Made Surya Adhiwirawan FYP Thesis

7/31/2019 Made Surya Adhiwirawan FYP Thesis

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STABILIZATION OF 960 NM LASER USING

POUND-DREVER-HALL TECHNIQUE

SUBMITTED

BY

MADE SURYA ADHIWIRAWAN

DIVISION OF PHYSICS & APPLIED PHYSICS

SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES

A final year project reportpresented to

Nanyang Technological Universityin partial fulfilment of the

requirements for the

Bachelor of Science (Hons) in Physics / Applied PhysicsNanyang Technological University

June 2012


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Abstract

Frequency stabilization of 960 nm laser could not simply be done by using Doppler-free saturated

absoption spectroscopy since there is no convenient atomic transition for locking a laser at

that particular wavelength. We designed a system where a 780 nm laser that is locked at

52S1/2 52P3/2 trasition of Rubidium (Rb) atom can be used as primary reference to stabilizethe length of a high finesse cavity. The stable cavity is then expected to be applied in a Pound-

Drever-Hall technique for laser stabilization to lock the 960 nm laser.


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Acknowledgement

My greatest gratitude goes toward my supervisor, Asst. Prof. Rainer Helmut Dumke, who

has been helping me, guiding me, and teaching me a lot in the making of this project. Huge

thanks to my lab-mate: Maral, Mingli, Andrew, Fong En, Kin Sung and Mohan for all the

awesome help and patience in answering my questions and doubts. Thanks to my best friends

Nino, Alvin, and Adhit for the endless support and all the good time and laughter every night

after my every restless day at lab. Thanks to my sister Udayapinasthikaswasti for the constant

support, encouragement and advice whenever I need her. Thanks to Dian Charlo for being a

really nice roomie. And lastly, a big thanks to my parents, my brothers, and all who have been

supporting me all this time. Thank you so much.

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Contents

1 Introduction 7

1.1 Past Works on Laser Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Organization of the reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Theory 10

2.1 Fabry-Perot Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.1 Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Free Spectral Range, Finesse and Cavity Linewidth . . . . . . . . . . . . 12

2.2 General Laser Feedback System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Pound-Drever-Hall Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Experimental Realization 18

3.1 The Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.1 Laser Box Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.2 Saturation Spectroscopy Setup . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.3 Final Setup of 780 nm Laser Stabilization . . . . . . . . . . . . . . . . . . 24

3.2 Cavity Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 The Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2 Other Components for Cavity Stabilization . . . . . . . . . . . . . . . . . 30

3.2.3 Final Setup of Cavity Stabilization . . . . . . . . . . . . . . . . . . . . . . 33

3.2.4 Initial Design of the Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 960 nm Laser Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Stabilization Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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4 Summary and Outlook 38

4.1 Overall Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Future Application of the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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List of Figures

2.1 Reflected and transmitted light in a Fabry-Perot cavity. . . . . . . . . . . . . . . 11

2.2 FSR and cavity linewidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 General laser feedback system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Demodulation signal after the lock-in amplifier . . . . . . . . . . . . . . . . . . . 16

2.5 Setup of laser stabilization using PDH technique. . . . . . . . . . . . . . . . . . . 16

2.6 Demodulation signal using PDH Technique . . . . . . . . . . . . . . . . . . . . . 17

3.1 Photo of laser diode that we use (left) and the schematic diagram showing its

internal connection (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Input current vs output intensity of the free running laser diode. . . . . . . . . . 19

3.3 Combi Controller. Temperature controller (left) and current controller (right) . . 20

3.4 (a) Atoms move in different direction give rise to doppler broadening. (b) Broad-

ening of the frequency spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Distribution of atoms in ground state (a) before laser absorption and (b) after

laser absoption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Doppler-free saturation spectroscopy setup. Two laser beams (pump and probe

beam) in opposite direction are overlaped inside Rubidium vapor cell to excite

Rb atoms at central frequency, the probe beam is then detected by a photodiode. 24

3.7 Design of 780 nm Laser Stabilization Setup. The laser is split into two: first

one goes to double-pass AOM system to gain some frequency modulation and

another one goes to Doppler-free saturation spectroscopy setup. Both signals are

then combined in mixer to be used as a feedback to the laser. Note that TC

(Temperature Controller) and CC (Current Controller) are directly connected to

the laser box to maintain the temperature and give input current, respectively. . 25

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3.8 Wavelength range of the plano mirror. Red and Blue line represent the 45o and

0o angle of incidence, respectively. (Image Courtesy of Photonik Singapore Pte

Ltd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.9 Wavelength response of the concave mirror CVMB-R10-350 (Image Courtesy of

Photonik Singapore Pte Ltd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.10 Plano-concave cavity configuration. Note that the length of the cavity L is equal

to the radius of curvature rc of the concave mirror. . . . . . . . . . . . . . . . . 27

3.11 In this measurement, the ECDL operates at 79.47 mA and temperature23oC.

The resistance value in the temperature controller can easily be converted to

temperature unit using a simple formula in this Combi Controllers manual book. 27

3.12 Piezoelectric ring (green-coloured) oscillates the mirror. While scaning in its

amplitude range, at some points the mirror will exactly at the resonant state of

the cavity. This resonant was observed as a series of peak in the oscilloscope (See

Figure 3.15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.13 Cavity test setup. The photodiode was detecting reflection signal from the cavity 28

3.14 Function generator in operation. Triangular waves of frequency 500 Hz, ampli-

tude 4 Vand DC Offset -7% were given to the piezoelectric ring. . . . . . . . . . 29

3.15 Photograph of what we obtain from this cavity test setup. The upper signal

is coming from Channel 1, which is the triangle wave given to the piezo and

Channel 2 is the signal from photodiode. Channel 2 was inverted because it is

more convenient to see the resonant states indicated as peaks. . . . . . . . . . . 29

3.16 (top) Electro Optic Modulator, (bottom) typical EOM Driver Circuit use CRT

Driver to amplify the oscillationg signal from function generator (Image courtesy

of Texas Instrument) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.17 Photodiode used in our experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.18 Piezoelectric ring in our experiment. (Image Courtesy of PiezoMechanick Pte Ltd) 32

3.19 Cavity Stabilization Setup. PDH signal is fed back to the cavity to adjust its

length back to resonant state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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3.20 As mentioned previously at section 2.3, the error signal from PDH techniques has

this kind of shape. It has a very steep slope at zero crossing. The critical point,

or the ending of these two slopes, found out to be at v/2 and v/2 where vis the cavity linewidth. In our experiment the cavity linewidth is expected to be

around 250

450 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.21 Dimension and components of the initial cavity design. . . . . . . . . . . . . . . . 35

