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 EngineeringChairman, Department Committee on Graduate Theses

OFTECHNOLOGy

OCT 0 3 2007 ARCHIVESLIBRARIES

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 2007S ?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, de-signed to be used as a seed laser for a 390 nm source, was built using polarization-maintainingcomponents to address polarization drift. The fiber laser operated at a center wavelength of1560.0 nm with an output power of 1 to 2.5 mW, and mode-locked with a repetition rate of31.1 MHz. The laser also exhibited bandwidth tunability from 0.045 to 0.095 nm, as a func-tion of the input pump power. A commercial 5 W erbium-doped fiber amplifier and a secondharmonic generation crystal were used to obtain pulses at 780 nm with an average power of3 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 oflight generated from spontaneous parametric downconversion (SPDC) into single-mode opti-cal fibers, which are useful for transporting entangled photons. Using a setup with a tunable532 nm pump waist in a nonlinear crystal, we achieved an effective coupling efficiency of48.8% of the 797 nm signal light into a single-mode fiber, higher than previously obtained inthe laboratory. Efficient single-mode operation of SPDC would enable the construction of ahigh-flux fiber-coupled source of nondegenerate entangled photons at 797 nm and 1600 nm.

Thesis supervisor: Franco N. C. WongTitle: 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

2.3

Nonlinear optical processes . ...............

Nonlinear crystals and quasi-phase-matching techinque

3 Pulsed polarization-maintaining erbium-doped fiber laser

3.1

3.2

3.3

3.4

3.5

Motivation . .................

Overall design ................

Seed laser design ..............

Use of polarization-maintaining fiber . . .

Construction of the source . . . . . . ...

3.5.1 Pump diode set-up . . . . . . . ..

3.5.2 Gain fiber evaluation . . . . . . ..

3.5.3 Continuous-wave laser construction

3.5.4 From cw laser to pulsed seed laser .

3.5.5 Adjustment of the repetition rate .

. .. ... ...... ...... . 13

. .. ... ...... ...... . 14

... .. ...... ....... . 15

... . ....... ........ 1 7

.... ...... ......... 18

.... ..... ..... .... . 19

. . . . . . . . . . . . . 20

. . . . . . . . . . . . . 2 1

. . . . . . . . . . . . 22

3.5.6 Characterization of the seed laser . .................. . 26

3.5.7 Testing the Erbium-doped fiber amplifier . ............... 27

3.5.8 Construction of the second harmonic generation stages ....... . 30

3.6 Summary .......... ..... . .. .... . .... ....... 31

4 Spatial mode manipulation in spontaneous parametric downconversion 33

4.1 Mode-matching and fiber optics . .................. ... . 33

4.2 Optimizing the single-mode operation of SPDC . ............... 36

4.3 Experimental setup for optimizing coupling efficiency . ............ 42

4.4 Optimization procedure . ..... .............. .. . . . .. 44

4.5 Coupling efficiency results . . . ... ................ ... . . . 45

4.6 Summary ................... ... . ... ... ..... 46

5 Conclusions 47

6 Acknowledgements 49

1

2

3

4

5

6

7

8

9

10

List of Figures

Overall block diagram of the source ...............

Schematic of the seed laser. ..................

Comparison of standard and polarization-maintaining fibers

Pulsed regim es .........................

Spectrum of the seed laser ...................

Sample of bandwidth dependency on pump current . . . . .

EDFA output power as a function of EDFA pump current

EDFA output spectrum .....................

SHG output power as a function of SHG input power . . . .

Mode-matching example ....................

. .... ... . 15

. .... .... 16

. . . . . . . . . 17

. .... ... . 24

..... ... . 27

. . . . . . . . . 28

. . . . . . . . . 29

.... .... . 30

. . . . . . . . . 31

.... ... .. 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 situ-

ation 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 ob-

tained. 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 com-

munication. 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 pho-

tons 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 material-

dependent, and are useful for a wide variety of applications, including in our case, the gen-

eration of polarization-entangled photon states.

2.1 Basic theory of nonlinear optics

In conventional linear optics, the medium's induced polarization vector is linearly propor-

tional 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 pro-

cesses. The Kerr effect, for instance, is of interest to us in that it is unwanted in our experi-

ments. 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 phos-

phate (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 break-

down 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:

27rkpkski 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 non-

linear 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 har-

monic 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 commercially-

obtained 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 """" EDFA """t HG SHG ..... 390nm980nm 1560nm 1560nm 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 Er-

doped 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 high-

intensity pulses in the cavity, and with proper alignment, can be used to achieve a mode-

locking 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

matorieric 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 polariza-

tion 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 thecladding 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 out-

put coupler (Lightel PMC-S-12-9010-1550-1-B-0) and PM circulator (AC Photonics PMC-1-

1-5-1-10-1-0-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 mode-

locked 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 mode-

locking 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 LJ. I IQ-switching Double-pulsing Properly mode-locked

Figure 4: Pulsed regimes: In the Q-switching scenario, very large pulse envelopes are ob-served, repeating on the order of kilohertz, with underlying repeating pulses at the intendedrepetition rate. In double pulsing, the laser is mode-locked but starts with two pulses simul-taneously being amplified at each round trip. In a properly mode-locked scenario, consistentheight pulses are observed at the intended repetition rate.

