feasibility study for the frequency stabilization of the prima...

Institute of Microtechnology, Neuchâtel YS, 24.07.02

Feasibility Study for theFrequency Stabilization of the

PRIMA Metrology Laser

Doc No. VLT-TRE-IMT-15731-2868.

Technical representative : Samuel Lévêque

Written by: Y. Salvadé, O. Scherler

Supervised by: R. Dändliker

Address: Institute of MicrotechnologyUniversity of NeuchâtelRue A.-L. Breguet 22000 NeuchâtelSwitzerland

Phone: +41 32 718 3200Fax: +41 32 718 3201

Date: July 2002


2

Table of contents

1 Applicable document. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Review of the specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1 Requirements ...............................................................................................................44.2 Frequency noise spectrum of the Nd:YAG laser ..................................................................54.3 Required frequency noise spectrum. ..................................................................................84.4 Principle of the stabilization loop....................................................................................9

5 Frequency reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 15.1 Relative stabilization................................................................................................... 115.2 Absolute frequency references at 1.3 µm.......................................................................... 135.3 Frequency reference around the second-harmonic wavelength................................................ 145.4 Possible frequency references......................................................................................... 14

6 Absolute frequency stabilization on Iodine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 46.1 Introduction............................................................................................................... 146.2 Arie technique............................................................................................................ 146.3 Saturation spectroscopy ............................................................................................... 156.4 Second harmonic generation.......................................................................................... 15

7 Stabilization on ultra-stable Fabry-Pérot cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 17.1 ULE or Zerodur cavities ............................................................................................... 217.2 Cavity stabilized on a master laser ................................................................................. 22

8 Stabilization techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 48.1 Side-of-fringe locking.................................................................................................. 258.2 Center-of-fringe locking............................................................................................... 268.3 Frequency dithering. .................................................................................................... 29

9 Test plan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 09.1 Beat frequency measurement.......................................................................................... 309.2 Phase measurements at large distances ............................................................................ 319.3 Comparison with an Agilent interferometer ..................................................................... 31

1 0 Possible concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 210.1 Stabilization technique................................................................................................. 3210.2 Frequency reference ..................................................................................................... 32

1 1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4

1 2 Acknowledegements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5

INSTITUT DE MICROTECHNIQUE UNIVERSITE DE NEUCHATEL

Rue A.-L. Breguet 2 Phone: +41 32 718 3211CH - 2000 Neuchâtel, Switzerland Fax: +41 32 718 3201http://www-optics.unine.ch


Frequency Stabilization of the

PRIMA Metrology Laser

Feasibility study

Y. Salvadé, O. Scherler and R. Dändliker

1 Applicable document

[AD1] “Technical Specifications for the PRIMA Metrology System”, VLT-SPE-ESO-

15730-2211

[AD2] “Technical specifications and Statement of work for the Light Source of the PRIMA

Metrology System”, VLT-SPE-ESO-15731-2637, Draft issue.

2 AcronymsAOM Acousto-optic modulatorDWDM Dense wavelength division multiplexingFM Frequency modulationFP Fabry-PérotFSR Free Spectral RangeFWHM Full width at half maximumKTP Potassium titanyl phosphateNPRO Non-planar ring oscillatorOPD Optical path differencePI Proportional-IntegratorPRIMA Phase referenced imaging and µas astrometryPZT Piezo translatorQPM Quasi-phase matchingSHG Second-harmonic generationULE Ultra-low-expansion


4

3 Introduction

The laser source of the PRIMA metrology shall be compatible with the requirements specified

in AD1. The critical aspects are the emitting wavelength, the optical power, the coherence length

and the frequency stability of the laser. The NPRO Nd:YAG laser (Lightwave model no 125 or

Innolight Mesphisto product line) emitting around 1319 nm has already been identified as the

most suitable laser for this application. This laser seems to fulfill all the requirements regarding

its emitting wavelength, optical power and coherence length. The frequency stability of

commercially available lasers (Lightwave, Innolight) is however not sufficient to achieve 1 nm

accuracy over 100 mm. This feasibility study will be focused on the possible frequency

stabilization techniques for the Nd:YAG lasers to achieve the desired frequency stability. The

preferred solution will be selected, as well as the possible remaining critical aspects. Finally, a

test plan will be proposed to verify by measurement the stability of the final PRIMA laser

source.

4 Review of the specifications

4.1 Requirements

Table 1 summarizes the requirements for the laser source. Comments have been added, to

indicate the potential critical aspects.

Aspects Requirements Comments

Wavelength Between 1.1 –1.5 µm to avoidstraylight on existing stellarphotodetectors

No major problems. Achievedwith NPRO Nd:YAG laseremitting at 1.319 µm

Coherence length > 260 m (maximal opticalpath difference)

No major problems. Easilyachieved by commercialNPRO Nd:YAG laser.

Optical power Given by the power lossesalong the VLTI paths, thelosses of the fiber couplersand AOMs, beam injectionand extraction, as well as thepower required by the laserstabilization part.

The highest power availablefor NPRO Nd:YAG lasers is200 mW at 1319 nm.According to the recent testsperformed at Paranal, thisoptical power is amplysufficient.

Frequency stability(over at least the measuringtime of 30 min)

better than 1.10-8 to achieve1 nm accuracy over 100 mm.Corresponds to a frequencyinstability ∆ν < 2 MHz

Critical aspect

Wavelength calibration better than 1.10-8 Critical aspect


5

accuracy A frequent calibration isrequired only if a long-termstability is not ensured.

Short term frequencyfluctuations

See chapter 4.2

If possible, the correspondingphase fluctuations must belower than 2π/132 (5 nm) forthe highest specifiedbandwidth, i.e. 8 kHz

Critical aspect

Table 1: Requirements of the laser source.

4.2 Frequency noise spectrum of the Nd:YAG laser

1.1.1 Measurementsof the beat frequency measurements

990

980

970

960

950

Bea

t fre

quen

cy [

MH

z]

6050403020100

Time [min]

Figure 1: Power spectral densities of the individual phase measurements at largeoptical path difference.

During previous tests of the recently developed phase-meter prototype, we measured the beat

frequency between two free-running Lightwave Nd:YAG lasers (model no 125). Results are

shown in Fig. 1. Assuming identical contributions for both lasers, we could deduce the psd of

the frequency noise for a single laser.

The presented measurements were performed after more than 1 hour after the lasers were turned

on. The drift during the first hour of operation exceeds however 100 MHz. Note that the

reproducibility of the laser frequency, after turning off and on the lasers, was found to be better

than 1 GHz.


6

4.2.2 Measured phase fluctuations at large OPD

The phase-meter prototype was tested by means of a heterodyne interferometer with a very large

optical path difference, provided by a 1 km fiber delay (1.5 km of OPD). The individual phase

was measured by means of the phase-meter. At low frequencies (< 1 Hz), the phase noise is

probably dominated by the drifts of the optical path difference. However, at higher frequencies,

the contribution of the laser frequency noise becomes the dominant factor except for a few

vibration frequencies.

10-6

10-4

10-2

100

102

104

106

Phas

emet

er P

SD [

digi

t^2/

Hz]

101

102

103

104

Frequency [Hz]

Individual phase Phase difference

Figure 2: Power spectral densities of the individual phase measurements at largeoptical path difference

The statistical properties of the random phase fluctuations (noise) are conveniently described by

power spectral densities (psd). It can be shown [1] that the relation between the psd of the

instantaneous phase fluctuations S f∆φτ( )and the psd of the laser frequency fluctuations S fδν ( )

is

S f S f

ff∆φ δντ

τ ττ

( ) ( )sin= π π

π

4 2 2

2

. (1)

where τ is the interferometric delay, i.e. OPD/c. However, the instantaneous phase can never be

observed physically, because of the finite detection bandwidth. Integrated phase fluctuations

have therefore to be considered.