3.22 3D model of the initinal cavity design . . . . . . . . . . . . . . . . . . . . . . . . 36

3.23 Stabilization setup for 960 nm laser. Once we have a stable cavity, we can use it

as reference. The PDH signal in this setup is fed back to the 960 nm laser. . . . 37

4.1 Diagram of overall setup design. The grey part is the 780 nm laser stabilization

setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Diagram of Grating-stabilized ECDL Design [13], The design of our laser box is

inspired by design of L. Ricci et al. and C.J. Hawthron et al. : (A) Top View,

(B) Side View. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Photograph of the ECDL box with the top and the side cover openned. The cable

connection on the top of the image are connecting the ECDL to the temperature

controller, current controller and PI Controller. . . . . . . . . . . . . . . . . . . . 42

4.4 PI Controller Circuit. It consist of series of Proportional-Intergral components

and a trangle/TTL signal source. (Image source: LPTF_PID - Universitat Han-

nover) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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Chapter 1

Introduction

1.1 Past Works on Laser Stabilization

Development of laser with narrow linewidth has openned possibilities for many experiments in

the field of quantum information [1, 2], laser cooling [3, 5, 6], high precession measurement [7],

frequency metrology [4] and many more. Various sophisticated techniques have been used to

achieve a minimum bandwidth possible, however the challenge is not just about minimizing the

bandwidth, but also on how to do it in various frequency. In fact, the method used to stabilize

a laser at one frequency could be quite different with the one used for another frequency.

A typical commercial He-Ne laser has frequency bandwidth around 1500 MHz. This band-

width is definetely not suitable for high precision application which requires range of bandwidth

tolerance of few hundreds Hertz or may even be around 1 2 Hz that is required in precisionspectroscopy on Calcium ions [9]. Some methods such as polarization spectroscopy, Dichroic-

Atomic-Vapor Laser Lock (DAVLL), Dither Lock [8], Doppler-free saturated absorption spec-

troscopy [10] and Pound-Drever-Hall technique [9] have been used to minimize the bandwidth

and keep the laser stably operating at certain central frequency. Most the them are basically

using atomic spectroscopy technique, in which having a laser beam interact with gaseous sample

of atoms, and that will then trigger some atomic transitions with correspond to certain wave-

length. By some lock-in and servo circuits, the signal received would then be fed back to the

laser.

DAVLL method was invented by Cheron et al. in 1994 and first demonstrated on alkali

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vapour by Corwin et al. in 1998. This technique uses a magnetic field to split the Doppler-

broadened absorption signal into its Zeeman components, inducing circular dichroism and bire-

fringence of the atomic vapor. The signal is then brought to lock-in amplifier and servo as

feedback to the laser. A reseach done by C. Lee et all found that DAVLL method is capable of

reducing laser bandwidth to 16 MHz [12]. Dither lock, on the other hand, works by modulating

input current of the laser diode. Similarly, it also uses atomic vapor as main reference and

feedback loop to stabilize the laser. A study has shown that Dither lock is capable of reducing

bandwidth up to 3 MHz [8]. Polarization spectroscopy was first demonstrated by Wieman and

Hansch in 1976 on the Hydrogen Balmer- line. Here the laser beam is divided into two, one is

probe beam and another one is pump beam which are counterpropagating to one another inside

an atomic vapor cavity to trigger exication at certain central wavelength. The probe beam

is then divided into two polarized beam using a polarizing beam splitter and both signal are

combined and processed in the lock-in and servo circuit as feedback signal. Bandwidth locking

by using this method was obeserved to reach 2 MHz [8].

Doppler-free saturated absorption spectroscopy was first developed by the research group

of Arthur L. Schawlow, who won the Nobel prize on 1981. It works in almost the same way

with the polarization spectroscopy. This method is insensitive toward doppler-broadening due

to red-shifted and blue-shifted absorption frequency because of random velocity of the atomic

vapor that is used as reference. Doppler-free saturated absorption spectroscopy is the one that

we use in our experiment to lock the 780 nm laser. Using this spectroscopy, 14 2 MHz of

linewidth had ever been successfully achieved [14]. Details on how this method works will be

explained futher in Chapter 3.

Pound-Drever-Hall (PDH) technique of laser stabilization was named after R. V. Pound,

Ronald Drever, and John L. Hall who invented it in 1983. This method used an ultra-stable

cavity as reference. Basically, this method works by actively tuning the laser to match the

resonance condition of the cavity. A previous research using PDH technique on laser stabilization

on 729 nm Titanium-Sapphire laser for spectroscopy of Calcium ion has successfully achieved

1.7 0.1 Hz linewidth [9].

In this project, the main objective is to design a system to lock a 960 nm laser. At this

wavelength, stabilization of laser could not simply be done by using Doppler-free saturated

absoption spectroscopy since there is no convenient atomic transition for locking a laser at 960

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nm. Therefore we propose a design to lock 960 nm laser using PDH technique, and hence using

a cavity as the reference. Since we could not provide advance mechanical support for an ultra-

stable cavity, we also propose the design of cavity stabilization technique using a stable 780 nm

as the reference. Furthermore, the 780 nm laser itself has its own stabilization system, i.e. using

the Doppler-free saturated absorption spectroscopy of Rubidium atomic vapor cell.

1.2 Organization of the reports

In Chapter 2 of this report, some background theories related to the project are presented.

Section 2.1 will explain the reflection-transmission behaviour of a Fabri-Perrot cavity, continued

by mathematical expression of its properties such as the free spectral range (FSR), finesse and

linewidth. General laser feedback system is then introduced in Section 2.2, where a simple laser

stabilization using modulator-oscillator-LIA (Lock-In Amplifier) is being used as an example.

In Section 3.3, the theory behind Pound Drever Hall Technique is briefly explained.

Chapter 3 contains the experimental realization of this project. The first part (Section 3.1)

is going to discuss in detail about the building of stabilization system for a grating-stabilized

External Cavity Diode Laser (ECDL), in which we would like to achieve a very stable 780 nm

laser with narrow bandwitdh. This stable laser is then to be used as a reference to stabilize our

cavity (Section 3.2). Once the ultra-stable cavity is achieved, we are going to explain how to

use it to stabilize the 960 nm laser using the PDH Technique (Section 3.3). Furthermore, the

initial design of our cavity which have yet to be built is also going to be shown (Section 3.4).

