActive fiber, however, provided excellent results,
and within 1-2 meters of fiber provided a gain factor of approximately 20 to 30. We therefore
chose to use the CorActive fiber as our gain fiber.
3.5.3
Continuous-wave laser construction
Next, a continuous-wave laser was built. This was accomplished by splicing a PM 90-10 output coupler (Lightel PMC-S-12-9010-1550-1-B-0) and PM circulator (AC Photonics PMC-11-5-1-10-1-0-C-0) to the gain fiber and WDM previously used for the gain fiber evaluation.
We attached the Bragg grating to the middle port of the circulator and built the entire cw
laser system without the circulator associated with the saturable absorber (which is used for
passive mode-locking operation). While polarization-maintaining splicing was performed for
the circulator and coupler, the Bragg grating used (Teraxion, custom-made, 1560.0 nm, 25
GHz bandwidth) was not etched on a polarization-maintaining fiber. As a result, the laser's
peak wavelength and spectrum changed if the fiber grating was shifted or curled. To solve
this, we removed most of the non-PM pigtail on the Bragg grating, re-spliced it, and then
housed the entire length of the Bragg grating section, including the short length of non-PM
fiber, in a thin 25 cm long brass tube. Since the laser was built on a 12 x 12 in aluminum
breadboard, the brass tube was taped directly to the breadboard for added stability. This
21
kept the entire non-PM section and Bragg grating straight and greatly improved the stability
of the output spectrum. The output power of the cw laser was approximately 15 mW, with
the pump current still at 560 mA.
3.5.4
From cw laser to pulsed seed laser
A pulsed laser, such as the seed laser being constructed, periodically emits short pulses
with high peak powers, as compared to the steady output of the commonly used cw laser.
There are generally two common methods for generating such a pulse train: Q-switching and
mode-locking. In a Q-switched pulsed laser, extremely high-intensity pulses are produced at a
relatively low repetition rate (typically on the order of kilohertz). This is created by placing
a variable attenuator, such as an (active) attenuator component, or a (passive) saturable
absorber, inside a laser cavity, and configuring the system in a way such that the gain medium
attains a high population inversion, possibly near saturation, before suddenly changing the
quality factor of the cavity to output the large amount of stored energy in the gain medium.
The repetition rate of a Q-switched pulsed laser is dependent largely on the configuration,
attenuator, and input power, and not on the laser cavity round-trip time.
A mode-locked pulsed laser, on the other hand, produces a much higher repetition rate
(tens of megahertz is common) and much shorter pulses (which can be anywhere in the
femtosecond to picosecond ranges). In a mode-locked laser, the longitudinal modes of the
laser cavity are in phase and they constuctively interfere to yield a short pulse (with a pulse
width that is inversely proportional to the mode-locking spectral width). For our system,
the cavity length is much larger than the wavelength, and the mode spacing for the ring
configuration is given by Sf = c/L, where L is the round-trip cavity length. In a modelocked laser, the various modes of a laser cavity operate with a fixed phase relationship
to each other, typically producing a pulse train, with the overall repetition of the pulses
being at a frequency of c/L. Mode-locking can be accomplished actively or passively. Here,
we pay particular attention to passively mode-locked lasers, which typically use a saturable
absorber to partially attenuate low-intensity light while permitting high-intensity light under
saturation. This can cause a fluctuation in the laser cavity to be preferentially amplified,
leading to a train of pulses as the laser's output coupler takes out a fraction of each pulse
while the gain medium amplifies it again at the next round-trip. After the laser is in modelocking operation, additional fluctuations will not be amplified in the ideal case, and only
the existing pulse train will continue to be selected and trigger stimulated emission at each
round-trip.
Since we wish to build a passively mode-locked fiber laser, it is evident from the above that
two potential issues could arise. One is that since the same technology of saturable absorbers
is capable of producing both Q-switching and mode-locking operation, that a mis-configured
cavity could accidentally enter a Q-switching state. Another potential problem is "double
pulsing", in which two amplified pulses appear together at each repetition interval and are
both amplified during each round trip. However, with careful alignment and tweaking of
free-space components, it is usually possible to place the operation of the laser in the desired
state. Fig. 4 illustrates typical oscilloscope traces of lasers operating in the two pulsed modes.
