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Spring 2017

A Pound-Drever-Hall based Repetition RateStabilization Technique for Mode-locked LasersLiangyu ChenLiangyu.Chen@Colorado.EDU

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A Pound-Drever-Hall based Repetition Rate Stabilization

Technique for Mode-locked Lasers

by

Liangyu Chen

University of Colorado, 2017

A thesis submitted to the

Faculty of the University of Colorado in partial fulfilment

of the requirements for the degree of

Bachelor of Arts in Physics

Department of Physics

2017

This thesis entitled:A Pound-Drever-Hall based Repetition Rate Stabilization Technique for Mode-locked Lasers

written by Liangyu Chenhas been approved for the Department of Physics

Prof. Thomas Schibli

Prof. Tobin Munsat

Prof. Juliet Gopinath

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above

mentioned discipline.

iii

Chen, Liangyu (B.A., Physics)

A Pound-Drever-Hall based Repetition Rate Stabilization Technique for Mode-locked Lasers

Thesis directed by Prof. Thomas Schibli

Femtosecond mode-locked lasers have become one of the indispensable tools for spec-

troscopy and microwave generation for its capability to generate high-quality ultra-short

pulses, and thus optical frequency combs with a wide spectrum. Particularly, many applica-

tions of the optical frequency combs require the high spectral purity and long-term stability

of the combs, which are limited by the phase noise, or timing jitter, of the mode-locked lasers.

Therefore, several techniques have been successfully developed recently for stabilizing the

mode-locked lasers, although they suffer many drawbacks in the sense of applicability because

of their relative complex designs. In this thesis, an attempt to apply the Pound-Drever-Hall

technique, a powerful frequency stabilization technique for continuous wave laser, to the

mode-locked lasers is demonstrated with success. Our results indicate that with this simplified

and robust system, the repetition frequency of the mode-locked laser has been stabilized

and there is significant phase noise suppression at low frequency, and it is capable to reduce

the integrated timing jitter of the mode-locked laser by nearly four times without the need

of previously stabilized transfer lasers or RF signals as references. The success from this

stabilization system reveals the great potential of utilizing Pound-Derver-Hall technique

for future inspirations of a cost-effective and field-deployable system that could provide

state-of-the-art stabilization for the mode-locked lasers.

Dedication

To my dear friends and family, for their incredible support in the endeavour.

v

Acknowledgements

I would like to express my sincere gratitude to all the members of the Schibli’s Lab.

First and foremost, to Professor Thomas Schibli for his incredible mentoring that have guided

me to become a better researcher. I would like to thank Luke Charbonneau, a dear friend

and former graduate student from the lab, without whom this project wouldn not have been

possible. I would also like to thank Dr. Mamoru Endo for his incredible help during the final

stages of the project, and Tyko Shoji for his constant support as friend and colleague since

my first day working in the lab. Alas, there are many other who helped and supported me

along the path, I would like to thank everyone who has made this experience a wonderful

journey.

Contents

Chapter

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Microwave Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Long Distance Laser Sensing . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Dual Comb Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 The Basics of Mode-locked Lasers . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Mode-locking Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Active Mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.2 Passive Mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Noise of the Mode-locked Laser 10

2.1 Intensity Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Timing Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Timing Jitter Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.1 Comparing to Microwave Reference . . . . . . . . . . . . . . . . . . . 15

2.4.2 Using Intensity Electro-optical Modulation . . . . . . . . . . . . . . . 16

2.4.3 Optical Heterodyne Cross-correlation . . . . . . . . . . . . . . . . . . 19

vii

3 Laser Stabilization Technique 24

3.1 Passive Reference Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 The Pound-Drever-Hall Stabilization Technique . . . . . . . . . . . . . . . . 26

3.2.1 Conceptual Model of Pound-Drever-Hall . . . . . . . . . . . . . . . . 26

3.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.3 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.4 Noise Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Mode-locked Laser Stabilization Technique . . . . . . . . . . . . . . . . . . . 37

4 Experimental setup and results 41

4.1 500 MHz Modelocked Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Passive Reference Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Electro-optic Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.5 Environmental Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.6 Lock Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6.1 Noise Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.7 Phase Noise Measurement and Results . . . . . . . . . . . . . . . . . . . . . 54

5 Conclusion 59

5.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

References 61

Appendix

A Kigre Inc. Erbium-doped Ytterbium Glass, QX/Er Datasheet 65

viii

B Fiber-Based Lithium Niobate EOM-PM Datasheet 66

C Layertech Mirror Dielectric Coating Datasheet 67

Figures

Figure

1.1 Dual-comb spectrometer diagram . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 A schematic setup of an actively mode-locked laser . . . . . . . . . . . . . . 6

1.3 Progression of optical power and losses in an actively mode-locked laser . . . 7

1.4 A schematic setup of a passive mode-locked laser . . . . . . . . . . . . . . . 8

1.5 Progression of optical power and losses in a passively mode-locked laser . . . 9

2.1 Simulated intensity noise spectrum . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 A visual representation of timing jitter . . . . . . . . . . . . . . . . . . . . . 15

2.3 A block diagram for the intensity electro-optical modulation measurement

scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Optical heterodyne experimental setup . . . . . . . . . . . . . . . . . . . . . 20

2.5 Optical heterodyne cross-correlation experimental setup . . . . . . . . . . . . 21

2.6 Optical heterodyne cross-correlation discriminator signal . . . . . . . . . . . 22

3.1 The transmitted signal from a Fabry-Perot cavity . . . . . . . . . . . . . . . 27

3.2 The reflected signal from a Fabry-Perot cavity . . . . . . . . . . . . . . . . . 28

3.3 experimental schematics of a Pound-Drever-Hall stabilization technique . . . 29

3.4 The amplitude and phase of the reflection coefficient of the caivty . . . . . . 30

3.5 Reflection coefficient in the complex plane . . . . . . . . . . . . . . . . . . . 32

3.6 The PDH error signal with F = 447 cavity . . . . . . . . . . . . . . . . . . . 35

x

3.7 The PDH error signal with F = 3140 cavity . . . . . . . . . . . . . . . . . . 36

3.8 Concept for full frequency comb stabilization with two CW laser . . . . . . . 38

3.9 Experimental setup for full frequency comb stabilization . . . . . . . . . . . 39

4.1 A schematic of the experimental setup . . . . . . . . . . . . . . . . . . . . . 42

4.2 The circuit diagram for the PI servo loop filter . . . . . . . . . . . . . . . . . 46

4.3 The experimental environmental isolation setup . . . . . . . . . . . . . . . . 47

4.4 Transmitted signal without phase modulation . . . . . . . . . . . . . . . . . 48

4.5 Reflected signal without phase modulation . . . . . . . . . . . . . . . . . . . 49

4.6 Transmitted signal with phase modulation . . . . . . . . . . . . . . . . . . . 50

4.7 Reflected signal with phase modulation . . . . . . . . . . . . . . . . . . . . . 51

4.8 The experimental PDH error signal . . . . . . . . . . . . . . . . . . . . . . . 52

4.9 The transmitted signal through the reference cavity with lock engaged . . . . 53

4.10 The phase noise measurement results using the intensity electro-optical modu-

lation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.11 The phase noise measurement results using the optical heterodyne cross-

correlation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Chapter 1

Introduction

The goal of this project is to suppress phase noise and timing jitter of a mode-locked

laser with a PDH based setup. The frequency lock should be sensitive, robust and have long

term stability, and the setup does not require building other lasers or mode-locked lasers as

reference. The thesis will outline the motivation and the background of this project, including

a introduction to the properties of mode-locked lasers. In chapter 2, the different sources of

noise will be introduced and analysed, including a focused discussion on the timing jitter. In

chapter 3, the Pound-Drever-Hall stabilization technique will be introduced and explained

with conceptual and quantitative models. In chapter 4, the experimental setup of this project

will be detailed as well as an analysis of the result. In chapter 5, an outlook will be provided

for possible improvements.

1.1 Motivation

Lasers have been essential tools in science and technology since the successful demon-

stration in 1960. Many exciting developments followed shortly after as researchers poured in

with numerous ideas on its improvements and possible applications. The mode-locked laser,

or frequency comb, was one such amazing product developed by Hargrove in 1964 [1]. It

is capable to produce pulse trains consisted with ultra-short pulses with incredible spatial

coherence. The magnificent invention enabled novel investigations in the field of spectroscopy,

metrology and microwave generation that requires a very quiet and stable source that normal

2

lasers simply could not provide. Therefore, it is crucial to continuously refine and improve

upon the outstanding capability of the mode-locked laser. In practice, the effort is focused

on stabilization and noise suppression of the mode-locked laser, especially focusing on the

timing jitter that could disrupt a perfectly periodic pulse train that many applications depend

greatly on. Currently, there are many successful stabilization techniques developed for the

mode-locked laser involving full frequency comb lock. Although these stabilization techniques

can achieve significant noise suppression, they are usually very complex and difficult to

construct, therefore limiting the options for possible applications. Examples of effort to

reduce the complexity and improve the applicability of the system will be presented later, as

a recurring theme in either continuous wave laser or mode-locked laser stabilization technique.

As a commonality, they usually required previously frequency stabilized continuous wave

lasers, using a powerful technique called the Pound-Drever-Hall technique, as references

for the frequency comb. Therefore, this project will attempt a different path from these

well-established methods and employ the Pound-Drever-Hall technique to the mode-locked

laser without any intermediate steps, stabilizing its repetition frequency directly. This method

would significantly reduce the complexity, and in turn, enable more on-field applications for

mode-locked laser with appreciable timing jitter and phase noise suppression.