In the last chapter, Chapter 4, we give a brief outlook and summary containing the over-

all design setup of this project, what we have done and also suggestions for future work or

application.

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Chapter 2

Theory

2.1 Fabry-Perot Cavity

2.1.1 Reflection and Transmission

Fabry-Perot Cavity consists of two mirrors, coaxially alligned and separated at a distance L.

When a beam of light with wavelength projected to one of the mirror, some of the light will

be transmitted and some will be reflected. The transmitted (Et) and reflected beam (Er) are

given by

Et = tEi (2.1)

Er = rEr (2.2)

where t and r are the transimission and reflection coeffiecient, respectively. They are related by

r2 + t2 = 1 and 1 r, t 0.Basic setup of Fabry-Perot cavity can be seen in Figure 2.1. Mirror 1 and 2 have their own

relection (r1, r2) and transmission (t1, t2) coefficients. Multiple reflections and transmissons

between those mirrors create multiple beams that interfere with each other. This interference

determines the output of the cavity with respect to certain wavelength. When double length of

the cavity is (2L) exactly multiple of, then resonance would happen in the cavity. At resonance,

the the total transimission of that particular wavelength will be at maximum (100%), and hence

the total reflection will be minimum (0%).

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Figure 2.1: Reflected and transmitted light in a Fabry-Perot cavity.

Suppose the incident light beam is Ei = E0eit, and is phase shift due to light path

while travelling from one mirror to another and back again. The total reflected beam is given

by

Er = Ei(r1 + t1r2t1 + t1r2r1r2t1(

)

2

+ t1r2r1r2r1r2t1()

3

+ ...)

= E0eitr1 + t21r2(1 + r1r2 + (r1r2)2 + ...)

= E0eit

r1 + t

21r2

1 r1r2

If the reflection coefficient of both mirrors are really high ( > 99%), we can use approximation

that r1 = r2 and t1 = t2, which yields

Er = E0r1eit

1

1

r21

(2.3)

Moreover, = e2(2L

), where 2L is the length of one roundtrip between the mirrors. From

this expression, it is clear that there will be no reflection (Er = 0) when = 1, or 2L/ = n,

where n is an integer. This properties will be useful for future application of the cavity which

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is going to be discussed in the next chapter.

2.1.2 Free Spectral Range, Finesse and Cavity Linewidth

Free Spectral Range (FSR), finesse and cavity linewidth (or also known as Full Width at Half

Maximum, FWHM) are three other important parameters of a cavity, especially for our ap-

plication. Both are defining how good is the cavity in differentiating between one resonant

wavelength and another resonant wavelength.

F SR is the distance between two frequency modes peaks where the interference of light is

highly constructive (i.e. the resonance state). Cavity finesse (F) roughly represents how contrast

is the the maximum transimission value of the cavity with respect to its lowest transmission

value. Whereas, cavity linewidth or F W H M is the width of frequency range at half maximum

of the transmission peak.

Figure 2.2: FSR and cavity linewidth.

To find the equation that expresses F SR, suppose a light of wavelength matches one mode

of the cavity, and another light with wavelength is in the next mode of the cavity. We can

write m = 2L and (m + 1) = 2L. Then if we substract these two equations, we obtain

(m + 1)m = 2L 2L

1 = 2L

2 = 2L

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where = . And since = c/f, we can write equation above as

c2

2Lf2= c

1

f 1

f

c

2Lf2=

f

f(f +f)

f = c2L

1 +

ff

f

1 c

2Lf

=

c

2L

f =c/2L

1 c2Lf (2.4)

This f is actually the FSR. In our case, c/2L f, therefore

F SR =c

2L

(2.5)

In our experiment, since the length of the cavity is L = 350 mm, the FSR is 428 M Hz.

Cavity finesse F is directly related to reflectivity of the mirrors. It can be calculated using

the following equation [3]

F =

R

1R (2.6)

for our cavity, F is between 1000 and 2000. In Figure 2.2 we can see that F has higher peak

contrast compared to that of F, hence F > F.

F W H M is simply calculated using the following equation

v =F SR

F(2.7)

In Figure 2.2, we can see that as F SR increases, we can expect that the width of each peak

becomes wider and wider. However bigger finesse will keep the width of the peak narrow. Later

in the next section, we can see that v of the cavity determines the slope of the locking signal

and therefore the performance of the lockin in Pound-Drever-Hall technique. For our cavity, the

FWHM is expected to be around 250 450 Hz.

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2.2 General Laser Feedback System

In general, to set a laser to work at certain frequency, we use a feedback system. Meaning that

we are setting a system that is able to detect the amount of error or displacement of frequency

value from the original set point, and use a servo to set the value back to the desired value.

Figure below describes a laser feedback system in general

Figure 2.3: General laser feedback system.

Suppose we give certain set-point to the Piezoelectric Transducer (PZT) of the laser to

achieve lasing state at a desired frequency. Because of varying temperature or any other un-

expected factors, the position of the grating (or internal cavity length) may displace. This

displacement causes slight error in the wavelength (hence frequency) value and therefore spoil

the experiment. To handle this, we put a chopper, or anything that would give modulation

frequency to the output light.

This frequency would then go to the experiment, and it would get some noises due to

the environment (such as, light-buld frequency in the room, sunlight frequency, noises from

instruments, unexpected interference, etc). This noise has to be dismissed, therefore before we

sent the signal to the servo (PI Controller) we have to send the signal to a lock-in-amplifier,

which basically will mix the signal from photodiode with the frequency of local oscillator to let

the original signal from the laser pass while cancelling the noise. Additionally we may put a

low-pass filter to extract any resulting DC component.

From the lock-in-amplifier, the signal will be passed to PI controller, which would recognize

the amount of error brought by the signal, and try to adjust it back to the original set point

which is the desired value. Output signal from PI Controller will be sent back to the laser box,

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and will change the PZT voltage to let it back to the correct position.