With knowledge of these potential obstacles in achieving proper mode-locking, the cw
JI
Q-switching
Double-pulsing
LJ. I I
Properly mode-locked
Figure 4: Pulsed regimes: In the Q-switching scenario, very large pulse envelopes are observed, repeating on the order of kilohertz, with underlying repeating pulses at the intended
repetition rate. In double pulsing, the laser is mode-locked but starts with two pulses simultaneously being amplified at each round trip. In a properly mode-locked scenario, consistent
height pulses are observed at the intended repetition rate.
laser cavity was cleaved apart at one point and a second circulator (AC Photonics PMC-1-15-1-10-1-0-C-0) was inserted in order to include a saturable absorber. The saturable absorber
chip (Batop 1550-30-0) was fixed to a small aluminum disc and mounted on a 3-knob locking
mirror mount. The 3 mm aspheric lens was mounted with an X-Y translating mount and
roughly aligned to a 3 mm distance from the saturable absorber. The collimator was mounted
using an 2-knob tilting mount approximately 2 cm from the aspheric lens, and spliced to the
second circulator now in the cavity. At this point, lasing will only occur if the center port
of the second circulator reflects light back into the cavity; that is, there exists a properlyaligned round trip path out of the collimator and coupled back into the same fiber. The
alignment of the free space components was a challenge, but done with the help of using a
high reflector (HR) mirror in place of the saturable absorber at first (thus creating a cw laser
again), and then substituting the HR mirror for the saturable absorber and fine-tuning the
alignment. Using a sensitive fiber-coupled power meter with the laser output also facilitated
the alignment process, as minor changes in power often hinted towards the proper alignment
as the geometry of a component was tweaked.
Once the saturable absorber was aligned properly, pulsing was easy to observe with a
high-speed Thorlabs InGaAs photodiode, but as pointed out before, Q-switching situations
occurred if the alignment was not correct for mode-locking. In some cases, a situation was
seen where the laser could be aligned to mode-lock, but if it was powered down and powered
up again, it entered into a Q-switching state with some high probability. However, with
enough tweaking of the saturable absorber alignment and focusing, it was possible to find an
alignment where the laser consistently entered a stable mode-locking state within 1 second
of starting up. Initially, the seed laser operated at a repetition rate of approximately 13 MHz
and an average output power of about 2 mW.
3.5.5
Adjustment of the repetition rate
To achieve the desired 31.1 MHz repetition rate of the design specifications, excess fiber was
removed from the ring cavity. The excess fiber removal was a challenging process, because
of PM components that required proper fiber orientation as well as tight splices that had
to be made. Though we had initially used an Ericcson PM fusion splicer and another older
splicer using a tungsten filament, the final re-splicing was accomplished with a much more
reliable Fujikura PM splicer at Lincoln Laboratory. First, extra fiber lengths were removed
from the middle port of the circulators, as cutting down on those lengths would have double
the effect due to the round trip through those fibers. After that, further fiber lengths were
removed between components, but the gain fiber was left intact. With careful estimation, we
achieved a repetition rate of 31.15 ± 0.05 MHz. This frequency should also be fine-tunable
by adjusting the distance from the collimator to the aspheric lens and saturable absorber.
This completed the construction of the polarization-maintaining seed laser.
3.5.6
Characterization of the seed laser
Using an optical spectrum analyzer, we characterized the seed laser and found it operating
accordingly to what we had expected. The center wavelength was very stable over time and
centered around 1559.88 nm. With the initial pump power settings, we observed an average
output power of 2.2 mW and a bandwidth of 0.09 nm (FWHM); the spectrum is shown in
Fig. 5. However, one interesting aspect, which was different from the non-PM seed source
built earlier [19], was that the bandwidth was tunable by adjusting the pump power. We
observed that a higher pump power supplied to the ring laser resulted not only in a higher
average output power, but also an increase in bandwidth. Since there was a limited operating
range of pump powers that would enable the ring laser to properly mode-lock, the bandwidth
tunability was limited to approximately 0.045 nm to 0.095 nm with the initial settings. A
graph of this dependence is shown in Fig. 6. However, the actual range of tunability was
heavily dependent on the alignment of the saturable absorber, but it should generally be
close to this range. Since the input specification of the EDFA allows for a range of average
powers from 1 to 5 mW without significant changes in the output, the average output of the
seed laser is essentially irrelevant as long as it is within this range, and the tunability can be
a potentially useful feature. The polarization extinction ratio of the seed laser was measured
using a rotatable wave plate, polarizing beam splitter, and power meter, and found to be
at least 20 dB with the axis of polarization stably fixed along the slow axis of the fiber.