1.1.1 Microwave Generation

Low noise microwave signals are highly desired to improve metrology, radar and

telecommunication. Traditional microwave generation method such as cryogenic sapphire

oscillator that requires a vacuum chamber and cooling to a few kelvin is very costly to

construct and maintain [2]. As a better alternative, mode-locked lasers are used in microwave

generation by converting their repetition rate to a RF microwave signal via a photodiode.

Through this way, essentially the relatively high stability of the mode-locked lasers are

transferred down to microwave without the space and cost to maintain a vacuum chamber.

Therefore, as the stability of the pulse train directly determines the quality of the microwave

3

signal, it is essential to suppress the timing jitter and stabilize the repetition rate of the

frequency comb as good as possible and ensure long term stability. Also, as the applications

for microwave generation are plenty, a portable and efficient system is mostly desired, further

motivate the attempt of this project.

1.1.2 Long Distance Laser Sensing

Because of its long coherence length, mode-locked lasers have been used in ultra long

distance metrology. For example, intra-satellite ranging, which are of great relevance for

space missions [3]. It have a very specific requirements and constrains on accuracy, sampling

rate, flexibility, complexity and reliability, which greatly limit the options of designs and level

of stabilization and mode-locked laser is among the best candidates for its superior spatial

coherence from ultra pulses. This serves as another neat example for the need of a robust

and reliable stabilization system that is capable of significant phase noise suppression.

1.1.3 Dual Comb Spectroscopy

Spectroscopy is a powerful technique in understanding the mechanics of elements and

chemicals. In particular, their vibrational, rotational and low frequency modes. It is also one

of the most important applications of femtosecond frequency comb. Traditional spectroscopy

method requires mechanical components, such as a scanning mirror mounted on a movable

stage, which could be a limiting source of noise. The latest the method in spectroscopy

utilizes the frequency combs of two mode-locked laser, eliminating any mechanical part in the

system [4]. The two frequency combs have a slight mismatched repetition rate depending on

the sample. The setup essentially is an interferometer of these two lasers, and the combined

light is sent through the sample. Any absorption from the sample will reflect in heterodyne

spectrum. This method provide much faster sampling rate, higher resolution and less noise

than any other mechanical method, and relying on the best stabilization technique that could

suppressing the timing jitter in the repetition rate to function at best performance. However,

4

employ a state-of-the-art stabilization technique on two sets of the mode-locked laser would

be an enormous effort, therefore, a simplified and effective noise suppression system will be

very appreciable.

Figure 1.1: A dual-comb spectrometer uses another comb rather than scanning mirrors as

the reference arm for the first comb. The scan rate and resolution is much higher than other

method in spectroscopy.

1.2 The Basics of Mode-locked Lasers

Mode-locked lasers are capable of producing trains of ultra-short pulses on the order

of picoseconds or femtoseconds in time domain [5]. This is achieved by maintaining a fixed

phase relationship between the longitudinal modes of the cavity. In contrast, a multi-mode

continuous wave laser would have a random phase relationship between the modes, therefore

the output would be a random interference pattern between the modes repeated every round

trip time in the cavity. In a mode-locked laser, ideally all the different frequencies oscillating

in the cavity will constructively interfere at one point and destructively interfere at everywhere

else. This will create a pulse circulating around the cavity rather than a continuous wave.

Thus repetition rate of this pulse train is essentially the free spectral range (FSR) of the laser

cavity, is simply found with:

frep =1

τ=

c

2L(1.1)

5

where τ is the cavity round trip time, c is the speed of light in the cavity medium and

L is the geometric length of the cavity.

Similar to the result of a Fourier transformation from time domain to frequency domain,

each pulse will contain a wide range of frequencies that are allowed by the cavity modes,

essentially creating a frequency comb consisting of the resonant frequencies of the cavity.

Thus each frequency component, or ”comb tooth”, in the frequency comb can be found with:

f(n) = f0 + nfrep (1.2)

where f0 is the offset frequency of the carrier envelope, and n is an integer that represents

a specific ”comb tooth”.

f0 of the pulse describes the phase difference between the carrier wave and the envelope.

There is a certain change in the envelope phase each round trip in the cavity and thus can be

related to the repetition frequency as:

f0 =∆φCEO mod 2π

2πfr (1.3)

where the mod 2π term means the fact that only the modulus 2π phase shift between

the carrier envelope and carrier phase, per round-trip, is relevant. The f0 stabilization is

important in full frequency comb lock, and will be explained in chapter 3, section 3.3.

Ideally, the repetition rate will remain constant during laser operation. However,

in practise, there are many possible sources of noise that could disrupt the perfect pulse

production. The focus of this project is to reduce the the timing jitter of the mode-locked

laser, which, simply put, describes the deviations of the temporal pulse position from those

in a perfectly periodic pulse train [6]. This thesis will continue to examine this type of noise

and the implement a stabilization technique based on the Pound-Drever-Hall approach.

6

1.3 Mode-locking Techniques

There are two major categories of mode-locking techniques: active and passive mode-

locking. At the start they are both in normal laser operation, producing a continuous wave

laser with random phase between different cavity mode. These techniques create a locked

phase relation from there through different means.

1.3.1 Active Mode-locking

In active mode-locking, an amplitude modulator is utilized, which amplified the pulse at

frequency at the free spectral range of the cavity all the cavity modes are linked to the phase

of this modulation, after a few thousands operations, pulses from the interference between

cavity modes are created inside the cavity. Then the selection process begins: the pulse pass

through at the correct times would experience minimum losses, and vice versa for the other

undesired pulses, creating a steady pulse oscillating around the cavity with the phase set by

the initial modulation signal.

Figure 1.2: A schematic setup of an actively mode-locked laser [7].

This method provides pulse shortening only to a limited extent, as there is a little

attenuation to the tails, but would be eventually offset by other effects such as gain narrowing

that could broaden the pulse [8]. Additionally, this pulse shortening effect is even less

effective for shorter pulse durations, thus essentially limits the pulse duration on the order of

picoseconds[8].

When compared with the later passive mode-locking in the field of ultra-fast optics,

7

active mode locking is at a disadvantage for the requirement for an optical modulator and

only capable to generate longer pulses. Therefore, it is mostly used when there is a need to

synchronize the pulse with a electronic signal or with other lasers, such as the cases in optical

fibre communication or laser array sensors.

Figure 1.3: Progression of optical power and losses in an actively mode-locked laser. The

modulator causes some losses for the pulse tails, effectively shortening the pulses [7].

1.3.2 Passive Mode-locking

As an improvement upon the active mode-locking, passive mode-locking incorporates

a saturable absorber into the laser resonator. The saturable absorber has a certain optical

loss at low optical intensities, which is then reduced at high intensities[9], essentially being

”saturated” with intense light.

8

Figure 1.4: A schematic setup of a passive mode-locked laser using a saturable absorber

mirror [7].

This saturation effect can occur in semiconductors, which will reduce the absorption for

photons above the bandgap energy when most of its electrons are excited into the conduction

band [9]. In passive mode-locking, a semiconductor saturable absorber mirror, or SESAM, is

commonly used for this purpose. The SESAM will attenuate low intensity light, creating a net

losses for the continuous wave light, and when a high intensity pulse is formed, it will saturate

the SESAM and experience a low loss. Thus, a short window of positve net-gain is formed

[5]. Meanwhile, as the tails of the pulse will have lower intensity, it has a pulse-shortening

effect as long as it can relax to the ground state quickly enough so that it could absorb

again before the arrival of the next pulse. Comparing to active mode-locking, utilizing the

saturable absorber allows the generation of much shorter pulses, on the order of femtoseconds,

as the saturable absorber can provide a much faster loss modulation than any electronic

modulator could achieve [5]. However, if the saturable absorber does not have the appropriate

properties, there can be many possible issues relating to passive Q-switching, which can incur

massive energy fluctuations in the laser cavity or other unstable mode of operation. Careful

consideration must be made in the construction of a passive mode-locked laser [5].

9

Figure 1.5: Progression of optical power and losses in a passively mode-locked laser with a

saturable absorber. The shorter the pulse, the faster the loss modulation will become. The

gain stays approximately constant, as the saturation of the gain medium is less noticable [7].

Passive mode-locked laser has been at the frontier of ultra-fast optics ever since its

invention. It is another key ”enabling technology” as scientists and engineers have given to

the invention of laser, providing us a new powerful tool to the understanding of our universe.

Chapter 2

Noise of the Mode-locked Laser

In this chapter, the types and sources of noise in a mode-locked laser system will be

explored and analyzed in order to understand what issues a stabilizing system needs to

address. Noises can generally be categorized into two major categories: quantum noise, which

is closely related to the spontaneous emission of photons in the gain medium, and technical

noise, which originates from the components and laser system construction, including the

noise from the pump source, from mechanical vibrations of the mirrors or from thermal

fluctuation [10]. At the end, three measuring methods for the timing jitter in mode-locked

laser are introduced with emphasis on the optical heterodyne cross-correlation technique,

which is the most sensitive of the three.

2.1 Intensity Noise

Intensity noise describes fluctuations in the laser output power of the laser. To measure

intensity noise, one would simply monitor the fluctuation of the output power over a desired

time interval using a photodiode. In experiments, the intensity noise is usually quantified by

the root-mean-squared value of the output power fluctuations [11], which is calculated with:

δPrms =√〈(P (t)− Pavg)2〉 (2.1)

where Pavg is the average power[11].