7

The measured phase fluctuations are given by a time averaged value of the instantaneous phase

fluctuations during the observation time T, namely

∆ ∆φ φτ τ, ( ) ( )T

t T

t

tT

t dt=−∫1

. (2)

The relation between the corresponding power spectral densities is thus given by

S f S f

fTfTT∆ ∆φ φτ τ,

( ) ( )sin= π

π

2

. (3)

Using Eq. (1), S f

T∆φτ ,( ) becomes

S f S f

ff

fTfTT∆φ δντ

τ ττ,

( ) ( )sin sin= π π

π

ππ

4 2 2

2 2

. (4)

If the interferometric delay is much smaller than the integration time (which is usually the case),

Eq. (4) can be approximated by

S f S f

fTfTT∆φ δντ

τ,

( ) ( )sin= π π

π

4 2 2

2

. (5)

If we assume that the phase noise measured in Fig. 2 is mainly caused by the laser frequency

noise spectrum, we can therefore deduce from Eq. (5) the power spectral density of the laser

frequency fluctuations. The integration time T was of 20 µs and the interferometric delay τ is

given by OPD/c. Since the index of refraction of the fiber is about 1.5 the OPD of a 1 km fiber

delay is of 1500 m. Figure 3 shows the deduced psd of the frequency noise. We assumed here a

white noise level after 10 kHz, but the 1/f part may still dominate at higher frequencies.

By integrating the psd from 0.1 mHz to 100 kHz, we calculated a frequency drift of

10 MHz/hour (standard deviation), which is consistent with the value given by Lightwave, i.e.

< 50 MHz/hour. If we integrate the psd from 1 Hz to 100 kHz, we find a standard deviation of

40 kHz/s, which is again close to the frequency jitter given by Lightwave, i.e. < 200 kHz/s. In

addition, we note also that this frequency noise psd is in good agreement with the psd measured

by Dubovitsky et al. [2].


8

100

102

104

106

108

1010

Freq

uenc

y no

ise

PSD

[H

z/H

z0.5 ]

10-4 10

-2 100 10

2 104

Frequency [Hz]

Measured by beat frequency Measured by phase noise measurements Estimated frequency noise

Figure 3: Estimated frequency noise spectrum of the Lightwave serie 125 Nd:YAGlaser. The white noise level around 10 kHz was assumed but not clearlyobserved.

4.3 Required frequency noise spectrum.

The variance of the measured phase fluctuations ∆φτ ,T

2

is obtained by using the Parseval

relation, which gives then

∆ ∆φτ φτ, ,

( )T S f dfT

2

0

=∞

∫ . (6)

As a rough approximation, we can assume that the frequency noise spectrum of the stabilized

laser is white within the detection bandwidth, i.e. S f Cδν( ) = 0 , for f < B = 1/2T. In that case we

have

∆φ π τ π ττ ,T C

TC B

2 20

22

022 4≈ = . (7)

To achieve the desired accuracy of 5 nm the maximal phase variations must be less than 2π/132.

Therefore, the standard deviation σφ must be less than 2π/400. Using Eq. (7), we see that the

value for C0 must fulfill the condition

C

B0

2

2 24<

σπ τ

φ (8)


9

For τ = 120 mm/c = 0.4 ns and B = 8 kHz, we see that C0 < 5 109 Hz2/Hz. The power spectral

density of the remaining frequency fluctuations must therefore be less than 5 109 Hz2/Hz (or

7.1 104 Hz/Hz0.5) for frequencies f < 8 kHz. The power spectral density shown in Fig. 4 allows

therefore to fulfill this requirement. As it can be seen, the cut-off frequency of the regulator does

not need to be higher than 1 Hz.

100

102

104

106

108

Freq

uenc

y no

ise

PSD

[H

z/H

z0.5 ]

10-4 10

-2 100 10

2 104

Frequency [Hz]

Free-running laser Stabilized laser Noise limit

Figure 4: Required frequency noise spectrum for the stabilized Nd:YAG laser.

4.4 Principle of the stabilization loop

4.4.1 Scheme

Laser Freq. ref.Error

signal det.

Reg.

PZTT

Figure 5: Generic scheme of the frequency stabilization loop.

The block diagram of the stabilization scheme is shown in Fig. 5. It is composed of a frequency

reference or frequency discriminator, an error signal detector block, a regulator which acts on the

fast and slow tuning inputs of the Lightwave electronic driver of the Nd:YAG. The fast

frequency tuning is provided by a piezo transducer which can change the cavity length by

stressing the non-planar ring oscillator (NPRO) crystal. The sensitivity varies from device to

device, but is typically of 2 MHz/V over a range limited to ±30 MHz. The time constant τ is less

than 1 ms, i.e. a bandwidth of 1/2πτ ≈ 10 kHz. The slow tuning is provided by changing the


10

temperature crystal. The sensitivity is of 2.4 GHz/V, and the maximal tuning range is of

several GHz between two mode hops. The time constant is however limited to 1 s.

We also note that the frequency can be changed by acting on the laser diode power

(several MHz/mW). A frequency stabilization by controlling the laser pump power was

proposed in [3]. In addition to the frequency stabilization, the intensity noise was reduced by

10 dB, showing that the 1/f noise part of the frequency noise psd is mainly caused by the

intensity noise of the semiconductor cavity which pumps the crystal.

4.4.2 Regulation loop

An appropriate feedback loop must be used to get the required psd. As long as the regulator

does not introduce additional noise, the psd of the frequency noise with electronic feedback is

given by [4]

S fH f

S fwith feedback free running∂ν ∂ν( )

( )( )

=

+ −

1

1 2 , (9)

where H(f) is the transfer function of the loop. In most regulated systems, PID (Proportional-

Integrator-Differentiator) servo loops are used for the stabilization. The transfer function of the

feedback loop is given by the product of the transfer function of the regulator with the transfer

function of the error signal detector.

10-3

10-1

10

1

103

Tra

nsfe

r fu

nctio

n

10-4 10

-2 100 10

2 104

Frequency [Hz]

Figure 6: Example of transfer function for the feedback loop.

Figure 6 shows the example of the transfer function of a system composed of an integrator

dominant for frequencies lower than 1 Hz, a proportional with a gain of 5 and a detection

bandwidth of 10 Hz. Figure 7 shows the expected frequency noise psd, calculated from Eq. (9).


11

We see that the noise level for frequencies f < 8 kHz is lower than the required level of 7.1 104

Hz/Hz0.5. A PI type regulator seems therefore to be appropriate for this application.

101

103

105

107

10

9Fr

eque

ncy

nois

e PS

D [

Hz/

Hz0.

5 ]

10-4 10

-2 100 10

2 104

Frequency [Hz]

Expected Free-running

Figure 7 : Expected frequency noise psd.

5 Frequency reference

As shown in Fig. 5, the stabilization loop requires a frequency reference. The laser frequency

will be stabilized with respect to this frequency reference.

5.1 Relative stabilization

5.1.1 Phase-locking

The frequency reference can be another “master” laser. The laser frequency laser is then

stabilized by beat frequency measurement and by means of an optical phase-locked loop, as

shown in Fig. 8. In the depicted scheme, the lasers are stabilized with a frequency difference

given by the electrical local oscillator LO. For example, these stabilization schemes are used for

laser satellite intercommunications with coherent detection [5]. We note that the lasers are not

only frequency locked, but also phase-locked. The absolute stability of the stabilized laser

depends therefore only on the absolute stability of the master laser. The maximal frequency

difference is limited to about 100 GHz by the bandwidth of the high-speed photodetector which

detects the beat note.


12

Master laser

Nd:YAG laser

Servo loop 2 LO

Figure 8: Principle of an optical phase-locked loop.

5.1.2 Fabry-Pérot resonator

The laser frequency can be stabilized to the resonance of an optical resonant cavity, e.g. a Fabry-

Pérot resonator. Figure 9 shows the transmission of Fabry-Perot resonator for different finesse.

1.0

0 .5

0 .0

Tra

nsm

issi

on

Frequency

F = 200 F = 50 F = 20 F = 2

νm νm + 1

Figure 9: Fabry-Pérot transmission vs frequency for different finesse F.