26
Given this analysis, we claim that the construction of a passively mode-locked polarizationmaintaining Er-doped fiber laser was successful and we accomplished the goal of achieving
polarization stability while still maintaining the desired characteristics for the rest of the
laser source.
2007 Apr 03 21:36
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Figure 5: Spectrum of the seed laser, measured by an optical spectrum analyzer, showing
a bandwidth of 0.090 nm, driven with a pump current approximately 470 mA, and with a
measured output power of 2.2 mW.
3.5.7
Testing the Erbium-doped fiber amplifier
The erbium-doped fiber amplifier (EDFA) was custom-made by IPG Photonics and accepted
a fiber input from 1 mW to 5 mW. The output cable with a 14 pm core diameter designed to
carry higher powers, was well-protected and factory-attached to a collimator. The maximum
rated input current was -6 A, yielding an output power of -5 W. Testing of the EDFA was
broken down into three subcategories: power output, polarization extinction and stability,
Sample of bandwidth dependency on pump current
E
cc
I
U-
ao
Input current (mA)
Figure 6: Sample of the bandwidth dependency on input pump current with the initial
construction.
and spectral characteristics. First, the power output of the EDFA was tested by attaching the
input to an Agilent cw laser module tuned to 1560 nm at a power of 2.2 mW, and the EDFA
output power was plotted as a function of input current. The seed source was then connected
and the same power measurement repeated, obtaining almost identical results in power
output, as one would expect. The power dependency on EDFA current was nearly linear,
and is shown in Fig. 7. Second, the polarization extinction of the EDFA was measured with
the Agilent cw laser and seed laser as inputs. Contrary to our expectations, the polarization
fluctuated rapidly, oscillating from one orientation to another on a time scale of 10-30 seconds
with a poor extinction ratio. Finally, we checked the spectrum of the laser using a spectrum
analyzer, and found that self-phase modulation (SPM) was taking place.
SPM is a phenomenon caused by the nonlinear Kerr effect in the fiber medium, in which
CL
CL
0.
0.
0
LL
0
LU
EDFA current (mA)
Figure 7: EDFA output power as a function of EDFA pump current.
the refractive index of the material exhibits a small dependence on the optical power travelling in the medium, greatly impacting the spectra of high-intensity ultrashort pulses. Typically, and in our case, the spectrum begins to broaden and separate into two or more spectral
peaks with increased SPM. Following this analysis, the EDFA was taken to IPG Photonics
for two modifications. First, to correct the polarization instability of the EDFA output, a
polarizer was inserted into the EDFA This ensured that all polarizations were kept along the
slow axis of the fiber and the polarization fluctuation problem was corrected. Second, the
length of the output fiber was shortened by 0.4 m (since such a long output fiber was not
necessary for our setup) that reduced the amount of SPM as shown in Fig. 8.
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before and after modifications.
3.5.8
Construction of the second harmonic generation stages
A separate breadboard was set aside for the construction of the SHG stages to convert the
1560 nm pulses to 780 nm and then to 390 nm. As part of this thesis, only the first stage was
completed, and the second stage will be built later to complete the source construction. The
first SHG stage used an MgO-doped PPLN crystal with a grating period of 19.47 pm and
dimensions of 10.15 mm by 2.00 mm by 0.50 mm. The crystal was anti-reflection coated at
1560 nm and 780 nm to prevent significant back-reflections from re-entering the EDFA (which
could cause stability problems) and to improve the efficiency. The crystal was placed in an
HC Photonics temperature-controlled oven with a precision of 0.1 0 C. The beam was focused
using a 150 mm lens after the collimated input and two alignment mirrors. Immediately
following the crystal, a 450 dichroic mirror separated the 780 nm light and passed through
the remaining 1560 nm light, which was beam-blocked for safety. The crystal was operated
at a temperature of 89.9 0 C, which was found to attain the maximum conversion efficiency
to 780 nm as measured by a power meter. A graph of the output power dependence on the
EDFA pump power for a fixed seed laser power is shown in Fig. 9.