11

As a laser can exhibit different rate of power fluctuations, the bandwidth of the

measurement devices could underestimate or distinct the noise at different frequencies.

Therefore, a power spectral density (PSD) is most useful in this case by measuring noise at

different frequency intervals in order to display the spectral distribution of the total noise

power.

From the power spectral density measurement, one can calculate the r.m.s. relative

intensity noise with:

dP

Pavg

∣∣∣∣rms

=

√∫f2f1SI(f)dt (2.2)

where f1 and f2 are the lower and upper noise frequency bonds for the interval, respectively,

and SI(f) is the power spectral density over that frequency interval [11].

In solid-state and in most diode lasers, there is a characteristic peak in the relative

intensity noise called the relaxation oscillations, which result from the dynamic interaction

between the energy in the light-field an the stored energy in the gain, if the excited-state

lifetime is much longer than the cavity damping time [12]. These under-damped oscillations

are a fine example of quantum intensity noise. In the frequency domain around fro, the

laser is highly sensitive to external perturbation. At frequencies well above fro, external

perturbations are strongly suppressed and follow a second-order low-pass-filter characteristic.

The impact of this quantum noise depends on many parameters. It can be minimized with

high intractivity powers, low resonator losses and a long round-trip time inside the cavity, all

of which had to do with the damping of the relaxation oscillations [11].

Another common noise source is the mode beating in the resonator when the laser is in

multi-mode operation. The frequency of the beat is strongly dependent on the laser type,

ranging from several Ghz for diode lasers to a few kHz for long fiber lasers [10]. However,

this does not play a role in mode-locked lasers.

At last, to minimize the intensity noise of the laser, there are many possible methods.

The first approach is to minimize any external influences on noise, such as using a low

12

Figure 2.1: Simulated intensity noise spectrum of a diode-pumped solid-state laser. Graycurve is plotted with a quantum-limited pump source. Red curve has a 30 dB excess noisefrom the pump source. Figure used with permission from Dr. Rdiger Paschotta [11].

noise pump source and constructing a mechanically stable laser system[10]. Secondly, one

can optimize the laser parameters to mitigate the effect of quantum noise by adjusting

the relaxation oscillation frequency into a less noisy domain or using a long low-loss laser

cavity[10]. Finally, the noise can be actively countered with a feedback system stabilizing the

output power. The potential of these methods greatly depends on the circumstances.

In the end, the ultimate limit of the intensity noise is the quantum shot noise, which is

basically the random occurrence of photons as discrete packets of energy[10]. In common

scenarios, the measured noise floor will be well above the quantum shot noise. However,

in ultra-fast optics experiments, it is quite often that we are trying to measure the noise

much below the quantum noise floor. or at least hope to achieve. As quantum shot

noise is proportional to the square-root of the average output power that falls onto the

photodector, essentially it is the signal-to-noise ratio of a Possion distribution, SNR =√N .

13

The photodetector often sets a piratical upper limit for the output power one can detect, so

that shot noise would often show up as the measurement noise floor.

Therefore, it is prominent at low optical intensity, and thus must be taken into consid-

eration when taking measurements.

2.2 Phase Noise

Phase noise describes the phase fluctuations of the electromagnetic waves of the laser

output. The present of the phase noise results in a finite linewidth in the frequency domain

for each frequency component in the laser output, and leads to a finite temporal coherence of

the laser. To have a numerical perspective, the coherence length could be merely centimetres

for a humble laser pointer, but could be of the order of millions of kilometers for single-mode

operation continuous wave lasers or mode-locked lasers depending on specific designs [13].

Fundamentally, the origin of the phase noise is again quantum noise that arises from the

spontaneous emission of the gain medium. The spontaneous emission essentially generates

photons with random phase and polarization, unlike the desired stimulated emission which

generates photons with the same polarization as the previous ones that are already oscillating

in the laser cavity. Additionally, it can be affected by other technical noises like the intensity

noise, which may lead to the coupling of those two noise [6].

In practice, phase noise is generally measured and quantified using a phase noise power

spectral density (PSD), Sφ(f). It is also common to use a frequency PSD to better understand

the phase noise. These two are directly related by:

Sν(f) = f 2Sφ(f) (2.3)

where Sν(f) is the frequency PSD and f is the respective offset frequency from the

carrier frequency [13]. It is derived from the fact that phase noise and frequency noise are

really the creation of one source, just a matter of perspective:

14

φ(t) =

∫f(t)dt (2.4)

f(t) =dφ(t)

dt(2.5)

In order to acquire data on phase noise one usually has to compare the desired source

with a known oscillator, preferably one with less noise than the source, and measure the beat

signal between them. This reference oscillator could also be another laser with the same

parameters or part of the same laser output with a known delay [6].

2.3 Timing Jitter

Timing jitter is another classification of noise in mode-locked lasers, which is commonly

discussed in the context of ultra-fast optics or microwave oscillators. As the output of a

mode-locked laser is a pulse train with repetition frequency, frep, the timing jitter describes

the deviations of the pulse position in time domain from a perfectly periodic pulse train,

as shown in figure 2.2[14]. It is mostly related to the phase noise corresponding to each

frequency component of the pulse train with a factor of the quantity square of the oscillator

frequency, f 20 . To be more precise, the timing jitter does not depend on f 2

0 , but the phase

noise does. Great effort has been made by Haus et al. in 1991 to tackle the timming jitter

with mathematical model in order to understand this problem more thoroughly [15].

Many other effects and noises can contribute to timing jitter in a mode-locked laser. It

can be affected by center frequency shifts as the same in a continuous wave laser, due to the

spontaneous emission form the gain medium. This will lead to a corresponding random shift

in the pulse position and changes in group velocity [15]. Timing jitter can also couple to the

intensity noise of the mode-locked lasers through the saturable absorber depending on its

recovery rate [15].

15

Figure 2.2: A visual representation of timing jitter. Case A shows a perfectly periodic pulsetrain. Case B shows a pulse train with timing jitter. Small pulse to pulse variations can resultin a large timing drifts on the pulse train. This is the characteristic of a random walk[14].

2.4 Timing Jitter Measurements

As a focus of this project, it is essential to have suitable methods to measure the timing

jitter of a laser. In this section three measuring methods will be examined. The later two

will be utilized in this project for the final measurement.

2.4.1 Comparing to Microwave Reference

This is the traditional method of measuring timming jitter developed in the early

days of active mode-locking, and the resolution is quite limiting. The pulse train from the

mode-locked laser is converted to RF signal at the frequency of the repetition rate of the laser

via a photodector. This signal is mixed with an electronically generated microwave signal

ideally at exactly the same frequency as the repetition frequency of the mode-locked laser [14].

16

The mixer essentially calculates the product between those two signals and the output will

be measured using a signal analyzer to get the power spectral density of the phase noise of

the device under tested. The sensitivity of this right straightforward method mostly depends

on the quality of the microwave reference. The sensitivity and resolution also depends on

the measurement bandwidth of the specific methods, but the carrier frequency is the most

important and limiting factor. Therefore, the resolution of the microwave reference method

with carriers on the order of Mhz, is pale in comparison to the optical methods comparing to

other lasers, utilizing the optical frequency as the carrier which is on the order of hundreds

of Thz.

2.4.2 Using Intensity Electro-optical Modulation

This method was developed in Schibli’s Lab, utilizing an ultra-stable low-noise 1 GHz

monolithic mode-locked laser, which is the only one of its kind in the world, also developed

in Schibli’s Lab. It is a rigid, one-piece, mode-locked laser with no mechanical parts. The

cavity is made out of the calcium fluoride CaF2 crystal which has low thermal expansion and

ultra high transparency, which length can only be controlled via thermal expansion. Thus,

the monolithic laser has ultra-low noise and ultra stable.

As a specific example with schematic shown in figure 2.3, our stabilized 500 MHz

mode-locked laser will first need to double its repetition frequency to have a main carrier

of1 GHz by using an optical interleaver, essentially overlapping one half of the pulse train

onto the other one delayed by a half of the round trip time in the laser cavity, which is 2 ns

for the 500 MHz laser.

Then, the light from the 500 MHz laser, now doubled to 1 GHz , is converted into a

RF signal via a photodiode. At the other end, the light from the 1 GHz monolithic laser is

sent into an intensity electro-optical modulator (EOM) with dual output. At the modulator,

due to its operation method, there is an output only if when a light pulse from the 1 GHz

monolithic laser is present, providing a regular sampling rate of the RF signal. After the

17

modulator, the two beams are focused onto a pair of balanced photodetectors. Ideally, if the

two photodiodes are well balanced and there are no RF signals applied to the modulator,

the signal from the balanced detectors should be exactly zero. Then, the RF signal from

the 500 MHzlaser is applied onto one arm of the electro-optical modulator. There will be

a sinusoidal discrimination signal from the balanced detectors, and the two lasers will be

loosely locked so that a 90 degrees relative phase difference between the two is maintained.

18

Interleaved 500 MHz MLL(1 GHz carrier output)

Ultra-stable Monolithic MLL(1 GHz carrier output)

(Fiber Couple) (Fiber Couple)

Dual-outputIntensity

EOM

(RF Input)

(Slow PZT)

Spectrum Analyzer

PI Servo to lock carrier

RF Amp

Figure 2.3: block diagram for the intensity electro-optical modulation measurement scheme.