High-finesse resonators allow substantial laser linewidth reduction. Sub-hertz relative frequency

stabilization of two Nd:YAG lasers was achieved by Day et al. [6], using a high-finesse cavity.

The absolute stability of the stabilized laser will be limited by the drifts of the resonance, caused

by a change of the cavity length. The use of ultra-low-expansion cavity [2] should allow to

minimize these drifts. Another solution consists of stabilizing the cavity with respect to a master

laser.


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5.2 Absolute frequency references at 1.3 µm

Absolute frequency stabilization can be achieved by stabilizing the laser frequency with respect

to an atomic or molecular absorption line. Several frequency references near 1.3 µm have been

used for absolute frequency stabilization [7].

5.2.1 Reported stabilization schemes

Table 2 shows a list of reported stabilization schemes with atomic or molecular frequency

references near 1.3 µm.

Name λ [µm] Reference Comments

Yamaguchi,82 1.278145 HF Highly corrosive materialChung, 88 1.3276 Ar optogalvanic effect must be usedBoucher, 92 1.3239 Rb transition between excited statesDennis, 02 1.314 CH4 Stabilization on a Doppler-

broadened line

Table 2: Reported frequency stabilizations with absolute frequency referencesaround 1300 nm

5.2.2 Frequency references around 1300 nm

The 1.3 µm Nd:YAG laser has a limited tunability of 50 GHz, i.e. the wavelength can vary

between 1319 to 1319.3 nm. Table 3 shows a list of atomic or molecular frequency references

which have some absorptions lines between 1319 and 1320 nm, and which may be suitable for

absolute frequency reference.

Material λ [µm] Comments

Carbon dioxide 1.31183–1.31997 Very weak lines, requiresabsorption paths of more than 10m

Water 1.280–1.320 Very weak lines, complex spectrumand heating is required

Hydrogen Fluoride 1.278–1.32124 Highly corrosive, causes handlingdifficulties

Hydogen Sulfide 1.280–1.320 ToxicNitrate NO3 1.315–1.320 Complex spectrum, we are not sure

that a transition exists within theNd :YAG tuning range.

Methane 1.312–1.320 Apparently, no absorption lineswithin the Nd :YAG tuning range[7]

Table 3: List of possible atomic or molecular absorption cells


14

5.3 Frequency reference around the second-harmonicwavelength

Arie et al. [8] reported the absolute frequency stabilization of a 1.3 µm Lightwave Nd:YAG laser

by locking its second-harmonic to an iodine absorption cell. Second-harmonic generation is

therefore required. At least five absorption lines can be used within the tuning range of the

Nd:YAG laser.

5.4 Possible frequency references

Carbon dioxide and water seems to have absorption lines in the Nd:YAG wavelength range, but

the required absorption path length is too long. The use of corrosive and toxic material like

hydrogen sulfide or hydrogen fluoride is also not recommended. Nitrate is a potential

absorption cell, but its spectrum is very complex and there are few studies of NO3 at 1300 nm.

In summary, there are no atomic or molecular absorption cells around 1319 nm which are

suitable for our application. Two concepts will be considered:

• Absolute frequency stabilization on iodine around 659.5 nm

• Stabilization on ultra-stable Fabry-Pérot cavities.

6 Absolute frequency stabilization on iodine

6.1 Introduction

Iodine absorption cells are often used for frequency stabilization. The drifts of absorption lines

are only of about 10 kHz/°C (–3x10-11/°C). The most notable iodine-stabilized laser is the He-

Ne laser, which is commonly used for practical length metrology. Arie et al. [9] did the first

iodine frequency stabilization of frequency-doubled Nd:YAG laser. These iodine stabilized

Nd:YAG lasers already demonstrated a remarkably low Allan deviation of 5 x 10-14 for an

integration time of 1 s [10]. They may be able to replace in the future the low-power He-Ne

laser.

6.2 Arie technique

As already mentioned, absolute frequency stabilization of the second-harmonic of the 1.3 µm

Nd:YAG laser was reported by Arie [8]. Ten absorption lines were observed within the tuning

range of the Lightwave Nd:YAG laser. The five strongest lines were identified in the iodine atlas

and are listed in Table 4.

The stabilization were realized on the P(48)6-6 transition. The width of the Doppler-broadened

line was estimated to be 800 MHz. It seems the line is composed of 15 unresolved hyperfine


15

structures. The absorption was estimated to be 0.56 m–1/Torr. The iodine cell was slightly heated

(57°C) to get about 3.5 Torr. The length of the cell was 13 cm, yielding an absorption of about

25%. The remaining laser frequency fluctuations were estimated to be less than 1 MHz.

Second-harmonic Fundamental Transition

659.588 nm 1319.176 nm P(49)6-6

659.570 nm 1319.140 nm R(55)6-6

659.549 nm 1319.098 nm P(48)6-6

659.531 nm 1319.062 nm R(54)6-6

659.530 nm 1319.059 nm P(111)5-5

Table 4: Absorption lines within the tuning range of the Nd:YAG laser.

6.3 Saturation spectroscopy

Significantly better frequency stability and reproducibility would be obtained by locking on the

Doppler-free lines, using saturation spectroscopy. This technique is commonly used for the

stabilization at 532 nm for the frequency-doubled Nd:YAG laser [9]. A pump beam

counterpropagates through the iodine cell, as depicted in Fig. 10. As a result, narrow peaks will

appear in the absorption profile, because of Doppler saturation. These peaks correspond the

hyperfine component of the absorption lines, and their width are typically of a few MHz. A

better sensitivity is therefore provided. However, several mW of second-harmonic are required

to achieve the saturation according to Arie [9].

Iodine

Saturation beam

Figure 10 : Saturaturation spectroscopy of iodine.

6.4 Second harmonic generation

6.4.1 Introduction

Second-harmonic generation is a second-order non-linear effect. For an anistropic non-linear

media, the polarization vector is related with the electrical field by

P E d E E i j ki ij j ijk

jkjj k= + =∑∑ε χ0 2 1 2 3 , , , , (10)


16

where the coefficients dijk are elements of a tensor, which define the non-linear coefficients.

Because of symmetry properties of the tensor, the elements are usually listed in a 6x3 matrice

with elements dIk where the single index I = 1,...,6 replaces the pair of indices (i,j).

6.4.2 Phase-matching

Second-harmonic light is generated when the phase matching condition is fulfilled. In general

three-wave mixing, the phase-matching condition is

k k k3 1 2= + (11)

where k1 and k2 are the wave vectors of the incoming beams, and k3 is the wave vector of the

outgoing beam. If the three waves propagate in the same direction, we have

n(ω3) ω3 = n(ω1) ω1 + n(ω2) ω2 (12)

where ω1 and ω2 are the frequencies of the incoming waves and ω3 is the frequency of the

outgoing wave. For second-harmonic generation we have ω1 = ω2 and ω3 = 2ω1 and therefore

the phase-matching condition becomes

n(ω1) = n(2ω1). (13)

Since the non-linear media is always dispersive, this condition is in general not fulfilled.

• Birefringent phase matchning

Precise control of the refractive indexes is often achieved by using the birefringence of the non-

linear media, i.e. by appropriate selection of the polarization and direction of the incoming beam

relative to the crystal axes. Two types of phase-matching are usually employed:

Type I: In that case, the input and output waves are orthogonally polarized. The fundamental

wave is an extraordinary wave with a refractive index neω(θ), and the second-harmonic wave is an

ordinary one with a refractive index no2ω. The phase matching condition is fulfilled by selecting

an angle of incidence θ for which

12

2

2

2

2

2n n no o e

ω ω ω

θ θ

( )=

( )+

( )cos sin

. (14)

Type II: In that case, the incoming polarization is at 45°. We can therefore consider at the input

an extraordinary and an ordinary wave with refractive indexes neω(θ) and no

ω, respectively. The

second-harmonic wave is either an extraordinary or ordinary wave. Assuming that the second-


17

harmonic wave is an extraordinary ray with refractive index ne2ω(θ), the phase-matching

condition becomes

n n ne e o

2 12

ω ω ωθ θ( ) ( )= +[ ] . (15)

We note that half of the birefringence is used.