E
CO
0.
CO
o:
SHG input power from EDFA (W)
Figure 9: SHG output power at 780 nm as a function of SHG input power at 1560 nm
supplied by the EDFA.
3.6
Summary
A new, compact, passively mode-locked fiber ring laser with a repetition rate of 31.1 MHz
and average output power ranging from 1 to 2.5 mW was built, and will serve as the seed
laser for a 390 nm source. The use of polarization-maintaining fiber and components in the
seed laser was successful. We measured similar laser characteristics as an earlier non-PM
source [19] but this PM fiber laser had excellent polarization stability over a long time with
an extinction ratio of at least 20 dB. In addition, the new source exhibited a small amount
of bandwidth tunability (0.045 to 0.095 nm) by changing the pump power, which may be a
useful feature. The self phase modulation effect was also reduced from an earlier version of
this source by shortening the length of the output fiber from the EDFA. The first SHG stage
was built to convert the high-power 1560.0 nm light to 780 nm, obtaining 3W output from
5W input. The final component of the source, a second SHG stage, still remains to be built.
4
Spatial mode manipulation in spontaneous parametric downconversion
In research possibilities for future entangled photon sources, another device was planned and
investigated. Using a Sagnac geometry with type-I spontaneous parametric down conversion
(SPDC) in a periodically-poled lithium niobate (PPLN) crystal, we hope to create a highflux source, pumped at 532 nm and capable of producing entangled pairs at nondegenerate
wavelengths of 797 nm and 1.6 pm that can be efficiently fiber-coupled for easy transport.
We omit a description of the Sagnac geometry for producing entangled photons, which can
be found in a paper on a similar but degenerate Type-II source [7, 8], and in this research,
we focus entirely on the problem of coupling SPDC-generated light into optical fibers. We
first discuss the idea of mode-matching and why it is important to this problem, present a
proposed theory to optimize the coupling efficiency of SPDC-generated pairs into a singlemode fiber, and our initial results from the laboratory.
4.1
Mode-matching and fiber optics
In building this entangled source, we would like to couple both outputs into suitable singlemode fibers, as efficiently as possible. Since ideal single-mode fibers only carry a single optical
spatial mode, we must require two things of our beams: (1) that the beams are as singlemode as possible, and (2) that the beams are properly mode-matched into the fiber. We
now assume that our beams are single-mode (as is nearly the case for all lasers) and briefly
discuss mode-matching; then, we will discuss how to satisfy the former in SPDC.
33
Mode-matching is the technique of setting two spatial modes equal in order to achieve
efficient coupling and desired beam characteristics. For example, a single-mode optical fiber
has a pre-defined spatial mode that it will accept at the end, and nearly 100% efficient
coupling can be achieved theoretically only in the case where the propagation mode (which
can be described by the mode field diameter, waist location, and center, for example) of
the beam is matched to that mode. The desired mode of a single-mode fiber is the same as
that of a focused single-mode Gaussian beam that has a full waist equal to the mode-field
diameter of the fiber, and a waist location at the tip of the fiber. Thus, proper fiber coupling
often involves a combination of tweaking the beam diameter as well as a proper choice of
a focusing lens to couple into the fiber, along with precise X-Y-Z alignment capabilities. A
microscope objective lens is a good choice of a focusing lens, due to high manufacturing
quality. If properly aligned and mode-matched, the theoretical efficiency limit is to couple all
of the photons into the fiber; however, small losses may occur due to lack of anti-reflection
coating at the fiber tip and sometimes on the objective lens surfaces, and imperfect beams.
Efficiencies upwards of 80%, however, are not unrealistic, especially with good TEMoo lasers.
Mode-matching is perhaps best illustrated with a simple situation. If a single-mode fiber
has a mode-field diameter of 2wo, and a collimated beam with diameter 2W is used, then
we must find a lens that will focus the collimated beam to a diameter of 2w 0 , and place the
lens at a distance such that the focus is at the fiber tip. To determine the focal length of the
lens needed, we use the equation of propagation of a Gaussian beam in free space [20]
w(z)=wo
1
2
(6)
where A is the wavelength in the medium and w(z) is the spot size as a function of the
distance z from the focus. Setting w(z) = W permits us to solve for the distance from the
focus z. Selecting a lens of short focal length f = z, and placing it at a distance f from
the fiber tip, will more or less mode-match the given collimated beam to the fiber. A simple
diagram of this mode-matching setup is shown in Fig. 10. In this example, our input beam is
collimated; however, any beam can be mode-matched using an approprate lens configuration,
and can be calculated using the more fundamental and general technique of ABCD matrices
[20].
f
Figure 10: Example of mode-matching a collimated beam into a fiber using an appropriate
lens. The fiber cladding is not shown. Non-collimated beams can also be mode-matched and
require additional calculations.