laser cavity was cleaved apart at one point and a second circulator (AC Photonics PMC-1-1-

5-1-10-1-0-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 properly-

aligned 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 polarization-

maintaining 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 21:36SPECTRAL WIDTH : <ENUELOPE>THRESH LUL1 : 3.00dB K: 1.00 • : 0.090nm B:FIX /BLKTHRESH LUL2 : 13.00dB MODE : 1 C: 1559.882nm C:FIX /BLK

6.37pW/D RES:0.01nm SENS:NORII HLD AUG: I SMPL:AUTO

141

58.96

3822

25.48

12,74

UP81559.67nm 1559.92nm 0.05nm/D 1560.17nm

AUT AUT AUT VAC RER

Figure 5: Spectrum of the seed laser, measured by an optical spectrum analyzer, showinga bandwidth of 0.090 nm, driven with a pump current approximately 470 mA, and with ameasured 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,

i ;

.........: .........: ........ --- ...... 4 ..... •,•.......... •........... ............ -. ........... :............

.. .. .. .. ... i............, ........... i.... ......., ...... i ...........:,............i.............i ........... i............

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• ~ ~ . •! •i ...: ~~~ : i I ; i : : .

........... ,.............• ....... . . .J ........,.. L ........,.. .......... ,........... ,............ •............• ...........

........................ ... .......... --- . ........... r ...... ............... ............ ........... .

Sample of bandwidth dependency on pump current

E

cc

IU-

aoInput current (mA)

Figure 6: Sample of the bandwidth dependency on input pump current with the initialconstruction.

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

CL0.

0.

0

LL0LU

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 travel-

ling in the medium, greatly impacting the spectra of high-intensity ultrashort pulses. Typi-

cally, 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.

2BBT Apr 63 21:48PECTPL WIDWTH : <EIJELCPEDTHESiLULI 3.566 K : 1W WA B.172u OFIX 4B1KTS LUL213.B MOM MOD 2 AC 1559.87DmM IFIX 4LK

82. Or'S RES:B.B01n SWS: NORM HID 69.: 1 SPL: AUM

N.Z......... .0 .. 5.. ..... B B. ....... ..... ....IW32 ....... ....... ....... ........ ... .... .... ...... .. .. ... ... .... ... .... ..... .... ..

1559. 67rvr 1566.92. Q. 05WD 16M. 17raQW1121YL9t

Before modifications After modifications

Figure 8: Spectrum of the output of the EDFA when run at 6 A (approx. 5 W output power),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 0C, 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

2VT Apr 11 1S56SPCRA ID!H : 4EKEEUOPE> .0SLUU 3 . OW K: 08B.128M B:FIX 41K

7HR 1. WB MME I c C:FIX SLK0.3MAW/D FES:B.Blrin SENS:HIGI I AU: 1 SPL:6UTO

1639.75rm 15MB.Wru @.@5r. 15M.25r.rM 99s

IA402160

SMB

. .... ...

...... ........... .. ... ..... .. .....

. . . . . ... .... .. .. .. ....... ........... ...... ......

. ..... . ..... . ...... ...... ...... ......

II

EDFA pump power for a fixed seed laser power is shown in Fig. 9.

ECO

0.

COo:

SHG input power from EDFA (W)

Figure 9: SHG output power at 780 nm as a function of SHG input power at 1560 nmsupplied 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 paramet-

ric 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 high-

flux 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 single-

mode 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 single-

mode 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 single-

mode 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 2w0 , 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 appropriatelens. The fiber cladding is not shown. Non-collimated beams can also be mode-matched andrequire 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, re-

spectively, 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:

92 _6k2

ksz = kscosO, 2= k,(1 - -) = k8 2k8 (9)2 2 k,

where in the last step, the relation 0, = 6k,/k, has been employed. Likewise, for the idler,

kiz = kIcosi ki - -ki (10)2kh

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

where kp = kp for a collimated pump. Substituting for k,, and kiz gives:

Akz = kp - kq(1 - 6k)2k

2

8

sk2

202

Since kp - k, - k1 = 0, this relation simplifies to

6ks 6k2akz = . +2 k, 2 ki

Substituting this into Eq. 7 yields

6k2 6k2s +

2k, 2k (14)L

Eq. 8 can be used to simplify Eq. 7 to:

6k2 1 12 (k+ ) = (15)

(16)

which yields

s6k = kk 2-rxk, + ki L

7r

L'

kki 27rk, L

As mentioned earlier, 6k, is the transverse component of k, and determines the natural

(11)

(12)

(13)

divergence angle (half-angle) of the signal,

6ks ki 270• = = (17)s k I k, kL, L'(17)

and for the idler, it can be similarly derived that I6kjl = 16k,l, giving the natural divergence

angle of the idler,

6ks 6k8 k k, 2-7rOi = 1 1 = I I = = (18)

ki kk I I k kkpk L

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' + Ai1).

We note that k,8 2ki for this choice of wavelengths, such that Eq. 15 yields

6k1 = ',k (19)V 3L

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 - 20,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

divergence is then Op~ = ,,n, = 5.52 mrad. For a Gaussian beam, the divergence of a beam

is related to its waist (i.e. half-width at focus) wo by

0 = (21)

41

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 peri-

ods. 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 ad-

justments 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 erbium-

doped 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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