• Quasi-phase matching

Quasi-phase matching is an alternative solution. In this case, the phase mismatch of one section

is balanced against a phase mismatch of the opposite sign from a second section. Quasi-phase

matching is achieved when the ion- exchanged regions within the non-linear crystal periodically

reverse the direction of the permanent electric dipole. This reversal has the effect of turning the

orientation of the non-linear medium up side down, and causing a π phase shift in the

frequency-doubled light. In a properly quasi-phase matched crystal, this reversal is engineered

such that “newly” generated light adds constructively to the “old” light. As a result, the phase-

matching is much less critical. In addition, this technique allows to access the large d33 non-

linear coefficient which is not accessible with birefringent phase matching, giving rise to larger

conversion efficiency (see next section).

6.4.3 Efficiency

For low conversion efficiency, the efficiency of the non-linear conversion is of the form [11]

η ∝( )

( )I L d

kL

kLeff

2 22

2

2

2

sin ∆

∆(16)

where I is the incoming intensity (optical power per surface unit), ∆k is the phase mismatch, L

the crystal length and deff the effective non-linear coefficient which is a function of the dIk

coefficients. As a result, the intensity of the second-harmonic light is proportional to the square

of the incoming intensity. The phase mismatch is

∆k I n ne o( ) ( )= π −[ ]2 2

λθω ω

(17)

for type I phase matching, and


18

∆k II n n ne o e( ) ( ) ( )= π +( ) −

2 12

2

λθ θω ω ω

(18)

for type II phase-matching, where λ is the wavelength of the second-harmonic.

Note that the efficiency is ideally proportional to the square of the crystal length L. This is

however only true for waveguide structures where the light is confined in a small area over the

whole length of the crystal. For bulk crystals, the light must be focused at the center of the

crystal for an optimal efficiency. As a result, the total efficiency will be proportional to L

(instead of L2) since the beam focusing is limited by the crystal length [12]. Because of the

problems of crystal uniformity, the length of non-linear crystals is typically limited to a few cm.

6.4.4 Non-linear materials

Two non-linear materials are commonly used for SHG around 1–1.5 µm:

• Potassium titanyl phosphate (KTP)

KTP crystals are often used for frequency doubling at 1064 nm and 532 nm. They have

broad temperature and angular acceptances, which make them particularly attractive for

second-harmonic generation at room temperature. Type II phase-matching is always used,

although type I phase matching seems to be feasible.

• Lithium Niobate (LiNbO3) or Magnesium Oxide Doped Lithium Niobate (MgO: LiNbO3)

Lithium Niobate is a also widely used as frequency doublers for wavelength larger than

1 µm. With an appropriate MgO doping, non-critical phase matching can be achieved by

heating the crystal [9], leading to a large angular acceptances.

6.4.5 Possible schemes

As already mentioned, the efficiency is proportional to the input power. Ideally, one should

generate the second-harmonic directly at the output of the NPRO crystal, to take advantage of

the full power of the laser (> 200 mW). After SHG, the fundamental wavelength and the second-

harmonic should be separated by means of a dichroic beamsplitter, and then the fundamental

could be directed to the PRIMA metrology as the second-harmonic light could be used for the

frequency stabilization. This scheme would provide the best efficiency, since only a few µW of

the fundamental light is absorbed in the non-linear crystal. However, for convenience, an all-

fiber system composed of fiber-pigtailed Nd:YAG laser source and acousto-optic modulators is

desirable for the PRIMA metrology. To enable this all-fiber system, a fiber coupler must be

used to pick up one part of the fundamental light emitted by the Nd:YAG laser for the second-

harmonic generation. Recent tests of the metrology prototype at Paranal showed that 50 mW of


19

the 200 mW available can easily be raised from the laser light source, since we had to use grey

filters with 25% transmission to avoid saturation on the photodetectors [13]1. Therefore, we will

consider here an available optical power of 50 mW for the second-harmonic generation, in order

to consider the worst case.

Single pass with birefringent phase-matching

For instance, this scheme has been applied in [14] with a 5-mm long KTP crystal at room

temperature. The conversion efficiency was lower than 10-6 for an input power of 4 mW. If we

have 50 mW optical power available for the stabilization, we expect an optical power of more

than 300 nW with the same set-up.

As already mentioned, type II phase matching is always used for this material, probably because

of a larger non-linear coefficient. At 1064 nm, the phase matching is realized in the xy plane.

According to the values of the three refractive indexes nx, ny and nz given by the manufacturer,

the slope d(∆k)/dθ is small. This corresponds to a broad angular acceptance of 20 mrad for a

1 cm long crystal. At 1319 nm, however, the phase-matching must be done in the xz plane.

Numerical simulations (see Annex I) show that the angular acceptance is narrower, typically 0.1

deg (FWHM) for a crystal length of 10 mm. The same calculation was done for type I phase-

matching, which shows a very narrow angular acceptance of 0.03 deg (FWHM). The

temperature bandwidth of both phase-matching techniques is however very broad (a change of

10°C corresponds to an efficiency variation which is less than 10% for type II phase-matching).

Therefore, a temperature controller is probably not required for KTP crystals. However, we see

that the divergence angle of the beam must be smaller than 0.1 deg for an optimized phase

matching. On the other hand, the laser beam must be focused in the crystal to increase the

intensity, and thus the efficiency. The depth of focus of the beam must be roughly equal to the

crystal length for optimal operation. Assuming Gaussian beams, we must have L zR≈ , where zR

is the Rayleigh range of the beam.

KTP and LiNbO3 crystals are commercially available from e.g. JDS Casix (China), Deltronic

Crystal Industries (USA) or Red Optronis (USA). KTP crystals designed for frequency

doubling of 1319 nm are commercially available from Raicol, Israël. The price of a 3x3x8 mm3

is less than 1’000 € .

1 During the tests held at Paranal in April 2002, the optical train included neither the star separator nor the

PRIMA retro-reflector. Additional power losses are therefore expected.


20

Quasi-phase-matching with periodically poled Lithium Niobate or KTP

In LiNbO3 and KTP, quasi phase matching is achieved by periodic ferroelectric domain reversal

(periodically poled crystal). This technique allows to access the large d33 non-linear coefficient

which is not accessible with birefringent phase matching. The temperature bandwidth is higher

than 8 °C which eliminates the need of a precise temperature control. The company Innolight

(Germany) uses a periodically poled crystal for the Prometheus Nd:YAG laser emitting at both

1064 nm and 532 nm. Furthermore, this technique was applied in [8] at 1319 nm. For an input

power of 100 mW injected in the waveguide, more than 1 mW was generated, giving rise to a

conversion efficiency of 1%. The coupling losses were of about 40%. If we have 50 mW optical

power available, we should inject about 30 mW in the waveguide. We should then obtain a

conversion efficiency of 0.3%, giving rise to an output power of 100 µW, i.e. a factor 300 better

compared to a single pass birefringent phase-matched conversion efficiency.

Periodically poled lithium niobate structures are commercially available (INO, Canada; HC

Photonics, Taïwan) but require a custom designed mask. The overall price per piece is of about

4’000 € for 10 mm long crystals. According to HC photonics 10 µW can be generated in the

best case. The implementation of a waveguide is however not standard and would require more

efforts.

Periodically poled KTP waveguides are commercially available from AdvR Inc., Montana. They

could manufacture waveguides with the appropriate QPM structure (17 µm period) at the same

time they do another fabrication run, and then the price should be of 2’500 € /piece. A custom

fabrication run on a whole KTP wafer will cost about 35’000 € .

Since the manufacturers of periodically poled structures have generally no light source at this

specific wavelength to test the crystals, the structures would have to be done on a best effort

basis. A temperature tuning of the periodically poled crystal may be required to achieve the

quasi-phase matching because of manufacture tolerances.