4.2
Optimizing the single-mode operation of SPDC
Ideal single-mode optical fibers only accept a single spatial mode, and will only couple that
mode at maximum efficiency when that mode is properly mode-matched. Beams that contain
multiple spatial modes will not achieve a good coupling efficiency of the total amount of light
into single-mode fibers. The process of spontaneous parametric down conversion (SPDC),
which we depend upon to produce entangled photon pairs in this source, does not generally
produce single-mode outputs (both in the output signal and idler frequencies). The multiple
spatial modes generated in SPDC present a problem for coupling the entangled photons into
a single-mode optical fiber. The desire is to couple most of the SPDC light into single-mode
fibers, which can only be accomplished if the SPDC output is in a single spatial mode. It
has been pointed out that by focusing the pump beam, the SPDC can be made to emit into
nearly one single spatial mode [21]. In such a case, mode-matching that primary mode will
yield a high overall coupling efficiency.
A number of speculations have been made in the past on the condition necessary to
optimize the coupling efficiency from SPDC light. However, experimental coupling efficiencies
above 20% had been difficult to achieve in the long quasi-phase-matched crystals as we use
at MIT. High coupling efficiencies had been previously achieved with SPDC in beta barium
borate (BBO) using thin crystals, but the output flux of these experiments was generally
low [22]. In our case, we wish to take advantage of long periodically-poled crystals to achieve
a high output flux, but with a high coupling efficiency as well.
In our experiments, there are three important angle figures to consider:
* Pump divergence, denoted by Op, describes the far-field divergence angle due to focusing
of the Gaussian pump beam in free space. This is not to be confused with the divergence
in an output due to a focused pump, which may be different than the divergence of the
pump itself.
* Natural divergence angle, denoted by 0, and Oi for the signal and idler outputs, respectively, is the divergence due to the phase matching condition of the crystal as
determined by its length.
* Filter divergence angle, denoted by 4, and 4)i for the signal and idler respectively, is
the additional angular bandwidth through which phase-matching occurs due to the
finite bandwidth of the interference filters that are usually placed at each the output
to restrict the measured bandwidth.
A paper by Bennink, Liu, et. al. [21] provides evidence that a focused pump can achieve
higher coupling efficiency than a collimated pump. We are inspired by this work to consider
that efficient coupling could be achieved in a special case where the divergence in the signal
due to the pump equals the natural divergence of the signal, and that the divergence of the
idler due to the pump equals the natural divergence of the idler. However, as we shall see,
when the signal and idler are nondegenerate, these two conditions cannot be simultaneously
satisfied. We begin by evaluating the natural divergence angles, which are given by the case in
which the pump is collimated, that is, the pump beam propagates entirely in the z-direction.
Determining the natural divergence angles can be accomplished by first considering the
relation between the allowed phase mismatch along the z direction of the crystal, Akz, and
37
the length of the crystal L which determines the bandwidth of the crystal:
AkzL = -x.