Let us consider it quantitatively. Suppose that the original signal frequency from the laser

is o. This frequency is then modulated by A sint by the modulator. The resulting frequency

would be

(t) = o + A cost (2.8)

The frequency will correspond to a voltage V(). With Taylor expansion and noting that A2

terms and higher is very small, we obtain

V() = V(o) +dV

dA cost + O(A2)

V() V(o) + dVd

A cost

This term will them mixed with frequency from local oscillator cos(t + ) to be

V = V(o) cos(t + ) +dV

dA cost cos(t + )

= V(o) cos(t + ) +1

2A

dV

dcos(2t + ) +

1

2A

dV

dcos

by applying a low-pas filter, we can extract the third terms (the DC term) hence the error signal

that we sent to the servo is

V =1

2A cos

dV

d(2.9)

Note that the shape of error signal depends on the derivative of V with respect to . is the

phase difference which we can adjust to be equal to zero ( = 0).

In this experiment V as function of near the central wavelength shows a Lorentzian-shaped

graph. Its derivative can be seen in Figure 2.4 where there is steep curve at zero crossing. This

steep is the expression of error value that is going to be recognized by the PI Controller to be

able set how much change should it make on the PZT to set the laser frequency back to the

correct value.

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Figure 2.4: Demodulation signal after the lock-in amplifier

2.3 Pound-Drever-Hall Technique

Figure 2.5: Setup of laser stabilization using PDH technique.

This technique uses Electro-Optic Modulator (EOM) which will create frequency sidebands

driven by a local oscillator. Suppose the electromagnetic field of laser output from ECDL is

Eoeit. When passing through the EOM, its frequency will be modulated such that it becomes

E = Eoei(t+A sint), Where A is a constant determining the magnitude of modulation and

is the modulation frequency. This expression can be expanded using Bessel function to be

E Eo

Jo(A)eit + J1(A)e

i(+)t J1(A)ei()t

(2.10)

Note that here A is relatively small. Above equation shows that the laser after the EOM can be

described as three waves with frequency , +, and . The laser will then propagate intoan ultrastable cavity as shown in Figure 2.5. Each of the waves will be reflected by the cavity

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where the reflection coefficient is

R() =ErEi

=r(ei

FSR 1)1 r2ei FSR (2.11)

Such that the reflected wave can be written as

ER = Eo

Jo(A)R()e

it + J1(A)R( + )ei(+)t J1(A)R( )ei()t

(2.12)

The power of this reflected wave is proportional to photodetector voltage. It is given by

Pr = |Er|2 = ErEr

= Pc|F()|2 + Ps|F( + )|

2 + Ps|F( )|2

+2PcPs( {F()F ( + ) F ()F( )} cost+ {F()F ( + ) F ()F( )} sint) + (2 terms)

Where Pc is the power brought by central wavelength (Pc = E2oJ

2o ), and Ps is the power brought

by sideband frequency (Ps = E2oJ

21 ). Signal from photodiode will be sent to mixer, which will

mix them with the frequency from local oscillaltor (sint) to demodulated the signal. This will

produce lock-in signal as depicted in Figure 2.6. Further discussion about PDH technique will

be presented in Chapter 3.

Figure 2.6: Demodulation signal using PDH Technique

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Chapter 3

Experimental Realization

3.1 The Laser

3.1.1 Laser Box Setup

To begin the whole experiment, it is essential that we have good laser with good controlabilty

over its frequency, power, polarization and linewidth. In this experiment we built our own

grating-stabilized external cavity diode laser (grating-stabilized ECDL) as the main source of

the laser. This type of laser has widespread applications in optical and atomic physics. The

design uses a relatively inexpensive yet reliable diode lasers which is electrically driven by giving

them certain electric current. The diode is then coupled to a diff

raction grating which providesthe behavior of an external cavity to be used as the wavelength-selective element, which then

provides frequency-selective optical feedback to the diode laser. This concept of frequency

selective feedback allows the laser to achieve narrow linewidth and remarkable tunability.

According to Littrow configuration, the grating have to be aligned such that the 1st order

diffraction from the grating is coupled directly back into the laser while the 0th-order diffraction

is reflected as the output beam. A convex lens is properly placed in front of the laser diode to

collimate the laser beam. The lasing wavelength is dependent of the incident laser beam.

Diode laser that works at frequency near the 87Rb D2 transition of 780 nm are commercially

available. In this experiment we use laser diode model Roithner Lasertechnik ADL-78901TX

AlGaAs. This laser diode has a rated maximum power of 100 mW with peak frequency at

785 nm. This frequency is infrared-red range and is visible with bare eyes when we do the

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experiment.

Figure 3.1: Photo of laser diode that we use (left) and the schematic diagram showing its internalconnection (right)

The laser diode would produce the light when certain current is given to point 1 and 2. The

laser diode has current vs output relation as described in Figure 3.2. You can see that the laser

has threshold of emitting light at around 30 mA.

Figure 3.2: Input current vs output intensity of the free running laser diode.

A diffaction grating, model Thorlabs GH13-18V, is used in this experiment to create optical

feedback as well as transmitting the laser output. It has 1800 lines/mm such that the 1st

order and the 0th order is perpendicularly separated (approximately around 90o.) The grating

is oriented vertically so that it would be parallel to the laser polarization.

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We have a L-shaped metal piece and a grating mount as the main block to host the diode, the

diffraction grating and the collimation lens. They are made of Nickel Silver 1 with low thermal

coefficient and high thermal conductivity. This main block design has a cylindrical collimation

tube (model: Thorlabs LT230A) on it to ease us when aligning the laser diode and a collimation

lens (model C230TME, aspherical, focal length = 4.51 mm). This colimation tube allow the

lens to move forward and backward when we are looking for the exact position where the laser

is perfectly collimated. We have Silicone thermal compound material between the tube and the

block to provide good thermal conductivity. On the other hand, the grating mount has a place

for the PZT and screws for horizontal adjustment. This grating mount can easily be rotated

around an axis while we do alignment to achieve lasing state.

Temperature of the the laser diode, the block and grating mount must be kept stable, so

this design has Peltier element (thermoelectric cooler, Marlow Industries) between the blocks

and the external metal casing. A thermistor (R = 10k at 25o

C) is placed inside the block at

a distance 5 mm above the Peltier element. Together, they will be connected to a temperature

controller with a built-in PI controller.

The external metal casing is used to isolated the whole allignment from external disturbance

(i.e. thermal, mechanical and electrical disturbance). Some holes are drilled at one face of the

casing to put BNC and other external cable connections.

Figure 3.3: Combi Controller. Temperature controller (left) and current controller (right)

We also have combi controller, which is a temperature controller and current controller

combined. The temperature controller part has PID Controller which has to be set up to make

the temperature stabilization run faster. It is able to show our set-point temperature and the

actual temperature of the block. The current controller part allow us to adjust the amount of

current given to the laser diode as well as the power and the voltage. Overall drawing of this

1a alloy of 65% copper, 18% nickel and 17% zinc

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Grating-Stabilized ECDL design is shown in Appendix A.