Resonant doubling cavity

The use of a non-linear crystal in a resonant cavity enables high conversion efficiencies even for

low input powers. Lightwave developed a monolithic ring frequency doubler for their model 142

Nd:YAG laser, to generate the 532 nm wavelength. Conversion efficiency as high as 65% has

been reported [15]. Arie et al. [9] used also a resonant cavity to frequency double the 1.064 µm

wavelength, and obtained a conversion efficiency of 10%.

However, the resonant doubling cavity requires a servo controller to lock the resonant frequency

of the cavity to the laser frequency, thus increasing experimental complexity.


21

7 Stabilization on ultra-stable Fabry-Pérot cavity

7.1 ULE or Zerodur cavities

An alternative solution to atomic or molecular frequency reference is the use of an ultra-stable

Fabry-Pérot cavity. Considerable developments of ultra-low expansion Fabry Perot etalons

haven been realized over the last few years for DWDM applications. Dense-wavelength division

multiplexing requires stabilized lasers around 1.5 µm referenced to the ITU grid which defines a

set of channels with a frequency spacing of 100 GHz. Usually, air-spaced etalons are used for

this purpose. The spacer can be made of Zerodur or Corning ULE glasses, which have an

thermal expansion as low as 0±0.02x10-6.

Figure 11: Picture of commercially available etalons (SLS Optics).

7.1.1 Long-term drifts

Usually, air-spaced etalons stability are limited by the change of the refractive index of air

(10–6/°C). The long-term drifts can therefore be substantially improved by using a vacuum

chamber and a temperature controller. With evacuated operation, suitable temperature control,

optically contacted mirrors, ULE spacers, drift rates as low as a few kHz per day (10-11/day)

have been achieved [16]. Simplified versions of these etalons are now commercially available

(SLS optics), which should allow drifts less than 1 MHz/day (10-8/day). A free-spectral range of

10 GHz can be accommodated, which should ensure that the laser frequency stabilizes always

on the same resonance (the laser frequency reproducibility is less than 1 GHz). A finesse of 60

should be obtained, i.e. a resonance width of 130 MHz. The spacer is made of Zerodur. The

price of such a device is less than 2’500 € .

7.1.2 Special cares

Mechanical noise

Fabry-Perot etalons are interferometric devices and are thus sensitive to vibration. The vacuum

chamber must be placed on a passively isolated optical table, to minimize these effects.


22

Wavelength calibration

Probably, the drift of the resonance frequency won’t be much better than 10-8/day. Therefore, a

daily wavelength calibration with an accuracy better than 10-8 is mandatory. The wavelength

calibration can be made by comparison with a commercially available Agilent laser

interferometer. For this application, a possible solution consists of using the delay lines and its

internal metrology (Agilent interferometer), as shown in Fig. 12. Heterodyne apparatus of the

PRIMA metrology can be used to measure the displacement of the delay lines. By comparing

the results obtained with the internal metrology and the results obtained with the PRIMA

heterodyne apparatus, we can calibrate the frequency of the Nd:YAG laser with respect to the

Agilent laser wavelength. Since the absolute frequency stability of Agilent interferometers is

better than 10-8, a calibration accuracy with the same accuracy can be achieved provided that the

measured path length is long enough. Assuming 20 nm accuracy, the displacement of the delay

line should be of at least 2 m to achieve an accuracy of 10-8.

Agi

lent

lase

r

Agilent det.Probeν+f

ν PBS PBS

PBS

Ref

From AOMs

Delay lines

Figure 12 : Calibration of the wavelength by means of the delay line internal metrology.

7.2 Cavity stabilized on a master laser

To ensure that the Fabry-Perot cavity is stable during the measurement, the cavity can be locked

to master frequency stable laser. The stability of the cavity is then given by the absolute


23

frequency stability of the master laser. The principle is shown in Fig 13. Note that this concept

involves a piezo translator to change the cavity length. This is unfortunately not compatible with

ULE etalons, whose mirrors are optically contacted with the ULE (or zerodur) spacers. Optical

spectrum analyzer should therefore be used for that purpose.

The master laser can be a stabilized laser diode. The stabilization of a laser diode on a Methane

absorption line seems to be feasible [7]. However, three feedback loops must be implemented,

thus increasing the complexity. Agilent laser is again the most promising master laser (Price:

7’000 € ). In the limiting case, a small amount of light coming from the delay line internal

metrology can be picked up and brought by optical fibers to the interferometric lab, to avoid the

need of an additional Agilent laser and reduce the cost of the system. However, the cavity

mirrors of the Fabry-Pérot analyzer must be coated at both 633 nm and 1.3 µm. The price of

such an optical spectrum analyzer (commercially available from e.g. CVI, Burleigh or Coherent)

with custom designed mirrors is about 10’000 €. Another solution consists of locking the

second-harmonic at 659.5 nm to avoid the need of a custom coating.

Masterlaser

Fabry-Pérot cavity

Nd:YAG laser

PZT

Servo loop 1

Servo loop 2

Figure 13 : Principle of the stabilization of Nd :YAG laser, which is itself stabilized on amaster laser

Agilent laserSpectra-Physics

FP analyzer PZT

Lock-in

20 kHz+

PI

Figure 14 : Experimental set-up used for the preliminary tests.

To ensure that the same resonance is always stabilized on the master laser, the length stability of

the Fabry-Perot cavity must be of 10-5, assuming a free spectral range of 10 GHz. Preliminary

tests were realized to prove the reliability of the concept. An optical spectrum analyzer from our


24

stock (Spectra-Physics analyzer) was stabilized on an Agilent laser head, as shown in Fig. 14.

The FSR of the cavity was 8 GHz. We used a synchronous detection to stabilize the laser. The

cavity length was modulated by means of the piezo translator at a frequency of 20 kHz. A lock-

in amplifier is used for the error signal detection and a PI regulator was used for the active

stabilization. The output of the regulator was electronically added to the modulation signal of the

piezo translator to close the feedback loop. The stabilization loop was activated during two days.

By measuring the output of the integrator, we could estimate the drifts of the cavity. Results are

shown in Fig. 15. The drift was estimated to be about 4 GHz/day. Therefore, if the stabilization

of the cavity length is turned off during one day, a re-calibration of the optical wavelength is

recommended.

-6

-4

-2

0

2

Freq

uenc

y dr

ift [

GH

z]

403020100

Time [h]

Figure 15: Estimation of the frequency drifts of a commercially available opticalspectrum analyzer (Spectra-Physics).

8 Stabilization techniques

Different stabilization schemes have been used to lock a laser frequency to a resonance of a

Fabry-Pérot resonator or to the line of an atomic or molecular absorption cell [17]. The laser

frequency can be stabilized either on the flank or on the center of the resonance or absorption

line. Atomic absorption lines and high-finesse Fabry-Pérot resonance can be described in a

good approximation by Lorentzian line shape. The transmission through the frequency

reference can be written as

T C C( )νν

ν ν ν= +

( )−( ) + ( )1 2

2

0

2 2

2

2

∆

∆(19)


25

where ∆ν is the linewidth (FWHM), ν0 is the center frequency of the line, and C1 and C2 are

coefficients which depend on the type of frequency reference. For Fabry-Pérot etalons we have

∆ν = FSR/F where F is the finesse, C1 ≈ 0 and C2 = Tmax where Tmax is the maximal

transmission of the etalon. For absorption lines we have C1 ≈ 1 and C2 = –Amax where Amax is

the absorption coefficient of the line (about 25% for iodine at 659.5 nm and 3.5 Torr).

8.1 Side-of-fringe locking

In this technique, the laser frequency is stabilized to a fixed point on the flank of the line, as

hsown in Fig. 16 for an iodine absorption line. This scheme has been proposed in [14] for

coherent free-space optical communications. The principle of the stabilization loop is shown in

Fig. 17.