(7)
Noting that despite the pump being in the z-direction, phase-matching can still occur with
the signal and idler beams having z-components, as long as
sk,
=
-6ks
(8)
where 6k, is the transverse (i.e. x and y, not z) component of k, and 6ki is the transverse
component of ki. Note that in this paper, we generally use A to indicate small changes in the
propagation (z) direction and S to indicate changes in the transverse direction. To determine
the phase matching condition along the z-direction, Akz, we first find the z-components of
the signal and idler beams. This is given for the signal in terms of the small angle of the
signal 0, from the z-axis, which can then be approximated to second order using a Taylor
series:
ksz = kscosO,
92
_6k2
k,(1 - -)
2= = k 8
2
22kk,8
(9)
where in the last step, the relation 0, = 6k,/k, has been employed. Likewise, for the idler,
kiz = kIcosi
ki - -ki
2kh
(10)
Given these z-components of k, and ki, we can determine the phase mismatch along the z
direction:
Akz = kpz - ksz - kiz = kp - ksz - kiz
(11)
where kp = kp for a collimated pump. Substituting for k,, and kiz gives:
sk 2
2
Akz = kp - kq(1 - 6k)
2k
202
8
(12)
Since kp - k, - k1 = 0, this relation simplifies to
akz =
6ks
. +
6k2
2k, 2ki
(13)
Substituting this into Eq. 7 yields
6k2s + 6k2
2k,
2k
(14)
L
Eq. 8 can be used to simplify Eq. 7 to:
6k2 1
2 (k+
1
7r
) = L'
(15)
which yields
s6k
=
kk
2-rx
k, + ki L
kki 27r
k, L
(16)
As mentioned earlier, 6k, is the transverse component of k, and determines the natural
divergence angle (half-angle) of the signal,
0• s=
6ks
k
=I
ki 27
k, kL,L'(17)
(17)
and for the idler, it can be similarly derived that I6kjl = 16k,l, giving the natural divergence
angle of the idler,
6ks
6k
Oi = 1kiI 1= IIkk8 I=
k
k
=
k, 2-7r
kkpk L
(18)
Since in our case, we wish to use a PPLN crystal with a pump wavelegth of Ap =532
nm (in free space), a signal at As =797 nm, and an idler at Ai =1600 nm (noting that this
wavelength combination satisfies the required energy conservation relation AP = As' + Ai 1 ).
We note that k,8
2ki for this choice of wavelengths, such that Eq. 15 yields
6k1 =
',k
V 3L
(19)
Substituting from above and simplifying, the half-angle divergence in the crystal is then
8=
n(20)
where n, is the index of refraction of the crystal at the signal wavelength but the relation
is still expressed in terms of the free-space wavelength A,. Substituting our crystal length
of 20 mm, n, = 2.185, and A8 = 797 nm,we obtain 0, = 2.46 mrad. Multiplying this by
the signal index n8 again yields the external (free-space) divergence angle of the signal,
Ose
= 5.39 mrad. Likewise, given an idler index n, = 2.143, we can re-do Eq. 15 in terms of
the transverse component of the idler instead of the signal, and follow the same procedure
to find the external natural divergence angle of the idler, Oie = 10.69 mrad, observing that
in our specific case, :ie - 2 0,e.
Given the natural divergence angles of the signal and idler, we now turn to the issue of
focusing the pump beam to obtain a higher coupling efficiency. We hypothesize that a high
coupling efficiency will be observed if the divergence of the signal due to the pump focusing
is the same as the natural divergence of the signal, and the divergence of the idler due to the
pump focusing is the same as the natural divergence of the idler. However, it is not possible
to satisfy this condition for both the signal and the idler simultaneously in the nondegenerate
case. Nevertheless, we now consider each case independently, and in this paper, match the
divergence of the signal due to the pump to the natural divergence of the signal only, leaving
the idler unmatched, and attempt to efficiently couple the signal in an experiment. Since the
pump beam is now not collimated, but focused, we assume a range of transverse components
in the pump beam and an associated pump divergence angle Op. Since the phase matching
condition will only permit the pump, signal, and idler to be collinear, the divergence angle in
the signal due to the pump will simply be the divergence of the pump, giving us the desired
condition ,p = 0,. Thus, we set Op = 2.46 mrad. Given that n, = 2.245, the external pump
~ = ,,n, = 5.52
divergence is then Op
mrad. For a Gaussian beam, the divergence of a beam
is related to its waist (i.e. half-width at focus) wo by
0=
41
(21)
Substituting the value of the pump divergence Ope determined above yields a waist of 30.7
pm, which we hypothesize may give us a high coupling efficiency, despite the fact that we
have matched only the signal and not the idler, and will use this as a starting point in our
measurements.
4.3
Experimental setup for optimizing coupling efficiency
We have constructed a setup on an optical table to vary the SPDC pump focusing while
monitoring the coupling efficiency of the signal output at 797 nm. To provide a suitable
polarized and single-mode pump source for SPDC, the beam from an inexpensive, 85 mW,
532 nm laser was sent through two alignment mirrors, a half wave plate, and a quarter wave
plate, and coupled into a single-mode polarization-maintaining (PM) fiber patch cable. By
tuning the wave plates, a polarization extinction ratio of over 20 dB was achieved in the
other end of the PM fiber. The output from the PM fiber is also nearly single-mode. The
coupling efficiency of the 532 nm light into the PM fiber was near 60%, so the power level
was adjustable from 0 to approximately 50 mW.