The red solid lines represent optical beam (in fiber or wave guide) paths and the dashed black

lines represent electrical connections. [16]

19

For the noise measurement, at the output of the balanced detectors, if the two lasers

are perfectly quiet, the output will remain exactly zero. Therefore, any phase noise in the

RF signal will create a relative phase shift between the carrier frequencies of the two lasers

causing they to overlap, thus this frequency noise will be converted to intensity modulation

which would offset the balance. This offset then will be measured and recorded by the RF

signal analyzer. As EOM the essentially mix the signal down to DC with no carrier frequency

presented, it requires less dynamic range on the signal analyzer, allowing it to make more

accurate measurements comparing to measuring the noise at the 1 GHz carrier frequency.

Improvements and rigorous tests based on this method is still being conducted in

Schibli’s lab. Currently, the effort on suppressing the quantum shot noise and other technical

noise like the thermal noise has been successfully employed via creating multiple channels

of uncorrelated light paths and using two pairs of balanced detectors rather than a single

pair. After these improvements, the current limiting factor on noise measurement is the 1/f

flicking noise in the electro-optical modulator, which could only be improved by designing

better modulators or by using the cross-correlation techniques which will be introduced next.

2.4.3 Optical Heterodyne Cross-correlation

This is another method developed in Schibli’s lab, improved upon the optical heterodyne

technique. The optical heterodyne technique essentially compares the frequency components

from two uncorrelated mode-locked lasers [17]. This technique is conceptually simple and

extremely sensitive, capable of achieving less than 1 zs/√Hz resolution [17].

20

Figure 2.4: Experimental setup for the optical heterodyne technique [17]. The two lasers are

two 500 MHz mode-locked lasers with the same parameters. HWP, half-wave plate; QWP,

quarter-wave plate; BS, beamsptlitter; PBS, polarizing beamsplitter; LFP, low-pass filter;

LN-AMP, low-noise amplifier.

As stated, the current phase noise measurement setup used in this project is a improved

version of the one shown above, displayed in the schematic 2.5, introducing two more uncor-

related light path and have cross correlation between two pairs of balanced photodetectors

instead of one pair.

21

1GHz Monolithic Mode-Locked Laser

500MHz Mode-Locked Laser

∆2

QWPHWP

LPF

LPF

Mixer

PBS Lens

Photodiode

Grating

BoardbandMirror

LN-AMP

Collimator

LPF

Piezo Driver

Loop Filter

RF Signal Analyzer

Polarization Maintaining Fiber

PBS

PBS

Grating

Collimator

Figure 2.5: The curent experiemental setup for the optical heterodyne technique. HWP,

half-wave plate; QWP, quarter-wave plate; PBS, polarizing beamsplitter; LFP, low-pass filter;

LN-AMP, low-noise amplifier.

In this setup, the 1 GHz monolithic mode-locked laser in our lab is used as a reference.

The beams from the two lasers are first combined via a polarizing beam splitter with one

beam horizontally polarized while the other one is vertically polarized. The combined beam

is shone onto a diffraction grating to acquire the board spectrum. Another grating is used

here to recollimate the spectrum to parallel beam in order to avoid astigmatism at the cost of

around 43% of the total optical power. Then, the light passes through a half wave plate with

optical axes at 22.5 degrees with respect to the horizontal, essentially totalling polarization

by 45 degree. Afterwards, the spectrum is cut in halves using a high-reflectivity boardband

22

gold mirror. Each half of the spectrum is separated in two arms using another polarizing

beam splitter; one of the halves have an extra quarter wave plate in place to ensure there

is a 90 degree phase difference between the two arm so that the final discrimination signal

is sinusoidal and only have one zero-crossing which can be used as a locking point for the

feedback circuit. Then, the two beams from each half after the polarizing beam splitter are

focused onto a pair of balanced photodetectors respectively.

-0.10

-0.05

0.00

0.05

0.10

Vol

tag

e (V

)

400x10-62000-200

Time (S)

Figure 2.6: A example of the measured discriminator signal that is used as feedback to theloop filter.

When power on each photodiode is balanced so that the the DC output of each pair

of photodiode is zero, the signal is without signal from the carrier frequency and are left

with phase noise and offset frequency from each laser. A 120 MHz low-pass-filter is put

23

place between each pair of balanced detector and the mixer to block the beats between the

offset frequency which is above the Nyquist frequency. When the repetition frequencies of

these two laser are really close, the 500 MHz mode-locked laser is locked to the zero-crossing

in discriminator signal from the mixer, as shown in figure 2.6. The in-loop residual noise,

which is essentially the timing jitter between the two lasers, will be measured by a RF signal

analyzer. Comparing with the previous electro-optical modulation method, this method

directly compares the lasers at optical frequencies instead of converting to a RF carrier

frequency, thus have a greatly improved sensitivity. The benefit of having two pairs of

balanced detector is that: first, through optimization of optical compoenents, more light

can be collected in this method than in the original optical heterodyne method, increasing

signal to noise contrast; secondly, as there are now four light paths instead of two paths, the

polarizing beam splitter uncorrelated the quantum noise between each path, so the average of

the four can reduce the quantum noise; thirdly, similar to the last point, the thermal noise is

also uncorrelated between them, so the thermal noise will also decrease. Therefore, by using

crossing correlation between two pair of balanced detectors, much of the the technical noise

and quantum noise from the measuring devices. There are also many optimization along the

light path so more percentage of the light can be measure, further increase the signal to noise

ratio. Therefore, this method is capable of higher sensitivity and less systematic noise than

the other methods presented here.

Chapter 3

Laser Stabilization Technique

In this chapter, the idea of using an Fabry-Perot cavity as a passive reference is

introduced and explored. More will be dedicated on the Pound-Drever-Hall technique to

stabilize continuous wave lasers, including the conceptual understanding, experimental setup

and mathematical explanation. At the end, other current mode-locked laser stabilization

technique will be examined and compared.

3.1 Passive Reference Cavity

The fundamental idea behind most laser stabilization techniques is to have a much

quieter reference, so that when comparing to the reference, the measured noise is ideally

equal to the absolute noise from the laser. Therefore, the idea of using a passive reference

cavity as reference becomes fairly straightforward, which is essentially a much more stable

copy of the laser resonator, with no amplified spontaneous emission, no heat induced and

very little optical loss. This type of optical cavity made of two parallel mirrors is also called

Fabry-Perot cavity for its first appearance in the field of optics as Fabry-Perot interferometer

in 1899.

Today a Fabry-Perot optical cavity is usually made of two parallel planoconcave high-

reflectivity mirrors, in order to eliminate reflection loss and degenerate modes. Only when

the laser frequency is the same as or integer multiple of the resonance of the cavity, the light

could be coupled into the cavity and form a standing wave. Light that is not on resonant

25

would simply be reflected by the first mirror before it even enters in the cavity. The cavity

spaces needs to have low thermal expansion to prevent long term dirft. Mathematically, one

can find the change in length due to thermal expansion of the material using:

∆L ≈ αL∆TL (3.1)

where αL is the linear thermal expansion coefficient of the specific material, ∆T is the

temperature difference in kelvin. L is the distance between the mirrors [18].

This effect would become noticeable if the cavity is significantly shorter or having a very

high finesse. In these cases, the thermal expansion and the Brownian motion of the mirrors

becomes the limiting noise floor of the cavity. For most cases, the mechanical vibration of

the mirrors and the thermal fluctuation of the medium in the cavity contributes the most to

its noise, and this greatly depends on the quality of environment isolation of the cavity.

Another important property of the cavity is the Q-factor, which is commonly used

to describe the ”sharpness” of the resonance of a resonator. The higher the Q-factor, the

narrower the linewidth around the resonant frequency, and the higher the first order resonance

will be in amplitude [19]. In the case of an optical cavity, it is related to the finesse of the

cavity, which describes the optical losses for the light oscillating within the cavity, and found

by using:

F =c

2nL

∆ν 12

=π(r1r2)

14

1− (r1r2)12

(3.2)

where F is the cavity finesse, c2nL

is the free spectral range, ∆ν 12

are the full spectral width at

half-maximum, n is the index of refraction of the medium in the cavity, L is the length of the

cavity and r1 and r2 are the power reflectivity of the two mirrors in the cavity, respectively

[19].

26

And then the Q-factor can be found with:

Q = ν0Trt2π

l=

ν0

FSRF (3.3)

where ν0 is the optical resonance frequency and Trt is the round trip time, l is the fractional

optical power loss per round trip [19].

A high finesse cavity in laser stabilization is always appreciable in Pound-Drever-Hall

technique that will be discussed later, as this will increase the sensitivity to frequency shift

in the discrimination signal and thus can provide a better feedback.

3.2 The Pound-Drever-Hall Stabilization Technique

In this section, the Pound-Drever-Hall technique to stabilize continuous wave lasers

will be explained in details, including the conceptual understanding, experimental setup and

mathematical explanation.

3.2.1 Conceptual Model of Pound-Drever-Hall

Since the early days of laser technology, there have been many attempts to stabilize

lasers with a passive reference cavity. These early techniques mostly relied on the transmitted

signal from the cavity to provide the feedback to the laser [20]. The basic idea was that the

transmitted signal would be maximized if the laser frequency is on resonance. The major

problem is the coupling of intensity noise and frequency noise, as the deviation from the

maximum power could be caused by either the fluctuation in intensity or a drift in center

frequency. Therefore, such an error signal would not be robust. One approach to this problem

is to stabilize the laser intensity separately, which has been done with some success in the

seventies. As shown in figure 3.1, this signal is symmetrical around the resonant frequencies

that are integer multiple of the free spectral range. Thus, one can also employ the side-fringe

locking technique, which use the slope on either side of the transmission peak, where changing

27

frequency has a much larger effect on power transmission than intensity fluctuation [20].

