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An agile laser with ultra-low frequency noise and

high sweep linearity

Haifeng Jiang1,*, Fabien Kéfélian2, Pierre Lemonde1,

André Clairon1 and Giorgio Santarelli1

1Laboratoire National de Métrologie et d’Essais–Système de Références Temps-Espace, Observatoire de Paris,

UPMC and CNRS, 61 Avenue de l’Observatoire, 75014 Paris, France

2Laboratoire de Physique des Lasers, Université Paris 13 and CNRS, 99 Avenue Jean-Baptiste Clément, 93430

Villetaneuse, France

*jiang.haifeng@obspm.fr

Abstract: We report on a fiber-stabilized agile laser with ultra-low

frequency noise. The frequency noise power spectral density is comparable

to that of an ultra-stable cavity stabilized laser at Fourier frequencies higher

than 30 Hz. When it is chirped at a constant rate of ~ 40 MHz/s, the max

non-linearity frequency error is about 50 Hz peak-to-peak over more than

600 MHz tuning range. The Rayleigh backscattering is found to be a

significant frequency noise source dependent on fiber length, chirping rate

and the power imbalance of the interferometer arms. We analyze this effect

both theoretically and experimentally and put forward techniques to reduce

this noise contribution.

OCIS codes: (140.0140) Lasers and laser optics; (140.3425) Laser stabilization; (140.3518)

Lasers, frequency modulated; (140.3600) Lasers, tunable; (290.5870) Scattering, Rayleigh.

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1. Introduction

Simultaneous achievement of low frequency noise operation and precise, fast and linear

tunability is a challenge for laser technology. These features are key requirements for many

applications: coherent light detection and ranging (lidar) [1], high resolution spectroscopy [2],

optical tracking oscillator (including phase coherent tracking of optical signal from a satellite

[3]), heterodyne high resolution optical spectrum analyzer, optical processing of radio-

Page 3

frequency signals [4], coherent manipulation of atoms for quantum information storage [5],

low noise interferometric sensors [6] or optical frequency-modulated continuous-wave

reflectometry [7].

Lasers with sub-hertz line-width and fractional frequency instability around 10-15 for 0.1 s

to 10 s averaging time are currently realized by locking onto an ultra-stable Fabry-Perot cavity

using the Pound-Drever-Hall method [8-11]. However, this method requires fine alignment of

free space optical components, tight polarization adjustment and spatial mode matching.

Moreover, ultra-stable cavities are relatively expensive, bulky and fragile. Finally, this method

is not convenient to realize large range sweeping.

In the last two decades, several research groups have developed another approach for

short term laser frequency noise reduction, using large arm length unbalance fiber

interferometers [12-18]. Recently, we have dramatically improved the performance of such

systems by using a longer fiber spool and a heterodyne detection technique [19]. It was also

shown that this approach allows well controlled laser frequency tuning without acting on the

interferometer reference [13,16,17,20].

In this paper, we demonstrate the ultra-low frequency noise performance of a chirped

laser stabilized to a fiber-based interferometer. We analyze the noise sources and fundamental

limits of the method, in particular the impact of the Rayleigh backscattering (RBS), which

constitutes the present limit of our system.

2. Operation principle and experimental setup of the agile laser

10

-1

10

0

-60

-45

-30

-15

0

-90

Fourier frequency (normalized by 1/τ)

(b)

Magnitude[dB]

-180

-135

-45

0

Phase [degree]

(a)

Laser source

PD

interferometer

fRF

τ0

RF source

θRF

Output

Fig.1. (a) Heterodyne interferometer, PD (Photodiode); (b) transfer function of the

interferometer: relative magnitude |T(f)|/ 2πτ0 [black solid line] and phase [blue dashed line] of

frequency response of the interferometer.

The frequency of a laser can easily be locked onto the optical length L0 of a fiber by inserting

the latter into one arm of a Mach-Zehnder or Michelson interferometer which can then be

used as a frequency discriminator.

However, in this homodyne configuration the locked laser frequency ν0 is limited to a

discrete set of values (1/2+k) c/2L0, where k is an integer and c the speed of light in vacuum,

corresponding to the quadrature condition of the arm outputs cos(2πν0L0/c) to be 0. The

locked laser frequency can be tuned within a small range by adding a variable offset to the

error signal, but large range continuous tuning requires a corresponding tuning of L0.

Insertion of a frequency shifter in one arm of the interferometer as shown in Fig.1a

enables heterodyne detection. One of many advantages of this configuration is to allow the

tuning of ν0 without modifying the fiber length according to the locking condition:

, 0)](2 cos[

00

=−

tv

RF

θτπ

where τ0 =L0/c is the unbalance time delay of the interferometer and θRF(t) the phase

difference between the modulation and demodulation signals. The frequency equals to the

(1)

Page 4

sum of (1/2+k)/2τ0 and θRF(t)/2πτ0 , can then be tuned by controlling θRF(t), which can be

done more precisely and with a greater dynamic range than a control of L0.