0.9

0.8

0.7

0.6

0.5

Tra

nsm

issi

on

-2 -1 0 1 2Frequency detuning [GHz]

Working point

Figure 16 : Principle of side-of-fringe locking.

To suppress the effect of laser power fluctuations, the incoming laser power is measured at the

input of the frequency reference. A subtracter is then used to balance the intensities of the input

and output beams.

Nd:YAG SHG Freq. ref. Subtracter

PID

Figure 17: Principle of the stabilization loop for side-of-fringe locking.

To determine the sensitivity of the frequency discriminator, we calculated from Eq. (19) the

maximal slope of the lineshape function by calculating its first derivative. We found that the

slope is maximal and minimal at ν ν ν= ±0 2 3∆ /( ), and is


26

′ =T

Cmax

3 34

2

∆ν. (20)

For a Doppler-broadened iodine frequency reference, we have C2 = 0.25 and ∆ν = 800 MHz, we

found a slope of 0.4 GHz-1. A frequency deviation of 2 MHz will therefore introduce an

intensity variation of less than 0.1%. The two intensities must be balanced with an accuracy

better than 0.1% to achieve the desired frequency stability. In addition, the detection will be

sensitive to the 1/f noise of the electronic components and the voltage offset drifts of electronic

amplifiers, since the detection is performed at low frequencies. Stabilized (auto-zero) amplifiers

must be used to get the long-term frequency stability of 10-8. In addition, the technique is

sensitive to any change of the absorption coefficient of the iodine cell, which depends on its

internal pressure. An accurate control of the cell temperature is therefore mandatory (about

0.3°C of accuracy).

8.2 Center-of-fringe locking

8.2.1 Principle

The laser frequency stabilization on the center of an absorption line or Fabry-Pérot resonance is

widely used. The FM sideband technique introduced by Drever et al. [18] is probably the most

commonly used technique for that purpose. This technique was originally used by Pound in

1946 [19] for microwave stabilization. Another technique has been proposed by Hansch et al.

[20] for the frequency stabilization on reflective resonant cavity. However, this technique

involves a polarizing optical component inside the cavity, and is not suitable for the stabilization

on Zerodur Fabry-Pérot etalon.

The principle consists of using the first derivative of the frequency reference transmission as

frequency discriminant. Figure 18 shows the transmission of an absorption line, as well as its

first derivative. The value of the first derivative goes to zero when ν is equal to the center

frequency ν0, and changes sign whenever (ν – ν0) changes sign. Therefore, this is a convenient

error signal for the feedback loop of frequency stabilization. The laser frequency is thus

modulated to obtain an error signal proportional to the first derivative. The laser frequency νl

becomes then

ν ν νl FM ft= + πsin( )2 , (21)

where νFM is the frequency excursion and f is the modulation frequency. Assuming a

monochromatic wave, the transmitted light is given by

I I Tout l in l( ) ( )ν ν= (22)


27

where Iin is the intensity of the incident beam. By expanding T(νl) in a Taylor serie around the

average frequency ν, the transmitted intensity becomes to a first-order approximation

I I T T ftout in FM( ) ( ) ( ) sin( )ν ν ν ν1 2= + ′ π[ ] , (23)

where ′T ( )ν is the first derivative of the transmission curve with respect to the laser frequency.

Amplitude and sign of the sinusoidal function at the frequency f is thus proportional to the first

derivative of the transmission function.

0.95

0.90

0.85

0.80

0.75Tra

nsm

issi

on

-2 -1 0 1 2

Frequency detuning [GHz]

Der

ivat

ive

Figure 18: Transmission of an absorption cell (upper part) and its first derivative (lowerpart)

The stabilization principle is shown in Fig. 19 in the case of an iodine stabilization technique.

The intensity at the output of the frequency reference is synchronously detected at the frequency

f in order to obtain an error signal proportional to T’(ν). Here, an external frequency (or phase)

modulator is employed to perform the frequency modulation at the electrical frequency f.

Different options exist, including a modulation of the frequency reference instead of the laser,

and will be discussed in the next section. From Eq. (19), we can show that the slope of the

frequency discriminant is

S T

CFM FM FM= ′′ = −( )ν ν

νν0

22

8

∆, (24)

assuming frequency excursion smaller than the linewidth.

We note that this technique is insensitive to the laser power fluctuations and to the change of the

absorption coefficient of the cell. In addition, the synchronous detection allows to work at

relatively high frequencies (f > 10 kHz), where the 1/f noise of electronic components is not any


28

more dominant. The expected signal-to-noise ratio is therefore much higher than for the side-of-

fringe locking technique.

Laser I2

PI

PZTT

Mod

Lock-in

Freq. f

Figure 19: Principle of the FM sideband technique for an iodine stabilization.

8.2.2 Example: iodine stabilization

We consider here the frequency stabilization on a Doppler-broadened absorption line of an

iodine cell. We assume that we have an input intensity Iin of 0.3 µW after the second-harmonic

generation, a linewidth of 800 MHz and an absorption coefficient of 25%. In addition, we

consider the use of a commercially available photodetector with a voltage sensitivity SVP of 7

V/µW and a noise-equivalent power (NEP) of 2.1 pW/Hz0.5 (Analog Modules, model no

712A-2). The voltage sensitivity at the output of the photodetector will be

S I S S I

ASVF IN FM VP IN FM VP= = =8

0 522

max . ∆ν

ν V/GHz . (25)

The detection bandwidth does not need to be very high, since the cut-off frequency of the

regulator does not need to be higher than 1 Hz. Therefore a cut-off frequency of 100 Hz for the

lock-in amplifier is high enough. For a bandwidth B of 100 Hz, the voltage noise is

σV VPNEP S B= = 0 15. mV . (26)

The signal-to-noise ratio of the detected signal for a frequency drift δν is

SNR

S ft Sac

VF

V

VF

V

=( ) π( )

=( )δν

σ

δν

σ

2 2

2

2

2

2 12

cos. (27)

The minimal detectable frequency drift δνmin is the value for which SNRac= 1. We find a value

of δνmin = 400 kHz, which is well below the required 2 MHz frequency stability.

Synchronous detection should therefore allow to get the desired stability even for a second-

harmonic power as low as 300 nW.


29

8.3 Frequency dithering.

The frequency dithering can be realized by means of different techniques:

8.3.1 PZT tuning input of the laser

The piezo tuning input of the Nd:YAG laser can possibly be used for the frequency dithering.

However its tuning range is limited to ±30 MHz. In addition, this fast frequency tuning input

must also be used to compensate the “fast” frequency variations. In addition, the modulation of

the laser frequency will introduce an interferometric phase modulation, especially at long optical

path difference. This would require an averaging process over the modulation period to average

out this modulation.

8.3.2 Acousto-optic modulators

The acousto-optic modulator (AOM) can shift the laser frequency. This frequency shift is given

by the frequency of the electrical signal which is applied to the device. The bandwidth of this

frequency shift is typically 10% of the center frequency shift. A frequency shift of 800 MHz is

therefore required to achieve a modulation with a frequency excursion of 80 MHz. High

frequency shift acousto-optic modulators are commercially available from e.g. Brimrose (USA).

A beam scanning effect will be introduced, since the diffraction angle depends on the frequency

shift. This effect is not desirable for the locking on optical resonators, since the alignment may

be critical.

Another solution consists of generating a square modulation of the optical frequency by

switching on and off the acousto-optic device at a rate of a few kHz. When the AOM is on, the

diffracted beam is generated with a frequency of typically ν + 80 MHz, and when the laser is

off, the non diffracted beam at frequency ν is launched in the frequency reference. However, this

system may require additional optics to recombine the two beams.