However, besides the fact that this error signal still couples to the intensity noise, it also

suffers from the narrow locking range. It will easily break if the frequency drifts from one

side of the center frequency to the other side [20].

Figure 3.1: The transmitted signal from a Fabry-Perot cavity as a function of frequency inthe unit of free spectral range. The cavity has a very low finesse to display the features moreeasily [21].

A improved stabilization technique was demonstrated by R. Pound, R. Drever, and

John L. Hall in 1983, utilizing the reflected signal from the cavity instead of the transmitted

signal, and it is able to decouple the intensity and phase noise of the laser [22]. As shown in

figure 3.2, the reflected signal is zero when the laser is on resonance, regardless of the laser

intensity. Although the signal is still symmetrical around the resonance, thus, one can not

simply tell which side of resonance by measuring the amplitude [21]. However, the derivative

of this signal is asymmetrical, being positive above resonance and negative just below the

resonance, thus it can be utilized as an error signal used to lock the frequency at resonance.

Also, it is can be realized in practice as well: one can just dither the laser frequency with a

28

small variation and monitor the amplitude response, essentially measuring the slope with a

small df [21]. This conceptual idea only really works when the frequency detuning is slow

enough for the cavity to completely respond [21]. Otherwise, the output will not follow the

curve shown in figure 3.2 [21]. Although, the technique will still work at higher modulation

frequencies, and both the noise suppression and loop bandwidth will be improved [21].

Figure 3.2: The reflected signal from a Fabry-Perot cavity as a function frequency. If thefrequency is modulated with a small shift, one can tell from the slope that which side ofresonance the frequency is on [21].

3.2.2 Experimental Setup

The Pound-Drever-Hall technique aims to achieve this purpose experimentally. As

shown in figure 3.3, the light from the stabilization target laser is modulated with a small

frequency variation via an electro-optical modulator driven by a local oscillator [22]. The

modulation frequency needs to be well outside the linewidth of the cavity, which is in term

determined by its finesse, so it would completed reflected from the cavity. Then, the beam

enters the cavity: the frequency component that is on resonance will form a standing wave in

the cavity, transmitting a leakage signal out of the cavity. The transmitted light on the far

29

side will be monitored, and the one on the entry side will destructively interfere with the

light reflected from the first mirror of the cavity, whose amplitude depends on the frequency

detuning of the laser [22]. The optical isolator, usually a polarizing beamsplitter and a quarter

wave plate, picks up the reflected beam and sends it to be collected by a photodetector. The

output from the photodetector is compared with the local oscillator signal via a mixer [22].

The output of the mixer is essentially the product of the reflected signal and the modulation

signal, so the output contains a low frequency signal, which has the information about the

derivative of the intensity, and twice the modulation frequency. Then, there is a low-pass

filter to isolate the low frequency signal, and send it to the feedback loop to tune the laser,

locking it to the reference cavity [22].

The optical isolator, together with a Faraday isolator at the input, can prevent any

reflected beam to re-enter the laser cavity, which could destabilize the laser. The phase shifter

between the local oscillate and mixer provides a 90 degrees phase difference between signal

sent to the modulator and the mixer.

Figure 3.3: A basic outline of the Pound, Drever, Hall (PDH) stabilization setup. Solid linesrepresent the beam’s path, whereas dotted lines represent electronic connections [22].

The reflected beam, as briefly mention above, is actually a result of interference between

two different beams: one is the beam reflected from the first cavity mirror, which never

30

entered the cavity. The other is the leakage light from the standing wave oscillation in the

cavity. For a lossless symmetric cavity, they will have the same frequency and their intensities

are almost the same as well, depending on the choice of cavity mirror [21]. However, their

relative phase depends greatly on the the frequency of the laser with respect to the resonance

[21] as shown in figure 3.4. In the case when the laser frequency is perfectly the same as the

cavity resonance, the beams have the same amplitude and exactly 180 degrees out of phase,

and thus they completely destructively interfere and the reflected signal will be exactly zero

[22]. If the laser frequency is off resonance or integer multiple of the resonance, but near

enough than some light could oscillating in the cavity, the beams will not have exact 180

degree phase difference, so they could not cancel each other out. The phase of this resulted

reflect beam will indicate which side of resonance the laser frequency is on, and thus will be

explored mathematically in the next section for better understanding[22].

Figure 3.4: The amplitude and phase of the reflective coefficient of the caivty F (ω). Thediscontinuity in phase is caused by the reflected sign vannishing at resonance [21].

3.2.3 Mathematical Model

With the conceptual model established, a quantitative model is necessary to further

understand the technique. To describe the incident and reflected beam at one point outside

the cavity, their equations can be written as following, respectively:

31

Einc = E0eiωt (3.4)

Eref = E1eiωt (3.5)

where E0 and E1 is complex to account for the relative phase difference between them,

ω is the angular frequency of the laser [21].

Then, the amplitude reflection coefficient, F (ω), can be found for a lossless symmetric

cavity:

F (ω) =ErefEinc

=r(exp(i ω

∆νFSR)− 1)

1− r2exp(i ω∆νFSR

)(3.6)

where ∆νFSR = C2L

is the free spectral range 1.1, and r is the reflectivity of each cavity

mirror [22].

To better understand this complex equation, it is useful to plot it out and look at its

evolution. As shown in figure 3.5, F (ω) will always fall on the edge of the dash-lined circle

center along the real axis. The laser frequency ω will determine where exactly on the circle

the F (ω) lies. The right edge of the circle where it crosses the real axis is the resonance. It

crosses the origin because of the lossless symmetric cavity we assumed. As laser frequency ω

increases it will trace out this circle counter-clockwise [21]. As one can see, the intensity of

the reflected beam, |F (ω)|2, is symmetrical around the resonance, however, its phase, the

imaginary part, is different. Very near the resonance, F (ω) is almost only on imaginary axis,

being in the lower half when below resonance and upper half when above resonance.

This motivate the use of a phase modulator is necessary in the Pound-Drever-Hall

technique. The electro-optical phase modulator will create two sidebands with definite

phase relationship with the incident and reflected beam without entering the cavity, as their

modulation frequency is chosen to guarantee their reflection at the first mirror of the cavity.

As there is no way to measure the optical phase directly, these sidebands essentially serve as

32

Figure 3.5: A plot of the reflection coefficient, F (ω), in the complex plane. As the laserfrequency increases, the imaginary part will trace out a counter-clockwise circle. The rightedge of the circle where F (ω) cross the real axis is when the laser frequency is on resonance[21].

the phase reference to enable the phase measurement of the reflected verses the leaked beam

[21].

Phase modulation will have the similar effect as frequency modulation, so there will

be two sidebands around each frequency component with addition and subtraction of the

modulation frequency, respectively. To it show mathematically, the E field of the incident

light after phase modulation is:

Einc = E0ei(ωt+β sin(Ωt)) (3.7)

Then, it can be expanded using Bessel functions [22]:

33

Einc ≈ [J0(β) + 2iJ1(β) sin(Ωt)]eiωt (3.8)

= E0[J0(β)eiωt + J1(β)ei(ω+Ω)t − J1(β)ei(ω−Ω)t] (3.9)

where Ω is the phase modulation frequency, β is a constant known as the modulation

depth, and J0 and J1 are Bessel functions of the first kind [22]. This equation essentially

means there are three components in the incident beam: a main carrier with frequency ω

and two sidebands with frequency ω ± Ω.

The power in the sidebands are small if the modulation depth is small (β < 1) . Then,

we can treat these components as individual beams and apply the reflection coefficient

calculated before to each part in order to find the total electric field of the reflected beam

[22]:

Eref = E0[F (ω)J0(β)eiωt + F (ω + Ω)J1(β)ei(ω+Ω)t − F (ω − Ω)J1(β)ei(ω−Ω)t] (3.10)

As photodetectors can only measure optical power, we need to find Pref = |Eref |2 [22] :

Pref = |Eref |2 =Pc|F (ω)|2 + Ps[|F (ω + Ω)|2 + |F (ω − Ω)|2

]+ 2√PcPs

[Re[F (ω)F ∗(ω + Ω)− F ∗(ω)F (ω − Ω)] cos(Ωt)

+ Im[F (ω)F ∗(ω + Ω)− F ∗(ω)F (ω − Ω)] sin(Ωt)

]+ (2Ω-terms)

(3.11)

where the main carrier power, Pc = J20P0 , and the sideband power, Ps = J2

1P0, with P0 being

the total reflected power.

The resulting power is a wave with an envelope showing the beat pattern between the

two frequencies [21]. The Ω term originates from the interference between the main carrier

and the sidebands, and the 2Ω term is the cross term of the two sidebands interfering with

each other.

As it is better to ensure the sidebands are completely reflected of the first cavity mirror

in order to avoid transferring cavity power onto the sidebans, usually a fast modulation

34

is applied with Ω >> ∆ν, the linewidth of the cavity, and therefore it is safe to assume

F (ω±Ω) ≈ −1 [21]. With that assumption, the expression F (ω)F ∗(ω+ Ω)−F ∗(ω)F (ω−Ω)

is purely imaginary, and the cosine term in equation 3.11 become negligible [21]. Then,

the reflected signal is mixed with the modulation signal. To ensure the DC signal is zero

after the mixer, a 90 degree phase shift is introduced by the phase shifter mentioned in the

experimental setup.