To setup the laser for a proper operation, first we put laser diode inside the collimation

tube. Make sure the temperature controller and laser diode connection to the current controller

is right. If we increase the input current, a beam of light will appear. Now we can put the lens

inside the collimation tube to collimate the laser light, make sure the diameter of laser beam

at a distance far away from the laser box is the same everywhere. After we achieved collimated

light, we can adjust the grating position such that in a lasing state is achieved. This can be

done by setting the diode current slightly below the free running threshold of the diode and

then adjust the angular position as well as vertical and horizontal micrometer screws until there

is a sudden increase in the output intensity meaning that the lasing state is achieved. Make

sure that polarization direction of the laser is also in the right direction, i.e. the laser must be

linearly polarized parallel to the wider side of the metal casing.

3.1.2 Saturation Spectroscopy Setup

Saturation Spectroscopy (or also known as Doppler-Free Spectroscopy) is a very well known

spectroscopy technique used to narrow the bandwidth of the laser output. In our experiment,

we use 780 nm laser and the saturation spectroscopy as the main stabilization reference of the

whole system.

Saturation Spectroscopy is based on a physical phenomenon known as Doppler broadening.

It is known that atom and molecules undergo random motion due to its thermal energy, which

then yields different velocity in different direction. When a beam of light passes through those

atoms, some atoms will be blue-shifted, and some other will be red-shifted, depending on the

direction of their velocities. Frequency change due to doppler effect is given by

vs = v0

1 +

V

c

(3.1)

Blue-shift appears when the atom is approaching the laser V < 0, and red-shift appear when

the atom is moving away from the laser V > 0.

According to Maxwell-Boltzmann Distribution, probability to find atom with velocity be-

tween V and V + dV is

P(V)dV =

M

2kTexp

MV

2

2kT

dV (3.2)

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where T is the absolute temperature, M is the mass of the atom and k is boltzmann constant.

From these two equations above, we can obtain the probability of a photon with frequency

between vs and vs + dvs as follow

P(vs)dvs =c

v0

M

2kTexp

(vs v0)

2

v20

M c2

2kT

dvs

=2

exp

4(vs v0)

2

2

dvs

where = 2 v0c

2kTM is the linewidth parameter. The full width at half maximum (FWHM) of

the Doppler Broadened line is

vFWHM=

ln2 = 2v0c

2kT ln 2

M(3.3)

Figure 3.4: (a) Atoms move in different direction give rise to doppler broadening. (b) Broadeningof the frequency spectrum.

In room temperature 297 K at center wavelength 780 nm (frequency 3.841014Hz), Dopplerbroadening will have FWHM more than 250 MHz, which is too broad for our spectroscopy.

Therefore, a method called Doppler-free saturated absorption spectroscopy was developed to

reduce the doppler eff

ects.Suppose we have a gasseous sample with N(V)dV as a quantity that represent number of

atoms in the ground state with velocity between V and V + dV. When a laser beam with

frequency vo passes this gas, it will excite atoms at V = 0 which is at rest relative to the laser

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to make transition to the excited state. Thus this will cause depopulation or hole burning of

atom population at v = 0. If the laser has frequency v > vo, it will excite the blue-shifted atoms

or atoms at V < 0 and create a hole burning in that area. Similarly, if the laser has frequency

v < vo, it will excite the red-shifted atoms which are those at V > 0.

Figure 3.5: Distribution of atoms in ground state (a) before laser absorption and (b) after laserabsoption.

Doppler-free saturated absoption spectoscopy make use of two laser beam which are counter-

propagated and overlap with each other. One is called pump beam, another one is called probe

beam, in which pump beam has more intensity than the probe beam. These two beams are

originated from the same source to ensure both have the same frequency.

Suppose we have a pump beam with frequency v > vo. It would burn hole in V < 0 group

of atoms, however this hole burning will be much less stronger than the hole burning createdby the probe beam in the V > 0 group of atoms. When pump beam (and probe beam) has

frequency v = vo, both will create a huge hole burning in the group of atom at V = 0. Pump

beam with higher intensity will increase depopulation of atom at V = 0 such that there will

be very few atom left there. Finally it will reach saturation where the laser has excited most

of the atom such that the probe beam can easily pas the gaseous sample without absoption.

This hole burning is called lamb dip. Lamb dip can be several order of magnitude smaller than

the Doppler-broadened spectral feature. the width lamb dip is given by v = 2 which is the

natural width of a transition.

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Figure 3.6: Doppler-free saturation spectroscopy setup. Two laser beams (pump and probebeam) in opposite direction are overlaped inside Rubidium vapor cell to excite Rb atoms atcentral frequency, the probe beam is then detected by a photodiode.

Figure 3.6 describes the setup of our Doppler free saturated absorption spectroscopy. We have

gaseous tube containing Rb atoms vapor (Thorlabs CP25075-RB - Rubidium [Rb]), polarizing

beam splitter (PBS, Thorlabs PBS052), quarter wave plate (QWP, WPQ05M-780) for 780 nm

laser, neutral density filters (NDF, Thorlabs NE03B-B ), a mirror, a spherical f = 15mm lens

and a photodiode (BPX65-100R). Input light with polarisation parallel to the ground is coming

to the setup and is used as the pump beam. This light will then pass through the PBS without

change of polarization direction, passing through the tube to create hole burning and goes out

to the NDF and QWP twice to lower down the intensity as well as rotating the polarization

direction by 90o and come back to the tube as the probe beam. Finally the beam will be reflected

towards the lens by the PBS to be focused to the photodiode.

3.1.3 Final Setup of 780 nm Laser Stabilization

Once we have an operating laser box and Doppler-free saturation spectroscopy setup, we can

combine them to achieve a much narrower bandwidth of the final 780 nm laser output.

First, the output light with frequency from the laser box is both reflected and transmitted

by a PBS. the reflected one goes to Double-pass Acoustic Optical Modulator (AOM) system,

whereas the transmitted one goes to the experiment. The double-pass AOM system modulated

the light at radio frequency RF such that the output light will be +2RF. This light then goes

to the Doppler-free saturation spectroscopy section to be locked at 52S1/2 52P3/2 transitionof Rubidium atom to achieve a much narrower bandwidth. The light that is detected by the

photodiode will be mixed with radio frequency RF (RF) signal in a locking amplifier system,

and then to a Proportional-Integral controller (PI controller) as a servo. PI Controller has an

output to the piezoelectric transducer (PZT) to control the position of the grating such that it

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will adjust itself to the correct position where the lasing at 780 nm is achieved.