8.3.3 Electro-optic modulator

An electro-optic modulator acts as a phase modulator. Therefore, the phase of the laser light will

be given by

φ(t) = φ0 sin(2πft) (28)

where φ0 is the phase modulation amplitude. The induced frequency modulation is then

ν(t) = ν + (1/2π) dφ(t)/dt = ν + f φ0 cos(2πft). (29)

The frequency excursion depends therefore on the phase modulation amplitude φ0 and the

modulation frequency f. Assuming a phase amplitude of π (typical value), we must use a


30

modulation frequency f of 25 MHz to get the 80 MHz frequency excursion. The bandwidth of

the photodetector must therefore have a bandwidth larger than 25 MHz, in the case of iodine

stabilization. For instance, the Analog Modules photodetector that is mentioned above (model no

712A-2) has a bandwidth of 60 MHz, which is amply sufficient.

8.3.4 Modulation of the frequency reference

As already mentioned, another solution consists of modulation the frequency reference instead

of the laser frequency. For optical Fabry-Pérot analyzers, this modulation can be done by

applying a sine signal to the piezo translator which acts on one of the mirror cavity. However,

this stabilization cannot be applied for ultra-stable Fabry-Perot etalon, since the two mirrors

must be optically contacted with the ULE (or zerodur) spacers to get a high stability.

Several stabilization techniques [17] uses frequency modulation of an atomic or molecular

absorption line by Zeeman effect. For circularly polarized light, the absorption line will appear to

be shifted depending on the magnetic field applied to the cell. Although this technique can easily

be implemented for Rb absorption cell (1.87 MHz/Gauss), it can’t be used for iodine

stabilization, since the Zeeman shift of the absorption lines are very small; a transverse magnetic

field of 500 Gauss introduces a frequency shift less than 70 kHz [17].

9 Test plan

9.1 Beat frequency measurement

The remaining laser frequency fluctuations can be measured easily if two identical stabilized

lasers can be manufactured. If the two systems have independent frequency references and

stabilization electronics, the laser frequency fluctuations can be determined by measuring the

beat frequency resulting from the superposition of the two laser beams (see Fig. 1). Assuming

that the contributions of both lasers are identical, the standard deviation of the beat frequency

measurement is 2 times the standard deviation of the laser fluctuations. Note that frequency

stability is commonly evaluated by the Allan deviation [21]. For samples yk obtained with a

counter which measures the beat frequency, the Allan deviation is

σAllan k k kT y y2

12 2( ) ( ) /= −+ , (30)

where T is both the integration time and the sampling time (i.e. there is no dead time between

counts).


31

9.2 Phase measurements at large distances

As mentioned in section 4.2.2, the laser frequency noise psd at higher frequency (typ. 10

Hz – 10 kHz) can be deduced from the measurements of the interferometric phase fluctuations

at large optical path difference (e.g. > 1 km). Figure 20 shows a possible measuring set-up for

that purpose. The set-up is based on heterodyne detection. The interferometric phase is directly

measured by measuring the phase difference between the reference and probe signals.

ν−39.55 MHz(from AOM2)

ν−40 MHz(from AOM1) Reference

signal450 kHz

Probesignal

450 kHz

FC

1 km fiber delay

PC

P

P

Figure 20 : Possible set-up for measuring the phase fluctuations at large optical pathdifference.

9.3 Comparison with an Agilent interferometer

As already mentioned, the wavelength calibration can be made by comparison with a

commercially available Agilent laser interferometer. A heterodyne interferometer can be made

with the stabilized Nd:YAG laser. The Nd:YAG and Agilent interferometers can measure a

common optical path, as sketched in Fig. 12. By comparing the results obtained with the Agilent

interferometer and the results obtained with the Nd:YAG interferometer, we can calibrate the

frequency of the Nd:YAG laser with respect to the Agilent laser wavelength. Since the absolute

frequency stability of Agilent interferometers is better than 10-8, a calibration accuracy with the

same accuracy can be achieved. This calibration can be repeated several times in different

environmental and experimental conditions, to test the reproducibility of the absolute

stabilization.


32

10 Possible concepts

10.1 Stabilization technique

Two solutions were investigated: (i) side-of-fringe technique and (ii) FM sideband technique

with synchronous detection (also known as Pound-Drever-Hall technique). As already

discussed, the side-of-fringe technique is critical for a frequency reference with broad

linewidths. In the case of iodine stabilization, the system must stabilize the intensity which is

transmitted through the frequency reference which an accuracy better than 0.1 %. The

compensation for the laser intensity fluctuations must be done with the same accuracy. In

addition, the technique is sensitive to a change of the transmission of the frequency reference.

On the other hand, the FM sideband technique is not sensitive to any change of laser intensity or

transmission of the frequency reference. This technique also provides a better signal-to-noise

ratio, since the detected error signal is done at relatively high frequencies, where the 1/f noise is

negligible. In addition, the technique is probably the most commonly used (e.g. for atom

cooling) and the most documented.

Although the FM sideband technique is slightly more complex than the side-of-fringe locking

(frequency dithering is required), we strongly recommend it to ensure the long-term reliability.

10.2 Frequency reference

We can identify three possible solutions for the frequency reference:

10.2.1 Iodine absorption cell at 659.5 nm

This solution consists of using the concepts described by Arie. The second-harmonic is

stabilized on one of the absorption lines of an iodine cell around 659.5 nm. Saturation

spectroscopy is not necessary, since the accuracy of 2 MHz can be achieved with Doppler-

broadened lines [8]. The second-harmonic can be generated by a single-pass birefringent phase-

matched non-linear crystal, such as KTP (e.g. from Raicol, about 1’000 € ) or LiNbO3, since

only a few 100 nW of second-harmonic light is sufficient if we use a low-noise photodetector

(e.g. 712A-2 Analog Modules photodetector) and a synchronous detection such as the FM

sideband technique. The frequency modulation can be performed by means of an electro-optic

modulator (e.g. NewFocus EOMs, about 3’500 € ). The absorption cell should be slightly

heated (about 60°C) to get an internal pressure of 3-4 Torr. The frequency repeatability of the

Nd:YAG laser (typically < 1 GHz) should allow to stabilize always on the same absorption line

(for instance, the line at 659.588 nm is separated by 3 GHz from the closest weak absorption

lines). If necessary, a commercially available wavemeter (e.g. Agilent 86120B, 5’000 € ) with

moderate accuracy (±3 ppm) can be used to identify the absorption lines.


33

10.2.2 Ultra-stable Fabry-Pérot etalon.

Commercially available Fabry-Pérot etalons with ULE or Zerodur spacers (e.g. SLS Optics

etalons, 2’500€ ) allow a resonance frequency drift as low as 10–8/day, provided that the

temperature is controlled (accuracy better than 1°C) and that the etalon is evacuated. The 10

GHz Free Spectral Range should ensure that the laser is always stabilized on the same Fabry-

Pérot resonance. In addition, the high finesse of the resonator (> 60) allows a better sensitivity

of the frequency discriminant, since the linewidth is about 5 times better than the one of

Doppler-broadened absorption lines.

Despite this relatively low drift, daily calibrations of the wavelength are recommended to achieve

the desired accuracy. This calibration can be done by measuring the displacement of the delay

lines with the Nd:YAG laser interferometer, and by comparing the results with the results

obtained by means of an Agilent laser interferometer. The existing infrastructure (delay lines

with internal metrology) could be used for this wavelength calibration. Again, an electro-optic

modulator or possibly an acousto-optic modulator must be used for the electronic stabilization.

The second-harmonic generation is not required, but care must be taken to isolate the Fabry-

Pérot cavity from vibrations, and a vacuum chamber must be used. In addition the frequent

calibrations require more maintenance works.

10.2.3 Fabry-Pérot cavity stabilized on an Agilent laser head.

The laser is stabilized on the resonance of a resonant cavity, that is itself stabilized on an Agilent

laser head (7’000 € ) whose stability is better than 10-8. Commercially available optical spectrum

analyzers can be used as resonant cavity, with mirror coatings at both 1320 nm and 633 nm

(CVI or Toptica analyzers with custom designed mirrors, about 10’000 € ). The piezo translator

that is mounted on one of the mirror cavity will allow to modulate the resonance frequencies of

the cavity and to stabilize the length with respect to the Agilent laser. Preliminary tests showed

however that a re-calibration of the optical wavelength is mandatory if the stabilization of the

cavity length is turned off during more than one day.