Thus, the final error signal becomes [22]:

ε = −2√PcPsIm[F (ω)F ∗(ω + Ω)− F ∗(ω)F (ω − Ω)] (3.12)

Near resonance, the error signal is nearly linear and asymmetric, and can be approxi-

mated with [22]:

ε ≈ −8√PcPs

∆νδf = Dδf (3.13)

where ∆ν ≡ ∆νFSR

F is the linewidth of the cavity and D ≡ −8√PcPs

∆νis called the frequency

discriminant.

This linear relation is very useful as feedback via a servo loop, usually a PI or PID

controller, to the laser cavity or current control, locking the laser frequency to the resonance

of the reference cavity.

Furthermore, two graphs of the error signal from equation 3.12 are plotted to show the

effect of cavity finesse on the error signal with the same modulation frequency of 15 MHz

and free-spectral range of 500 MHz :

The most important features in these graphs are the slopes of their center fringe, or

frequency discriminant D in equation 3.13. As the feedback servo will lock to the zero crossing

of that center fringe, which is where the resonance is at, a small change in frequency will

change the voltage by Dδf amount. Essentially, it means, the frequency discriminant D,

determines the sensitivity of the servo lock. Comparing to earlier method, the fluctuation

35

Figure 3.6: A plot of the normalized PDH error signal as a function of frequency in the unitsof modulation frequency from resonance. The finesse 447.23 is calculated from having themirror reflectivity of 99.3%. The two intermediate curves are from the interaction of the tailsof the main carrier with the sidebands.

in intensity will not affect the location of the zero-crossing as the mixer is not sensitive to

amplitude modulation, although since the slope is depended on the carrier power, it does

have some effect on the sensitivity of the lock.

3.2.4 Noise Limitations

As any noise in the error signal itself is indistinguishable from the frequency noise in

the laser, it is important to understand what factors contribute to the noise in the error

signal. From the error signal equation 3.12, it can be derived that the deviation of the cavity

length from the resonance has the same order of impact as frequency detuning near resonance

[21]. In fact, among many possible parameters, including the intensity noise of laser, the

modulation frequency Ω, the modulation depth β, sensitivity of the photodiode, and the

36

Figure 3.7: A plot of the normalized PDH error signal as a function of frequency in the unitsof modulation frequency from resonance. The finesse 3140.02 is calculated from having themirror reflectivity of 99.9%. Note that its center slope is considerably sharper than that inthe previous graph.

relative phase difference between the signals sent to the mixer; none of these contributes to

the error signal to the first order [21]. The error signal is only first-order sensitive to the

sideband power fluctuations, which can be reduced by using a higher modulation frequency

Ω as most noises fall off at higher frequencies [21].

However, the quantum shot noise is the fundamental limit of how quiet the error signal

can be[21]. The quantum shot noise arose from the random occurrence of photon absorption

event in a photodector, and related to the quantum discreteness of photons. It has a flat

spectrum in PSD, constant along all frequencies, therefore it becomes prominent at very high

frequencies. Mathematically it is proportional to the square-root of the average intensity

the falls onto the photodector, essentially the signal-to-noise ratio of a Poisson distribution,

37

SNR =√N as mentioned in section 2.1. In this case, the reflected power falling on the

photodetector when it is on resonance is the average power in the two sidebands. Therefore,

mathematically, the quantum shot noise can be calculated as [21]:

Se =

√2hc

λ(2Ps) (3.14)

Dividing this equation by the frequency discriminant D will give the apparent frequency

noise [21]:

Sf =

√hc3

8

1

FL√λPc

(3.15)

where F is the finesse of the cavity, L is the length of the cavity, λ is the wavelength of the

laser and Pc is the carrier power.

This quantum shot noise will provide ultimate limitation on how quiet the error signal

can be.

3.3 Mode-locked Laser Stabilization Technique

There are many successful attempt to stabilize the mode-locked laser to suit the purpose

of their applications. As briefly mentioned in the motivation section 1.1, these techniques are

capable of full frequency comb lock, stabilizing both fr and f0. As a result the experimental

setup is usually fairly complex, thus motivating a constant desire for a simplified technique

with comparable noise suppression level.

In this section an example of this effort is detailed. It is presented by Swann et al.

[23], which seeks to reduce the complexity of the previously full frequency comb stabilization

method in the application of a portable microwave generation system with fiber based

mode-locked lasers [24].

38

Figure 3.8: The concept for microwave generation directly from a fiber mode-locked laser

[25]. In the frequency domain, the repetition frequency is stabilized via stabilization of the

3.74 THz wide comb across two individual frequency components.

The basic idea is to lock two continuous wave lasers, with center wavelength 1535 nm

and 1565 nm to a single PDH cavity. Those two CW lasers have a stabilized center frequency

will serve as the frequency standard for the two frequency components in a fiber based

mode-locked. Therefore, as two components are locked to two frequency absolutely, both fo

and frep can be stabilized simultaneously, achieving full frequency comb lock.

39

Figure 3.9: Schematic of the entire stablization system. The greeen background indicates an

air suspensed optical table. Colored lines mean the free-space optical path, brown lines mean

polariztion maintain fiber, black lines mean electrical signal. PDH: Pound-Drever-Hall locking

electronics, EOM: fiber-coupled eletro-optical modulator, AOM: fiber coupled acusto-optic

modulator BP: bandpass filter, PBS: polarizing beam splitter. [25]. In the frequency domain,

the repetition frequency is stabilized via stabilization of the 3.74 THz wide comb across two

individual frequency components.

The two wavelengths 1535 nm and 1565 nm of the cw lasers are chosen to match two

frequency components in the femtosecond fiber laser’s spectrum. The two lasers are first

locked to an optical cavity of 10 cm with finesse of 200000 using PDH technique. As the light

are mostly off resonance, only a few percent of the combined light is coupled into the cavity.

One half of the fs fiber laser output is combined with the two cavity stabilized cw lasers. The

40

combined light is spectrally filtered, and the heterodyne best at 1535 nm and 1565 nm was

measured, respectively. The two heterodyne signals are then used in a phasedlocked loop to

stabilize the femtosecond fiber laser [23].

This technique is already much simplified than previous attempts to lock fo and frep

separately, which would require using a nonlinear fiber for supercontinuum generation and a

f to 2f self-referencing scheme [24]. However, the compromise for reduction in complexity

is that the stabilization ”moment arm” is 3.74 THz, a great difference form that of the full

comb lock, which is ≈ 200 THz [23]. This would decrease the sensitivity of the optical locks

to the excess phase noise by a factor of(

3.74 THz200 THz

)2 ≈ 12500

comparing to full frequency comb

lock [23].

Considering the fact that most optical components are fiber based, this stabilizing

system is generally better suited for portable means than other state-of-the-art frequency

comb stabilization systems. However, this technique still require two PDH stabilized cw

1535 nm and 1565 nm transfer lasers, which mean that they are ”transferring” the stability

to the fs mode-locked laser, rather than stabilize the mode-locked laser directly. It is still a

complex system by itself, and this project will try reduce this complexity even further.

Chapter 4

Experimental setup and results

In this chapter, the experimental setup to apply the Pound-Drever-Hall (PDH) technique

on a mode-locked laser will be carefully detailed, and the results will also be presented and

examined. This is a collaborative project between me, Liangyu Chen, and Luke Charbonneau

M.S., a previous master student in Schibli’s lab who graduated in 2016. Therefore, in this

chapter I will refer to work that was done as part of his master thesis. Published data from

his thesis will be cited.

This project applies the PDH technique to mode-locked laser to stabilize its repetition

frequency directly. The aim is to suppress phase noise and timing jitter of the laser via

a robust PDH setup that does not require building other transfer lasers as reference as

required in the system described in section 3.3. This goal is achieved with a significant

noise suppression at low frequencies on a bulk erbium-doped ytterbium (Er:Yb) 500 MHz

mode-locked laser.

The experimental setup is shown in figure 4.1.

42

Figure 4.1: A schematic of the experimental setup. The purple rectangle represents a acrylic

box that provides environment isolation for the setup. The photodetector and oscilloscope

on the left-hand side of the schematic is only used for monitoring the transmitted signal from

the cavity [16].

4.1 500 MHz Modelocked Laser

This part was mainly built by Luke Charbonneau and it is well detailed in his thesis

[16]. First, a continuous-wave, bulk, free-space 1560 nm laser was constructed with erbium-

ytterbium gain medium (Kigre, Inc. - QX/Er - Datasheet: Appendix A) and was pumped

by a 980 nm laser diode (Gooch and Housego - Model #: D1306077) . The laser cavity has

a folded ”X” design and an asymmetric long and short arm, as shown in figure 4.1 . This

43

design was calculated with ABCD matrices for Gaussian beams [26] to achieve the correct

mode size at the center of the gain medium and at the SESAM. The exact dimension of each

arm is marked on the diagram. At the end of the long arm, a 0.5% output coupler was used

as the output of the laser. After tuning the laser resonator to reduce the lasing threshold, the

mirror in the short arm was replaced by a semiconductor saturable absorber mirror (SESAM)

. The asymmetric design was to ensure the focus on the SESAM is appropriate to trigger the

saturation behaviour.

The SESAM was commonly used in passively mode-locked laser as described earlier in

section 1.3.2. The SESAM used here has a combination of slow and fast saturable absorber.