The output end of the PM fiber, which was connectorized with an FC/APC connector,
was mounted near a microscope objective lens with a z-translation mount to fine-tune the
distance between the objective and fiber. After two alignment mirrors, the beam was then
focused using a Thorlabs 125 mm BK7 AR-coated lens. This choice of focal length permitted
a variation in beam waist near the value of wo =30.7 pm, as determined expermientally using
a beam scanner and by testing multiple objective lenses and focusing lenses available in the
laboratory. It was easily possible to adjust the objective lens to obtain beam waists of at
least 18 to 35 pm, which was a sufficient range to test the above hypothesis.
The crystal used was a PPLN crystal which was anti-reflection coated for three wavelengths
(532 nm, 800 nm, and 1600 nm), and contained five channels with different grating periods. A suitable channel was selected by estimating the required grating period using the
Sellmeier equations and phase-matched at a temperature of approximately 180'C to yield
SPDC outputs at 797 nm and 1600 nm. After the crystal, a second BK7 lens of focal length
125 mm, but AR-coated for 800 nm, was placed to approximately collimate the beam. The
beam was then passed through two 450 high reflectors to align the SPDC output, a dichroic
mirror which reflected most of the 532 nm light and passed the 797 nm SPDC output, and
a 0.11 nm bandwidth interference filter centered at 797 nm. An input coupler with fine adjustments was then used to couple in the 797 nm signal into a single-mode, non-PM optical
fiber, which was sent to a fiber-coupled Perkin-Elmer silicon photon counter for detection.
This provided a count of the fiber-coupled photons. In addition, when desired, another 450
high reflector was placed in the beam path, and the beam diverted to another focusing lens
into a free-space Perkin-Elmer photon counter to determine the total number of photons in
the beam. The fraction of photons given by the fiber-coupled detector and the free-space
detector (when the beam is diverted) would give the coupling efficiency.
4.4
Optimization procedure
First, the crystal was removed from the beam path and a beam scanner placed and translated
to monitor the beam waist of the 532 nm pump beam. The microscope objective lens at the
532 nm fiber output was translated until a beam waist of 23 am was observed, taking into
account that the beam waist location may be different as the beam is not collimated before
the focusing lens. When a minimum waist of 23 /m was observed, the crystal was placed
back into the beam path, centered at the beam waist, taking into account the change in waist
location due to the higher index of refraction of the crystal than air. The second focusing lens
was then set at a distance which approximately collimated the 532 nm beam. Temporarily
removing the interference filter and dichroic mirror, and disconnecting the second fiber from
the photon counter to avoid damage, the 532 nm beam was used as a guide to align the beam
path with the input coupler for the 797 nm photons. When a cursory alignment coupled a
significant amount of 532 nm light into the 797 nm fiber, the alignment was set as a starting
point and the dichroic and interference filters were added back to the setup. Switching off the
laboratory room lights and reconnecting the photon counter, a small amount of SPDC light
was usually detected by the photon counter (on the order of 5000-10000 counts per second,
over a noise level of 200-500 counts per second). The noise level was greatly reduced from
its initial level by enclosing the 797 nm fiber in additional opaque plastic tubing. From this
point, the entire setup after the crystal was tweaked, including the position of the second
focusing lens, the focal length of the objective lens of the input coupler, the angle of the
0.11 nm interference filter, and the alignment of the mirrors, to try to properly match the
signal light into the fiber. The free-space counts were also measured by diverting the beam
and focusing it into a free-space counter, as described earlier. When the maximum coupling
efficiency was achieved, the pump waist was tweaked by a tiny amount and the entire process
repeated again, expecting that some value of the pump waist would yield a particularly high
coupling efficiency.