Figure 3.7: Design of 780 nm Laser Stabilization Setup. The laser is split into two: first onegoes to double-pass AOM system to gain some frequency modulation and another one goes toDoppler-free saturation spectroscopy setup. Both signals are then combined in mixer to beused as a feedback to the laser. Note that TC (Temperature Controller) and CC (CurrentController) are directly connected to the laser box to maintain the temperature and give inputcurrent, respectively.

3.2 Cavity Stabilization

3.2.1 The Cavity

In our experiment we use a plano mirror and a concave mirror coaxially aligned and separated

by certain distance L to simulate a cavity. The plano mirror used is Photonik 700-1150nm

Broadband Dielectric Mirror PBB-R03-10 with the following detailed properties:

Properties Details

Material Fused SilicaThickness 6.0 mm (0.2 mm)Diameter 25.4 mm (0.1 mm)Flatness Lambda/10

Surface Quality 10-5 S/D

Front Surface R>99.5% for S and P polarizationBack Surface Fine Polished, uncoated

Clear Aperture >90% of diameterLaser damage threshold 2 kW/cm2 CW, 100 mJ/cm2 10 ns pulse

Table 3.1: Plano mirror properties

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Figure 3.8: Wavelength range of the plano mirror. Red and Blue line represent the 45o and 0o

angle of incidence, respectively. (Image Courtesy of Photonik Singapore Pte Ltd)

The concave mirror that we use is Photonik 400-900nm Broadband Concave Mirror CVMB-

R10-350 with following detailed properties:

Properties Details

Material Fused Silica (VIOSIL, Japan)Diameter 25.4 0.2 mm

Radius of Curvature (ROC) 350 0.1 mmFocal Length 175.0 mm

Edge Thickness 5.5 0.1 mmFlatness Lambda/4 @633 nm over 1 inch area

Surface Quality (Aft coating) 20-10 S/DFront Surface R?99% for S and P polarizationBack Surface Fine Polished

Clear Aperture >90% of DiameterLaser Damage Threshold 2kW/cm2 CW, 100 mJ/cm2 10 ns pulse

Table 3.2: Concave mirror properties.

Figure 3.9: Wavelength response of the concave mirror CVMB-R10-350 (Image Courtesy ofPhotonik Singapore Pte Ltd)

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The plano mirror is held in a mirror mount (KS1 - 1" Precision Kinematic Mirror Mount,

3 Adjusters) and the concave mirror is glued to a piezoelectric ring which is also attached to a

mirror mount (Thorlabs KS05 - 1/2" Precision Kinematic Mirror Mount, 3 Adjusters). We

chose a 0.5 mirror mount because the piezoelectric ring diamater is just slightly bigger than

0.5 so it will be more convenient to be glued to the optical mount. These two optical mounts

are connected together by a 40 cm metal rod made of stainless-steel (with coefficient of thermal

expansion 17.3 106K1) to keep the distance constant. Since this is a plano-concave mirror,we set the length of the cavity the same as the radius of curvature of the concave mirror. One

side of each of the mirrors is dielectrically coated, and this coated surface is positioned face-to-

face inside the cavity. The cavity holders are screwed on an optical table in our lab to minimize

any disturbance coming from ground vibration.

Figure 3.10: Plano-concave cavity configuration. Note that the length of the cavity L is equalto the radius of curvature rc of the concave mirror.

Properties of the cavity were observed by the following procedure. A laser beam from the

ECDL is directed to a polarizing beam splitter and a quarter-wave plate before being focused

by aspherical lens (f = 20 cm) to the plano mirror.

Figure 3.11: In this measurement, the ECDL operates at 79.47 mA and temperature23oC. Theresistance value in the temperature controller can easily be converted to temperature unit usinga simple formula in this Combi Controllers manual book.

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The laser beam will be reflected and transmitted back and forth in the cavity such that the

total reflection is propagating back to the lens and the quarter-wave plate before being reflected

to the photodiode by the polarizing beam splitter.

During this process, the length of the cavity is changed by giving oscillating signal to the

piezoelectric ring. We use function generator to create this signal. The waveform is triangle,

with amplitude 4 V, frequency 500 Hz and DC Offset 7%. Triangular wave was chosen becausewe want to scan the length of the cavity linearly with time.

Figure 3.12: Piezoelectric ring (green-coloured) oscillates the mirror. While scaning in itsamplitude range, at some points the mirror will exactly at the resonant state of the cavity. Thisresonant was observed as a series of peak in the oscilloscope (See Figure 3.15)

The signal from the function generator is connected to Channel 1 of an analog oscilloscope

and signal from photodiode is connected to Channel 2. The oscilloscope was triggered externally

to the function generator.

Figure 3.13: Cavity test setup. The photodiode was detecting reflection signal from the cavity

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Figure 3.14: Function generator in operation. Triangular waves of frequency 500 Hz, amplitude4 Vand DC Offset -7% were given to the piezoelectric ring.

Figure 3.15: Photograph of what we obtain from this cavity test setup. The upper signal iscoming from Channel 1, which is the triangle wave given to the piezo and Channel 2 is the signalfrom photodiode. Channel 2 was inverted because it is more convenient to see the resonant statesindicated as peaks.

Piezoelectric ring (model: Piezomechanik HPSt 150/14-10/25) has length-voltage response

approximately = 0.17 m/V. In this experiment, the oscilloscope is working in 2 V voltage

difference interval and 0.2 ms time difference interval. Thus we can observe from the graph in

Figure 3.15 that the voltage difference V between two consecutive peaks is

20.5 V (0.5 V

were just rough estimation), meaning that the distance travelled by the mirror from one peak

to another is x = V = 0.32 0.09 m.

x is in fact the distance between two positions where wavelength 780 nm is in resonant state

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inside the cavity, and that two consecutive resonant states could possibly occur if the length of

the cavity is moved by half of the central wavelength magnitude, i.e. 780 nm/2 = 390 nm. This

value is in the range ofx(= 0.320.09m) from our measurement. The error of measurement

may come from the rough estimation ofV and slight misalignment of the optical equipments

The height of the peak was measured from the graph and it was

4 mV. This could be

higher if the all the equipments were perfectly aligned and the laser and cavity were perfectly

mode-macthed.

