STABILIZATION OF 960 NM LASER USING POUND-DREVER-HALL TECHNIQUE SUBMITTED BY MADE SURYA ADHIWIRAWAN SICS AND A DIVISION PHYSICS AND APPLIED PHYSICS SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES nal year project re A final year project report presented to Nanyang Technological University in partial fulfillment of the requirements for the Bachelor of Science (Hons) in Physics June 2011 April 2012
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STABILIZATION OF 960 NM LASER USING
POUND-DREVER-HALL TECHNIQUE
SUBMITTED
BY
MADE SURYA ADHIWIRAWAN
LASER FREQUENCY STABILISATION WITH
MODULATION TRANSFER SPECTROSCOPY
SUBMITTED
BY
YONG MINGLI
DIVISION OF PHYSICS AND APPLIED PHYSICS
SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES
A final year project report
presented to
Nanyang Technological University
in partial fulfillment of the
requirements for the
Bachelor of Science (Hons) in Physics
June 2011
i
DIVISION PHYSICS AND APPLIED PHYSICS
SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES
LASER FREQUENCY STABILISATION WITH
MODULATION TRANSFER SPECTROSCOPY
SUBMITTED
BY
YONG MINGLI
DIVISION OF PHYSICS AND APPLIED PHYSICS
SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES
A final year project report
presented to
Nanyang Technological University
in partial fulfillment of the
requirements for the
Bachelor of Science (Hons) in Physics
June 2011
i
A final year project report
presented to
Nanyang Technological University
in partial fulfillment of the
requirements for the
Bachelor of Science (Hons) in Physics
LASER FREQUENCY STABILISATION WITH
MODULATION TRANSFER SPECTROSCOPY
SUBMITTED
BY
YONG MINGLI
DIVISION OF PHYSICS AND APPLIED PHYSICS
SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES
A final year project report
presented to
Nanyang Technological University
in partial fulfillment of the
requirements for the
Bachelor of Science (Hons) in Physics
June 2011
i
April 2012
Abstract
Stabilization of 960 nm laser could not be simply 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 stabilize the 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.
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
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
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 - Ø1" 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 - Ø1/2" 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× 10−6K−1) 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 Controller’s 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 because
we 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
28
Figure 3.14: Function generator in operation. Triangular waves of frequency 500 Hz, amplitude4 V and 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 β = 0.17 µm/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 ≈ 2± 0.5 V (0.5 V
were just rough estimation), meaning that the distance travelled by the mirror from one peak
to another is ∆x = β∆V = 0.32± 0.09 µm.
∆x is in fact the distance between two positions where wavelength 780 nm is in resonant state
29
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 of ∆x(= 0.32±0.09µm) from our measurement. The error of measurement
may come from the rough estimation of ∆V 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 + α1E + α2E2 + ... where α and α2 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 + αE. 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
30
Our EOM (LM0202P 0.10W) were expected to be driven by EOM Driver that operates at
certain frequency ωm. 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 ωm, the
refractive index would also change at the same rate, and therefore it produced sideband with
frequency ωm.
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(ωEt+ φE) and there is also signal from local oscillator VL = V2 sin(ωLt+ φL). The
mixer will produce the product of these signal which is
VEVL = V1V2 sin(ωEt+ φE) sin(ωLt+ φL)
VEVL = V1V2
(12
cos((ωE − ωL)t+ φE − φL)− 12
cos((ωE + ωL)t+ φE + φL))
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This output signal will then goes to a low-pass filter to cancel the high frequency term (ωE +
ωL). The maximize the output from the low frequency term, ωE − ωL is set to zero. Here, the
final 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. ωE = ωL is required for a stable DC offset, the resulting signal
would then be
VEVL =12V1V2 cos(φE − φL) (3.4)
The magnitude of the output depends on the phase difference between those two signals. Max-
imum output is achieved when φE − φL = 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 150/14-10/25
in 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.
32
3.2.3 Final Setup of Cavity Stabilization
Figure 3.19: Cavity Stabilization Setup
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 = Eoeiωt with
frequency ω and small bandwidth coming out from the section A. When passing through the
EOM the frequency of the beam will be modulated by frequency ωm so the electric field of the
laser will be
E = Eoei(ωt+β sinωmt)
where β 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
R(ω) is the reflection coefficient of the light at frequency ω, while Pc and Ps are constants that
represent power brought by center frequency and sideband frequency, respectively. Note that
2ωm 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 cosωmt+ =C sinωmt)
This signal is then mixed with signal from local oscilator (sinωmt) to extract the error signal
which is
ε = −B=C
where C = R(ω)R ∗ (ω + ωm)−R ∗ (ω)R(ω − ωm). Figure 3.17 describe the shape of the error
signal as function of ω
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
34
index β to get maximal value of√PcPs, which is proportional to the error signal. Dependence of
√PcPs to the modulation index β was previouly calculated in other thesis [9] and it was found
that the maximum happens when β = 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 1.2×10−6K−1 at temperature range 20−100oC, 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.
35
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.
36
Figure 3.23: Stabilization setup for 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 order
for 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.
37
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 β. Since cavity linewidth is not easily adjustable in our experiment therefore,
optimization of β value is needed. It turns out that when β = 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 and 960
2 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.
38
Both wavelength would then undergo the same path through the EOM and cavity. A dichroic
mirror (Thorlabs DMLP900 Ø1" 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
39
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 λ as long as the length of the cavity is exactly the largest common multiple of
360 nm and λ2 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.
40
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.
41
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.
42
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.
43
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