The details on SESAM is well established in the works of Ippen [27] and Prasankumar

[28]. There is a single InGaAs quantum well absorber layer close to the top of the SESAM

and the rest underneath is a semiconductor Brag mirror. For the designed wavelength the

Brag mirror serves as a near-perfect reflector, as reflection from each quarter-wave layer

always constructively interfere with the reflected light. The materials also have a larger

bandgap energy to ensure that no absorption occurs in the mirror. The quantum well at

the first layer create an interband relaxation transition for electrons from conduction band

to valence band. When high intensity light is shone on the SESAM, electrons accumulate

in the conduction band, leaving valence band depleted of electrons, therefore, reducing the

possibility of absorption . After this saturation process, the electrons can transit at the

interband energy level due to fast thermal relaxation, and then recombine with the carriers

in the valence band, which is a slow relaxation. With this combination of slow and fast

saturation behaviour, it is capable to self-starting mode-lock due to the slow behaviour and

further pulse-shortening due to the fast behaviour.

After aligning the SESAM and other optical components to achieve maximum output

power, the output of this now mode-locked laser was coupled into a fiber and used an optical

spectrum analyser and RF analyser to measure its main parameters:

44

λc = 1551 nm

∆λ = 13 nm

fr = 495.67 MHz

Pout ≈ 52.3 mW

(4.1)

where ∆λ is the spectral bandwidth of the pulses of the mode-locked laser.

From the measure repetition rate, 495.67 MHz, the length of the laser resonator can be

calculated with equation 1.1, which was 302.6 mm. A slow and a fast piezo were installed

on the mirrors of the laser resonator to allow small variations of the cavity length, which is

essential to lock the laser to the reference cavity. The slow piezo has a maximum displacement

of 1.1µm when applying a 75 V voltage. The output coupler was mounted on a movable

precision stage to allow tuning of the repetition rate within a large range.

4.2 Passive Reference Cavity

The passive reference cavity in this setup is composed of two concave mirrors (reflectivity ≈

99.3% at λ = 1551 nm, LayerTech - Coating Batch #: R1009002 and F115H010, (R1009002)

Dielectric Coating Datasheet: C) [16]. The finesse of the cavity can be found with

F =π(r1r2)

14

1− (r1r2)12

≈ 447.23 (4.2)

and the optical linewidth ∆νcav of the cavity was:

∆νcav =FSR

F=

495.67 MHz

447.23≈ 1.11 MHz (4.3)

The input coupling mirror has a radius of curvature of 1000 mm and the other mirror

has a radius of curvature of 500 mm , which were chosen to reduce the undesirable higher

order cavity modes. The length of the cavity was designed to match the length of the laser

resonator, so it would match the free spectral range of the mode-locked laser. One of mirror

45

of the passive cavity mounted on a moveable stage so its free spectral range could be tuned

accordingly to follow the repetition rate of the mode-locked laser has to be adjusted. A

plano-convex lens was placed before the entrance of the cavity to improve the coupling

efficiency into the cavity.

4.3 Electro-optic Modulator

This setup uses a fiber-based lithium niobate (LiNbO3) crystal electro-optic phase

modulator from EO-Space (Model #: PM-0K5-10-PFA-PFA, Datasheet: B) [16]. In an

earlier attempt, a free-space electro-optic phase modulator was constructed using a bulk

(LiNbO3) crystal. However, there were parasitic amplitude modulation coupled to the phase

modulation due to its high sensitivity to the light path in the crystal. Therefore, a fiber-based

electro-optic modulator was used instead, providing a higher bandwidth and much less

amplitude modulation (AM).

The modulator was driven by a Ω = 15 MHz sinusoidal signal with 4 V peak-to-peak

from a Rigol function generator. The modulation frequency chosen to be much larger then

the linewidth of the cavity, ∆νcav ≈ 1.11 MHz.

4.4 Electronics

For this setup, a low-noise, passive photodetector with no amplification was used to

collect the reflected signal. The final signal was obtained by mixing the reflected signal

with the phase shifted signal from the local oscillator using a high voltage phase detector

(Minicircuits: Model #: MPD 1+). A 10.7 MHz low pass filter (Minicircuits: Model #: BLP

10.7+) is used to filter out 15 MHz the modulation signal. Then, the signal was sent to a

proportional-integrator (PI) servo loop with dual output for fast and slow piezo mounted

in the cavity. The fast loop only has a proportional-integrator, and will respond to the fast

components in the error signal up until 188.7 kHz, which is the measured bandwidth, and the

slow loop with an extra slow integrator will handle any long term drifts. The circuit diagram

46

of this servo loop is provided in figure 4.2.

Figure 4.2: The circuit diagram for the PI servo loop filter [16].

4.5 Environmental Isolation

To provide suitable environmental isolation, the setup was constructed on top of a

optical breadboard with damping material as substrate, and was inside a 1 inch-thick acrylic

box to prevent air fluctuations and provide thermal isolation to some extent. The box was

placed on a high-performance Laminar flow optical table as standard for optical experiments,

which is able to minimize the effects of mechanical and acoustic vibrations from the lager

47

surrounding environment.

Figure 4.3: The experimental environmental isolation setup described in section 4.5. The box

at the left contains the mode-locked laser and the refrence cavity. The optical heterodyne

cross-correlation setup is at the right on the air suspended optical table.

4.6 Lock Performance

First, the resonance of the cavity was scanned by sending a periodic triangular-sloped

signal to the slow piezo while tuning its center voltage, and the transmitted and reflected

signals were monitored so that the resonance could be easily identified. The transmitted and

48

reflected signal without phase modulation are shown in figure 4.4 and figure 4.5, and the

signals with phase modulation are shown in figure 4.6 and figure 4.7, respectively.

4

3

2

1

0

Tra

nsm

itted

Sig

nal

(V

)

-0.10 -0.05 0.00 0.05

Time (s)

Transmitted Signal Scanning Signal (not to scale)

Figure 4.4: Reference cavity resonances without phase modulation. The red trace shows

the main resonance, the peak is around 3.00 V, with around 577µW of optical power on the

photodetector. The resoponsitivity of the photodiode is 1.04 A/W@1590nm and the gain

is 5kV/A . The blue trace represents the scanning signal, driving the slow piezo at 10 Hz

and 500 mVpp. There are also higher order resonances presented in the cavity, but they fall

outside of the scan range.

49

8

6

4

2

0

Tra

nsm

itted

Sig

nal

(V

)

-0.10 -0.05 0.00 0.05

Time (s)

0.20

0.15

0.10

0.05

0.00

Refle

cted Sign

al (V)

Transmitted Signal Reflected Signal

Figure 4.5: The blue trace is the reflected signal from the cavity, the mean of the higher

values is 187 mV and the mean of the lower peaks is 85 mV, with 3.62 mWoptical power on

the photodiode at the maximum. The red trace shows the transmitted signal as reference.

Note that the reflected signal is well above zero on resonance due to cavity loss, higher cavity

modes.

From the graph 4.5, the contrast between the strength of the reflected signal when the

light was on resonance and it was off resonance would tell how much light had been coupled

into the cavity, essentially refreshing to contrast between the lowest point and the highest

point in the reflected intensity graph 4.5:

DC Voltage− Reflected Peak Voltage

DC Voltage=

102 mV

187 mV= .545 ≈ 55% (4.4)

50

Therefore, the coupling efficiency was measured to be approximately 55%. It was largely

limited by the transverse modes in the cavity as a wider scan would show that there are

several other transverse modes presented. The highest one being around 70% of the main

peak.

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Tra

nsm

itted

Sig

nal

(V

)

-0.10 -0.05 0.00 0.05

Time (s)

Transmitted Signal Scanning Signal (not to scale)

Figure 4.6: Reference cavity resonances with phase modulation at modulation frequency

Ω = 15 MHz with 4 V peak-to-peak. The red trace is the transmitted signal with peak value

at 2.82 V and the blue trace shows scanning signal as the same as in the previous graph.

Since the electro-optical phase modulator has transferred some power to the sidebands which

are completely reflected from the cavity, therefore the maximum signal when on resonance

is reduced. Note that the smaller peaks around the main resonance are sidebands from the

pulse with frequencies f ± Ω and transmitted through the cavity when scanning through

these frequencies.

From the measurement of main carrier transmitted power before and after the modu-

lation, approximately 12.73% of the main carrier optical power was transferred to the two

51

sidebands.

8

6

4

2

0

Tra

nsm

itted

Sig

nal

(V

)

-0.10 -0.05 0.00 0.05

Time (s)

0.20

0.15

0.10

0.05

0.00

Refle

cted Sign

al (V)

Transmitted Signal Reflected Signal

Figure 4.7: The blue trace is the reflected signal from the cavity. The red trace shows the

transmitted signal as reference. Note the reflected signal is the result of interference between

two beams: the two sidebands that are reflected from the first cavity mirror, and the leakage

signal from the cavity when it is on resonance.

The error signal can also be seen at the output of the mixer with the frequency scanning

mentioned above in shown in figure 4.8.

52

-0.4

-0.2

0.0

0.2

0.4

PD

H E

rror

Sig

nal (

V)

-4x10-3 -2 0 2 4

Time (S)

Figure 4.8: The experimental PDH error signal when scanning the cavity near resonance.

The zero-crossing of the center fringe is the resonance and thus is used in the locking process.

The discrepancy between the measured signal the simulated signal shown in figure 3.6 is

likely due to the extra losses and higher order modes in the cavity.