4.5
Coupling efficiency results
With sufficient tweaking, we were able to achieve raw count rates of 1.7 Mc/s at the fiber
detector and 3.3 Mc/s at the free space detector for a pump waist of 29 ± 2 Im. The actual
value of the pump waist was extremely sensitive, but the beam scanner used to measure
the beam waist could not provide a higher precision than this value. The actual number of
photons was slightly higher, since the detctors required these values to be multiplied by a
correction factor from these indications (1.11 and 1.26, respectively, as linearly interpolated
from their datasheets). We also note that there is a fiber coupling loss of 3.6% at each of the
the input and output ends of the 797 nm fiber, based on the core index value of 1.48, obtained
from the optical fiber datasheets. Eliminating and compensating for the fiber coupling Fresnel
losses, we obtain an effictive coupling efficiency of 48.8%, which is significantly higher than
the 15% to 20% previously attained in the laboratory. It was also observed that at this high
coupling efficiency, all alignments were extremely sensitive, and even a slight change in the
objective focusing resulted in a sharp drop in efficiency. While these results have not been
reproduced since the setup was reconfigured, this is currently being investigated.
4.6
Summary
In this project, an optical table setup was constructed to investigate the effect of changing
the pump waist on the coupling efficiency of SPDC light into an optical fiber. Using a theory
inspired by Bennink et al. [21], we hypothesized that a high coupling efficiency would be
achieved when the divergence in the signal due to the pump matched the natural divergence of
the signal in the crystal, which occurs when the pump waist is -30.7 pm. In an experimental
setup designed to test this, we varied the pump focusing, carefully and extensively adjusting
and aligning all components to optimally mode-match the beam at every variation of the
pump focus. At a very specific waist setting that we could best measure to be 29 + 2 pm, we
achieved an effective coupling efficiency of 48.8% of the 797 nm SPDC light into an optical
fiber, a value significantly higher than previously achieved in the laboratory, and indicating
that a larger portion of the SPDC light is in a single optical mode. We hope to confirm this
measurement by reproducing it in a new setup, and utilize this knowledge in constructing a
Sagnac geometry entangled source at nondegenerate wavelengths, coupled into optical fibers
for both 797 nm and 1600 nm outputs.
5
Conclusions
Two separate projects were undertaken to try to improve technology for the generation of
entangled photons. In one project, a pulsed, mode-locked erbium-doped fiber laser, designed
to be used as a seed laser for a 390 nm source, was built using polarization-maintaining
(PM) fiber to address polarization drift in a previous non-PM version of the seed laser.
For the seed laser, we constructed a mode-locked pulsed laser with a repetition rate of 31.1
MHz, a center wavelength of 1560.0 nm, a tunable bandwidth (dependent on pump power)
from approximately 0.045 to 0.095 nm, and an output power from 1 to 2.5 mW. An erbiumdoped fiber amplifier (EDFA) and the first second harmonic generation (SHG) stage were also
attached to the setup. The EDFA amplified these pulses to an average power of 5 W, and the
first SHG stage yielded 3.3 W of output power at 780 nm (a conversion efficiency of -65%).
Since the seed laser was constructed from mostly polarization-maintaining components, its
output polarization was extremely stable over time. The second SHG stage remains to be
built and will complete the source. In a second project, motivated by the potential use of
SPDC in a Sagnac geometry to create an entangled photon source, we tried to optimize the
coupling efficiency of SPDC-generated light into single-mode optical fibers, which are useful
for transporting entangled photons. Using a setup with a tunable pump waist in a nonlinear
crystal, we measured the 797 nm signal coupling efficiency while making adjustments to all
parameters including fine-tuning the pump waist. We achieved an effective coupling efficiency
of 48.8%, higher than previously obtained in the laboratory, and hope to duplicate this result
and potentially construct a nondegenerate Sagnac geometry high-flux entangled source at
797 nm and 1600 nm.
6
Acknowledgements
A number of people should be acknowledged for making this research possible:
* Dr. Franco Wong, for supervising and advising all the work leading to this thesis.
* Onur Kuzucu and Taehyun Kim, graduate students whose earlier work led to the
problems investigated here, and who provided much help and advice in the laboratory.
* Jason Sickler, graduate student who provided advice and donated time to help use
his PM splicer.
* Jeff Chen, graduate student who allowed and helped me use his PM splicer, and
donated a section of Er-doped fiber for testing and use.
* Bryan Malinsky, Lincoln Laboratory employee who provided splicing help off-campus
after the other splicers were not in service.
This work was funded by the Disruptive Technologies Office (DTO).
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