3.2.2 Other Components for Cavity Stabilization

Electro-Optic Modulator (EOM)

Common application of the Electro-Optic Modulator (EOM) is to give sidebands to the monochro-

matic laser beam that passes through it. The working principle of an EOM is based on a

phenomenon known as Electro-Optic effect, which is a change in the optical properties (i.e. re-

fractive index of the material inside our EOM) in response to an electric field that varies slowly

compared with the frequency of laser.

Suppose the refractive index n to be a function of the applied electric field n = n(E). If we

expand it in terms of E, we have n = no + 1E+ 2E2 + ... where and 2 are the first order

and second-order electro-optic effect coefficients. Higher order coefficients are usually small and

negligible in practical magnitude of applied eletcric fields therefore we can approximate it to

n

no + E. For laser beam that propagates in z direction, response towards electrid field at

x and y axis may differ and this creates birefringence.

Figure 3.16: (top) Electro Optic Modulator, (bottom) typical EOM Driver Circuit use CRTDriver to amplify the oscillationg signal from function generator (Image courtesy of Texas In-strument)

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Our EOM (LM0202P 0.10W) were expected to be driven by EOM Driver that operates at

certain frequency m. The EOM driver obtains signal input reference from a function generator

and amplifies the signal using CRT Driver (LM2432 220V Monolithic Single Channel 37 MHz

HDTV) as depicted in Figure 3.16 (bottom). If the EOM were operated at frequency m, the

refractive index would also change at the same rate, and therefore it produced sideband with

frequency m.

Photodetector

Photodetector or photodiode that we use in out experiment is the ultra high speed photodiode

BPX65-100R. The rise and fall time of the photocurrent for this type of photodiode is 12 ns.

Figure 3.17: Photodiode used in our experiment.

Photodiode has a PIN structure, in which a layer of intrinsic I material is positioned in

between a layer of p-type P material and a layer of n-type N material. When photodiode receive

a photon with sufficient energy, photoelectric effect occurs, thereby creating a free electron and a

hole. If this happen at junction depletion region, the electron and hole are swept away (electrons

move toward the cathode, and holes move toward the anode) from the junction by the electric

field in the depletion region, and photocurrent is generated.

Frequency Mixer and Low-Pass Filter

Just like its name, a mixer is basically used to combine two input signals. The output from the

mixer is a product of the input signal. Suppose that the input signal from the experiment is

VE = V1 sin(Et + E) and there is also signal from local oscillator VL = V2 sin(Lt + L). The

mixer will produce the product of these signal which is

VEVL = V1V2 sin(Et + E) sin(Lt + L)

VEVL = V1V2

1

2cos((E L)t + E L) 1

2cos((E + L)t + E + L)

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This output signal will then goes to a low-pass filter to cancel the high frequency term (E +

L). The maximize the output from the low frequency term, E L is set to zero. Here, thefinal output of mixer and low-pass filter will be a DC offset. This is quite important in our

experiment since we are going to cancel the noise and will only extract certain frequency for

feedback signal to the laser. E = L is required for a stable DC offset, the resulting signal

would then be

VEVL =1

2V1V2 cos(E L) (3.4)

The magnitude of the output depends on the phase difference between those two signals. Max-

imum output is achieved when E L = 0.

PI Controller

PI controller is used to correct the error between a measured process variable (PV) and the

desired set-point (SP). The output from PI controller will then affect the manipulated variable

(MV). For this cavity stabilization, for example, the voltage measure by photodiode is the process

variable, the 780 nm laser frequency cavity resonant state is the set-point , and the position of

piezoelectic-ring is the manipualted variable. The schematic diagram of the PI controller can

be found in Appendix B

Piezoelectric Ring

As mentioned in section 3.2.1, we use piezoelectric ring model Piezomechanik HPSt 150/14-10/25in our experiment. Piezoelectric ring basically works by adjusting its length for a given voltage

difference. When an oscillating signal is given, the length of piezoelectric ring will oscillates in

the same frequency.

Figure 3.18: Piezoelectric ring in our experiment. (Image Courtesy of PiezoMechanick Pte Ltd)

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3.2.3 Final Setup of Cavity Stabilization

Figure 3.19: Cavity Stabilization Setup. PDH signal is fed back to the cavity to adjust its lengthback to resonant state.

The idea behind Pound Drever Hall technique is to have a cavity reference with constant length

to be used as reference for stabilization of 960 nm laser. In reality, constant length or stable

cavity is really hard to achieve. The length of the cavity may easily vary due to several things,

such as slight thermal expansion of the metal rod that connect the mirrors, or any other external

vibration. The idea behind this section is to lock the cavity length using the stable 780 nm laser

as the reference.

Figure 3.16 shows the setup design of cavity stabilization. Laser beam E = Eoeit with

frequency and small bandwidth coming out from the section A. When passing through the

EOM the frequency of the beam will be modulated by frequency m so the electric field of the

laser will be

E = Eoei(t+ sinmt)

where is the modulation index. This modulation frequency is coming from a local oscillator

(function generator).

The laser will then going through multiple transmission and reflection in the cavity. The

intensity of light that are reflected back from the cavity and detected by the photodiode is

described as follow

Pref = Pc|R()|2 + Ps|R( + m)|

2 + Ps|R( m)|2

+2

PcPs( {R()R ( + m)R ()R( m)} cosmt

+ {R()R ( + m)R ()R( m)} sinmt) + (2mterms)

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R() is the reflection coefficient of the light at frequency , while Pc and Ps are constants that

represent power brought by center frequency and sideband frequency, respectively. Note that

2m terms is relatively very small, so we can neglect them. In a simpler way, we can write down

above equation into

Pref = A + B (

{C} cosmt +

{C} sinmt)

This signal is then mixed with signal from local oscilator (sinmt) to extract the error signal

which is

= B {C}

where C = R()R ( + m)R ()R( m). Figure 3.17 describe the shape of the errorsignal as function of

Figure 3.20: As mentioned previously at section 2.3, the error signal from PDH techniques hasthis kind of shape. It has a very steep slope at zero crossing. The critical point, or the endingof these two slopes, found out to be at v/2 and v/2 where v is the cavity linewidth. Inour experiment the cavity linewidth is expected to be around 250 450 Hz.