To initiate the lock to the cavity, the scanning interval was decreased step by step while

adjusting the voltage to the slow piezo to zero-in on the resonance. When the frequency was

really close to the resonance, the scanning was stopped and the output of the PI controller

was connected to the slow and fast piezo instead. A manual tuning of slow piezo signal was

usually required to let the fast lock engage on the resonance. Then, the slow integrator was

turned on so that the slow lock was engaged as well. The combination of slow and fast piezo

would simultaneously compensate for both fast noise up to the bandwidth of the fast loop at

188.7 kHz , and low frequency noise and long-term drifts caused by acoustic oscillations and

thermal fluctuations. To determine its long-term stability, the lock was kept in operation

for around 8 hours, and the voltage drift on the slow piezo was measured to be 0.168 V per

53

hour. Given the fact that the slow loop was supplied with ±15 V, the minimum time for

the slow piezo to run of range if the drift is constant in one direct would be ≈ 90 hours,

therefore providing a lower bound for long-term stability of the lock without excessive external

disturbance. The transmitted signal through the reference cavity while the lock was engaged

is shown in figure 4.9.

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Tra

nsm

itted

Sig

nal

(V

)

121086420

Time (s)

Figure 4.9: The transmitted signal through the reference cavity with lock engaged for

measurement period of 12 s. Note that the height of signal roughly corresponds to the

maximum resonance peak at 2.82 V shown previously in figure 4.6.

4.6.1 Noise Limitation

With the parameters of these major components settled and measured, we can find the

shot noise limitation of the error signal with equation 3.14 provided in the previous chapter:

54

Sf =

√hc3

8

1

FL√λPc

=

√hc3

8

1

(447.23)(302.62× 10−3 m)√

(1551.67× 10−9 m)(1− 0.13)(0.55)([3.62× 10−3 W])

= 2.39× 10−3 Hz√Hz

(4.5)

where Pc is the measured reflected power with the correction of the percentage of coupling

efficiency and the percentage of power transferred to the sidebands during modulation. This

calculation provides the minimum shot noise floor that can be reached with this method.

4.7 Phase Noise Measurement and Results

As the goal of this project was to minimize the timing jitter of the mode-locked laser

in the most robust and stable way as possible. The phase noise of the stabilized laser was

measured and compared with the the free-running mode-locked laser. Two sets of data using

the two methods described in section 2.4.2 and in section 2.4.3 was presented and compared

here.

This first set of measurement was taken by Luke Charbonneau M.S. in 2016 using the

electro-optical modulation method described in section 2.4.2[16].

55

Figure 4.10: The phase noise measurement results, with a 1 GHz carrier, using the method

described in section 2.4.2. The integrated timing jitter (from 100 Hz to 10 MHz) was 173.11 fs

for the free-running 500 MHz mode-locked laser and 46.91 fs for the reference cavity-locked

500 MHz mode-locked laser over the same integration interval [16].

This power spectral density (PSD) measurement shows a significant phase noise sup-

pression, ≈ 20 dB, from ≈ 100 Hz to ≈ 1.1 kHz for the cavity-locked 500 MHz mode-locked

laser when compared to the free-running operation[16]. The small peak at ≈ 9 kHz was the

servo bump from the electronics. The peak at ≈ 45 kHz is the relaxation oscillation from

the 500Mhz laser. The integrated timing jitter from from 100 Hz to 10 MHz was 173.11 fs

for the free-running 500 MHz mode-locked laser and 46.91 fs for the cavity-locked 500 MHz

mode-locked laser with a 1 GHz carrier. This suggests an improvement of a factor of ≈ 4 in

56

amplitude or a factor of 16 in PSD.

The integrated timing jitter in fs is calculated from:

< τ >=1

2πf0

√∫ f2

f1

Sφ(f)df (4.6)

where < τ > is the integrated timing jitter at carrier frequency f0, the phase noise

power spectral density, Sφ(f), is integrated from f1 to f2.

A major concern arose from the measurement was the that the measurement suggested

no noise suppression beyond ≈ 1.1 kHz, which was not expected as the bandwidth of the

fast piezo and fast servo loop was much higher than that, in the order of ≈ 100 kHz. One

of the speculation at the time for the reason of this noise floor was the flickering noise

of the dual-output modulator used in the setup [16], as that noise floor does display the

characteristic of a 1/f drop with respect to frequency. Therefore, further investigation was

put in place and a setup using the optical heterodyne method described in section 2.4.3

was constructed, as this method provide more sensitivity to the phase noise by using the

optical frequency of ≈ 200 THz as the carrier frequency instead of 1 GHz used in the previous

method. The details about these methods are discussed in section 2.4.

57

-180

-160

-140

-120

-100L(

f) @

10

GH

z ca

rrie

r [d

Bc/

Hz]

102

103

104

105

106

107

Frequency offset [Hz]

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Integra

ted Tim

ing Jitte

r (fs) Free-running 500MHz Cavity-locked 500MHz Free-running Integrated Timing Jitter Cavity-locked Integrated Timing Jitter Electronic Noise Floor

Figure 4.11: The phase noise measurement results, scaled to a 10 GHz microwave carrier, using

the method described in section 2.4.3. The integrated timing jitter (from 100 Hz to 10 MHz)

was 1.79 fs for the free-running 500 MHz modelocked laser and 0.58 fs for the reference cavity-

locked 500 MHz mode-locked laser over the same integration interval. The peak at 14 kHz

was the servo bump from the electronics. The peak at around 40 kHz was the relaxation

oscillations from the 500 MHz laser as seen before. The huge peaks at around 600 kHz in

the blue trace and 2 MHz in the red trace was the oscillations in the laser cavity of 500 MHz

due to misalignment, and the fact that the pump current was changed between those two

measurements.

These two measurements shown in figure 4.11 and figure 4.10 agreed with each other

on the effect of low frequency phase noise suppression, although shown in different degrees

58

as their gain and slow integrator corner was set to different values. However, the ≈ 1.1 kHz

frequency cutoff for noise suppression still persisted, and this plateau did not change with

different gain on the cavity lock. This let to the belief that this plateau from 1.1 kHz to

9 kHz, was real noise from the 500 MHz mode-locked laser since the noise from the monolithic

laser was much much lower. The reason for its insensitivity to noise suppression was that we

locked the reference cavity loosely to the 1 GHz monolithic laser to ensure their repetition

frequency are close. However, as the monolithic laser does not use any piezo actuator, its

cavity length is changed via thermal expansion of the cavity medium. Therefore, by its design,

the temperature change could not response faster than ≈ 1 kHz. Although that still does not

answer the fact the why the PHD lock would have no effect beyond 1.1 kHz, which have a

much higher bandwidth. Most investigations should be conducted on the issues relating the

the setup itself.

Chapter 5

Conclusion

At the beginning of this thesis, in section 1.1, the importance of noise suppression

and motivation for an innovating stabilization system is established. After a explanation

of the sources of noise and latter the details of timing jitter, the optical heterodyne cross-

correlation method is highlighted as the most sensitive technique for measuring phase noise

and timing jitter 2.4.3. Latter, the Pound-Derver-Hall (PDH) technique is examined in detail,

with comparison between that and another mode-locked laser stabilization technique, the

differential frequency comb lock 3.3, highlighting the simplicity and effectiveness of the PHD

technique used in this project for mode-locked laser stabilization. Then, the experimental

setup and the final phase noise measurements are presented and analysed.

Finally, with the data gathered in the previous section 4.7, it is safe to conclude that

with the free-space low-finesse reference cavity used in this setup, the Pound-Drever-Hall

technique had successfully been applied on a mode-locked laser and capable to reduce the

low frequency noise from mechanical and acoustic vibrations to 10 or even 100 times lower,

and 3 to 4 times better in terms of timing jitter. This improvement could greatly help the

applications that require long term stability and coherent length, which are more affected by

low frequency drifts. These applications include microwave generation, long distance laser

sensing and dual comb spectroscopy discussed in section 1.1.1, 1.1.2and 1.1.3 respectively.

With a setup that was simple and robust compared to other stabilization techniques, the

timing jitter of the mode-locked lasers used in many applications could have been improved

60

with considerably less effort. The success from this simplified and robust system reveals

the great potential of utilizing Pound-Derver-Hall techniques for future inspirations of a

cost-effective and field-deployable system that could provide state-of-the-art stabilization for

the mode-locked lasers with portability and long-term stability.

5.1 Outlook

Mechanically, there is still a lot room for the setup to improve. Using a higher finesse

cavity would certainly increase the sensitivity to smaller frequency drift by producing a

steeper discriminator slope in the error signal, as shown in section 3.2.3. The cavity could also

use a highly transparent and low thermal expansion material, such as calcium fluoride (CaF2)

crystal, as the medium of the cavity instead of being in free-space. This could essentially

bring down the noise level of the reference cavity to that in the monolithic laser.

However, it still have short-backs besides technique limitations. As mentioned in the

earlier chapter 1.2, the frequency comb of the mode-locked laser has two major defining

factor, the offset frequency, fo, and repetition frequency, frep. The reference cavity could

only stabilize the frep by its design. As its free spectral range is fixed and the PDH lock is

essentially trying to change the length of the laser resonator so that the frequency component

of the mode-locked laser is trying to match resonant frequencies in the cavity. If there is fo

in the comb, the PDH lock have no way to distinguish this frequency offset from a change in

frep, and there is no way for it to align the frequency components with a frequency offset to

the cavity resonances only by changing the spacing between the components. This becomes

a issue when a fully stabilized frequency comb is needed as reference for applications like

microwave generation. Much more investigations are needed to solve this issue.

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Appendix A

Kigre Inc. Erbium-doped Ytterbium Glass, QX/Er Datasheet

Appendix B

Fiber-Based Lithium Niobate EOM-PM Datasheet

Appendix C

Layertech Mirror Dielectric Coating Datasheet

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