Aspect Iodine stab. FP etalon Stabilized FPcavity

Cost + + –Complexity + + +Long-term reliability + + – +Power budget – + + + +

Table 5: Summary of the advantages and drawbacks of the three presented techniques.

Table 5 summarizes the advantages/drawbacks of the exposed techniques.


34

11 Conclusion

We exposed three possible techniques:

• Stabilization on an iodine absorption cell.

• Stabilization on an ultra-stable Fabry-Pérot etalon.

• Stabilization on a Fabry-Pérot cavity, whose length is stabilized with respect to an Agilent

laser head.

The solution based on a stabilized Fabry-Pérot cavity is slightly more expensive than the other

solutions, but the price difference is still acceptable (10’000 € ). The experimental complexity of

the three methods is very similar. The iodine stabilization requires more optical power than the

other techniques because of the second-harmonic generation. This drawback is not critical, since

the optical power of the Nd:YAG laser is high enough. The most important feature is the long-

term reliability offered by the iodine stabilization, which doesn’t require a frequent calibration of

the wavelength. Only one calibration is recommended after the installation at the Paranal

observatory. We have therefore a preference for this solution, because of its potential long-term

reliability and since it would minimize the required maintenance efforts.

Regarding the electronic stabilization technique, the FM sideband technique, usually known as

the Pound-Drever-Hall technique, seems to be the most suitable technique to ensure the long-

term stability, since it is not sensitive to variations of the laser power and of the cell absorption.

Finally, three different tests are recommended to verify the stability of the frequency locked

Nd:YAG laser, i.e.:

• Beat frequency measurements between two identically stabilized lasers.

• Interferometric phase measurements at large optical path difference

• Comparison with an Agilent interferometer.

12 Acknowledegements

The authors would like to thank S. Lévêque from ESO Garching, Ronald Holzwarth from Max

Planck Institute (Garching, Germany) and P. Thomann, Observatoire Cantonal de Neuchâtel

(Switzerland), for their very helpful contribution.


35

References[1] Y. Salvadé et al., "Limitations of interferometry due to the flicker noise of laser

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Interferometer Laser Gauges”, Proc. SPIE 3350, 973 (1998).

[3] B. Willke et al., “Frequency stabilization of a monolithic Nd:YAG ring laser by

controlling the power of the laser-diode pump source”, Opt. Lett. 25, 1019 (2000).

[4] K. Petermann in Laser diode modulation and noise (Kluwer Academic Publishers,

Dordrecht, 1988) 294.

[5] R. Czichy, “Miniature Optical Terminals”, Space Communications 15, 105 (1998).

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NdY:AG Lasers Locked to a Fabry-Pérot Interferometer”, IEEE J. of Quantum

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York, 1991).

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36

[17] T. Ikegami et al. in Frequency stabilization of semiconductor laser diode (Artech

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(1966).

Annex IAnnex I : KTP crystal- Type I phase matching

Units

µm ..1 10 6 m

mm .10 3 m

Refractive indexes

Sellmeier equations

nx ,λ ∆T 3.0065.0.03901 µm2

λ2 .0.04251 µm2

.0.01327 λ2

µm2..1.1 10 5 ∆T

ny ,λ ∆T 3.0333.0.04154 µm2

λ2 .0.04547 µm2

.0.01408 λ2

µm2..1.3 10 5 ∆T

nz ,λ ∆T 3.3134.0.05694 µm2

λ2 .0.05658 µm2

.0.01682 λ2

µm2..1.6 10 5 ∆T

Wavelengthsλh .0.6595 µmλf .1.319 µm

nxf ∆T nx ,λf ∆T =nxf 0 1.7339 nxh ∆T nx ,λh ∆T =nxh 0 1.76072

nyh ∆T ny ,λh ∆T =nyh 0 1.77026nyf ∆T ny ,λf ∆T =nyf 0 1.74164

nzh ∆T nz ,λh ∆T =nzh 0 1.85919nzf ∆T nz ,λf ∆T =nzf 0 1.82153

Plane xz

nf ,θ ∆Tcos θ 2

nxf ∆T 2

sin θ 2

nzf ∆T 2

1

Phase matching angle (type I phase-matching, e-ray at fundamental o-ray at SH)

∆kI ,θ ∆T ..2 π

λhnf ,θ ∆T nyh ∆T θ .23.5

180π (phase mismatch)

θpm ∆T root ,∆kI ,θ ∆T θ θdeg ∆T .θpm ∆T

π180 =θdeg 0 41.15232

=θpm 0 0.71824Phase mismatch effect

I-1 YS

Annex I

Crystal length: L .10 mm

Efficiency η ,θ ∆T

sin .∆kI ,θ ∆TL

2.∆kI ,θ ∆T L

2

2

Temperature change DeltaT in degree Celsius

∆T ..,100 99.1 100

100 50 0 50 1000.99992

0.99994

0.99996

0.99998

1

η ,θpm 0 ∆T

∆T

=η ,θpm 0 10 1

Angle acceptance

θ ..,θdeg 0 0.2 θdeg 0 0.1999 θdeg 0 0.2

40.9 41 41.1 41.2 41.3 41.40

0.5

1

η ,.θ180

π 0

θ

I-2 YS

Annex IKTP crystal- Type II phase-matching

Units

µm ..1 10 6 m

mm .10 3 m

Refractive indexes

Sellmeier equations

nx ,λ ∆T 3.0065.0.03901 µm2

λ2 .0.04251 µm2

.0.01327 λ2

µm2..1.1 10 5 ∆T

ny ,λ ∆T 3.0333.0.04154 µm2

λ2 .0.04547 µm2

.0.01408 λ2

µm2..1.3 10 5 ∆T

nz ,λ ∆T 3.3134.0.05694 µm2

λ2 .0.05658 µm2

.0.01682 λ2

µm2..1.6 10 5 ∆T

Wavelengthsλh .0.6595 µmλf .1.319 µm

nxf ∆T nx ,λf ∆T =nxf 0 1.7339 nxh ∆T nx ,λh ∆T =nxh 0 1.76072

nyh ∆T ny ,λh ∆T =nyh 0 1.77026nyf ∆T ny ,λf ∆T =nyf 0 1.74164

nzh ∆T nz ,λh ∆T =nzh 0 1.85919nzf ∆T nz ,λf ∆T =nzf 0 1.82153

Plane xz

nf ,θ ∆Tcos θ 2

nxf ∆T 2

sin θ 2

nzf ∆T 2

1

nh ,θ ∆Tcos θ 2

nxh ∆T 2

sin θ 2

nzh ∆T 2

1

Phase matching angle (type II phase-matching, o-ray at second-harmonic)

∆kII ,θ ∆T ..2 π

λh.1

2nyf ∆T .1

2nf ,θ ∆T nyh ∆T θ .20

180π

θpm ∆T root ,∆kII ,θ ∆T θ θdeg ∆T .θpm ∆T

π180 =θdeg 0 60.36798

=θpm 0 1.05362

I-3 YS

Annex I

Phase mismatch effect

Crystal length: L .10 mm

Efficiency η ,θ ∆T

sin .∆kII ,θ ∆TL

2.∆kII ,θ ∆T L

2

2

Temperature change DeltaT in degree Celsius

∆T ..,50 49.1 50

60 40 20 0 20 40 600.2

0.4

0.6

0.8

1

η ,θpm 0 ∆T

∆T

=η ,θpm 0 10 0.94979

Angle acceptance

θ ..,θdeg 0 0.2 θdeg 0 0.199 θdeg 0 0.2

60.1 60.2 60.3 60.4 60.5 60.60

0.5

1

η ,.θ180

π 0

θ

=η ,θpm 0 .0.015

180π 0 0.92331

=.0.05

180π 8.72665 10 4 =

..9 10 4 π.2 1.319

1

933.00164

I-4 YS

feasibility study for the frequency stabilization of the prima...

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