With a very steep slope at zero crossing, the PI Controller as the servo will easily recognize

even a very small deflection from the resonant frequency vo and therefore can give corresponding

adjustment to move the piezoelectric ring back to the correct value where resonant occurs in

the cavity. Using this method, we can give a feedback system to the cavity such that it would

be able to have a constant or stable length to keep it in resonant state.

Furthermore, the steeper the slope, the better the system performance would be. While the

linewidth of the cavity cannot simply be minimized, it is possible to optimize to modulation

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index to get maximal value of

PcPs, which is proportional to the error signal. Dependence of

PcPs to the modulation index was previouly calculated in other thesis [9] and it was found

that the maximum happens when = 1.08, where

PcPs = 0.42.

3.2.4 Initial Design of the Cavity

At the initial stage of this project, we actually have planned to build a cavity which should be

more stable and more reliable than the one we used in our experiment. It consists of 4 metal

pieces of invar rod (Invar (FeNi36) is a nickel iron alloy, with a very low coefficient of thermal

expansion 1.2106K1 at temperature range 20100oC, which is better than stainless-steel)to be used as material that keep the distance between the two mirrors. The mechanical design

of this cavity can be seen in Figure 3.21 below.

Figure 3.21: Dimension and components of the initial cavity design.

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Figure 3.22: 3D model of the initinal cavity design

The mirrors will be held by 2 Removable Cage Plate (Thorlabs CP90F) which are attached

to the invar rods. This design will improve the performance of the cavity in terms of reducing

possibilities of cavity length fluctuation caused by thermal expansion. The removable cage plate

also has some screws for fine alignment.

3.3 960 nm Laser Stabilization

Suppose we do not have gaseous sample of any atoms that has transition in wavelength of

960 nm, therefore we cannot do Doppler-free saturated emission spectroscopy for this laser.

However, once we have stable cavity, we can apply PDH Technique to the 960 nm laser to lock

its frequency.

3.3.1 Stabilization Setup

The basic principle of this setup is basically quite similar with our previous cavity stabilization,

except for this one, the error signal is fed back to the PZT of 960 nm laser.

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Figure 3.23: Stabilization setup for 960 nm laser. Once we have a stable cavity, we can use itas reference. The PDH signal in this setup is fed back to the 960 nm laser.

Previously the cavity has been mode-matched with 780 nm laser and therefore L = n 780 nm2 ,

where n is an integer. To be able to perform stabilization for 960 laser, the cavity length has

to satisfy L = n 960 nm2 , where n is also an integer. Here, we can conclude that: in orderfor this 960 nm laser stabilization to work, we have to set the length of the cavity such that its

value is the largest common multiple of 360 nm and 480 nm.

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Chapter 4

Summary and Outlook

4.1 Overall Setup

In this report, the building of a 780 nm grating-stabilized ECDL has been explained in detail.

Doppler-free saturated absorption spectroscopy has also been presented as our method to stabi-

lize the 780 nm laser. The setup explained in section 3.1 is the reference for cavity stabilization

setup (section 3.2), where the error signal from the cavity is fed back to the piezoelectric ring

in one of the mirror so it will adjust the cavity back to the correct position. Error signal in this

setup basically has PDH error signal characteristic, in which the it has very steep crossing near

zero value. The slope of this steep crossing was found to be related to the cavity linewidth and

modulation index . Since cavity linewidth is not easily adjustable in our experiment therefore,

optimization of value is needed. It turns out that when = 1.08, the maximum steepness of

the slope can be achieved hence making the cavity performance better. Section 3.3 is discussing

about how to use the stable cavity to stabilize the 960 nm laser. The basic principle is again

similar with cavity stabilization, where we can use PDH error signal as the feedback. One im-

portant thing to note when we want to stabilize the 960 nm laser is that the length of the cavity

must be divisible by both 7802 nm and9602 nm since we expect the cavity to support resonant

state of both wavelength.

To combine the design of cavity stabilization in section 3.2 and design of 960 nm laser

stabilization in section 3.3 we may put a non polarizing beam-splitter (Non-PBS) at the output

facet of both lasers (as shown in Figure 4.1) so that both wavelength overlaps one another.

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Both wavelength would then undergo the same path through the EOM and cavity. A dichroic

mirror (Thorlabs DMLP900 1" Longpass Dichroic Mirror, 50% Trans./Refl. at 900 nm) have

to be added to split both wavelength and let them be detected by two different photodiodes.

Signal detected by each photodiode would then used to stabilized the cavity and the 960 nm

laser accordingly.

Figure 4.1: Diagram of overall setup design. The grey part is the 780 nm laser stabilizationsetup.

In this project, we were using two mirrors coaxially aligned one another and placed them in

two optical mounts supported by a 40 cm stainless-steel rod as our cavity. We observe that the

cavity and the laser are able to achieve resonant state, identified by the occurence of periodic

peaks in the oscilloscope as we oscillate the mirror position by applying triangular wave to the

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piezoelectric ring. This peak occurs because when the length of the cavity is in resonant state

with the wavelength (780 nm) there will be no reflection signal from the cavity. The signal

detected by photodiode was inverted in oscilloscope, and hence this spontaneous absence of

signal would appear as a peak.

4.2 Future Application of the Design

In future, this design can be used to lock not only 960 nm laser, but also other lasers with

any wavelength as long as the length of the cavity is exactly the largest common multiple of

360 nm and 2 nm.

To reduce the linewidth of the cavity, mirrors with better reflection coeffient can be used.

For R > 99%, a slight difference in reflection coefficient may actually result huge difference in

the cavity linewidth. Moreover, there are huge room of improvement for the mechanical support

design of the cavity. In the future, with better mechanical support, better alignment and better

optimization of the whole setup, this system is actually very convenient to be used in the lab to

lock laser at various wavelength with relatively narrow linewidth.

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APPENDIX A

Design of the grating-stabilized ECDL

Figure 4.2: Diagram of Grating-stabilized ECDL Design [13], The design of our laser box isinspired by design of L. Ricci et al. and C.J. Hawthron et al. : (A) Top View, (B) Side View.

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Figure 4.3: Photograph of the ECDL box with the top and the side cover openned. The cableconnection on the top of the image are connecting the ECDL to the temperature controller,

current controller and PI Controller.

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APPENDIX B

Proportional Integral (PI) Controller Circuit

Figure 4.4: PI Controller Circuit. It consist of series of Proportional-Intergral components anda trangle/TTL signal source. (Image source: LPTF_PID - Universitat Hannover)

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