The transfer function relating the laser frequency fluctuations δν to the heterodyne signal

phase fluctuations is

) 1 (

)(

if

where f is the Fourier frequency. This function is plotted both for phase and magnitude in

Fig. 1b. At low frequencies (f<<1/τ0), the magnitude is approximately equal to 2πτ0, which

means that a longer fiber increases the discriminator slope. Standard deviation of the total

fiber length fluctuations δL, arising from spatially uncorrelated local length fluctuations, is

proportional to L0

the system less sensitive to the distributed fiber noise. However, for integer values of 1/τ0, the

interferometer transfer function has null amplitude corresponding to zero gain points in the

loop response. Maintaining a bandwidth larger than 1/τ0 is feasible, but requires a complex

servo-loop design [21]. If we restrict the bandwidth to below 1/τ0, there is a trade-off between

the lower noise floor for low Fourier frequencies (<<1/τ0) and the larger bandwidth of the

frequency noise rejection.

Output

rad/Hz,

0

2

e

fT

fi πτ−

−

=

(2)

1/2, while the error signal scales as L0. Consequently, a longer fiber makes

FM

Fiber Laser

1542 nm

AOM 0

AOM 1

PD

50/50

PI

Fast

Slow

FM

PZT

Michelson

Interferometer

VCO

1

2

tunable

synthesizer

fAOM1

2fAOM1+∆νRF(t)

2fAOM1

Optics part

Electronics part

~

FM: Faraday Mirror

( ) t

dt

d

laser

ντ∆+

Error signal

Fig. 2. Experimental setup frame scheme: VCO (Voltage Controlled Oscillator), AOM

(Acousto-Optical Modulator), PD (photodiode), PI (proportional-integral control system), PZT

(piezo-electric transducer).

Fig. 2 shows the experimental setup, where the optical signals, radio-frequency (RF)

signals and low frequency signals are drawn in red, blue and black respectively. The main

difference from our previous setup [19] is the use of a low phase noise tunable synthesizer

instead of a RF frequency multiplier. An acousto-optic modulator (AOM1) is placed into one

arm of the interferometer leading to a heterodyne beat-note signal at frequency 2fAOM1 at the

output of the photodiode. By using a Michelson interferometer configuration with two

Faraday mirrors, the polarization of the output waves in the output port is automatically

aligned, leading to a maximum beat-note signal without any polarization adjustment. The

tunable synthesizer provides an RF signal with frequency 2fAOM1+∆νRF(t). This signal is used

to demodulate the heterodyne signal. According to (1), when the control loop is closed the

frequency offset ∆νRF(t) will then induce a laser frequency change ∆νlaser(t) given by

v

t

tv

laser

==∆

,

)

t d

′

(

2

)(

)(

0

0

0

τπτ

θ

t

t

RF

RF

′

∆

∆

∫

(3)

Page 5

This expression shows that a constant frequency offset ∆νRF generates a linear laser

frequency sweeping with chirp rate ∆νRF/τ0.

The fiber delay line is a 2.5-km SMF-28 fiber spool (τ0~25 µs), placed in an air-sealed can,

to reduce the thermal and mechanical noises coupled from the environment. The

interferometer is housed in an aluminum box with thermal isolation (Mylar and thermoplastic

polymer foils), whose size is 260 mm x 260 mm x 165 mm, sitting on a commercial compact

passive vibration isolation platform. The servo-loop has a bandwidth of about 20 kHz with 3

integral correction stages to reduce the error during frequency sweep. Control of the laser

frequency is realized by using the piezoelectric transducer (PZT) stretcher port of the

commercial fiber laser for slow corrections on large range, and AOM0 for fast corrections. In

this experiment, all interferometer components are pigtailed off-the-shelf, which makes the

system alignment-free, simple and robust.

3. Measurements and discussion

3.1 Frequency noise and instability of the non-chirped laser

In non-chirped operation, the RF beat-note signal between the fiber-stabilized laser and a

high-finesse Fabry-Perot cavity-stabilized laser described in [22] is frequency-to-voltage

converted and analyzed by a fast Fourier transform analyzer. Frequency noise measurements

are presented in Fig. 3.

10

0

10

1

10

2

10

3

10

4

10

-2

10

-1

10

0

10

1

a

Frequency noise PSD [Hz

2/Hz]

Fourier frequency [Hz]

b

Fig. 3. Frequency noise PSD of lasers beat-note between (a) fiber-stabilized laser and an ULE-

cavity stabilized laser, (b) two ULE-cavity stabilized lasers. The frequency noise PSD of the

free running laser is given in [21]. Note that no drift is removed in these measurements.

For Fourier frequencies between 30 Hz and 3 kHz, trace (a) coincides with trace (b),

which means that, in this frequency range, the frequency noise of the fiber-stabilized laser is

at least as low as the frequency noise of one of the ULE-cavity stabilized lasers. At higher

frequencies, the noise increases due to the limited gain of the servo-loop. At low frequencies,

the fiber-stabilized laser has more noise due to the temperature fluctuations and low frequency

mechanical vibrations. The thermal sensitivity of the interferometer is ~10-5 /°C and we have

measured the relative vibration sensitivity to be a few 10-10/m/s-2. Compared to our previous

results obtained with a 1-km fiber [19], the performances in the decade 1 Hz-10 Hz have been

improved by up to 10 dB. This improvement is mainly due to the use of the air-sealed can.

The fiber fundamental thermal floor calculated using Wanser’s approach [23] is about 8x10-4

Hz2/Hz still 10 dB below our measured frequency noise. Using the beat-note signal frequency

recorded by a counter, we evaluate the laser frequency stability using the square root of the

Allan variance [24,25]. After removing a linear drift of about 1 kHz/s for a measurement of 5

minutes duration, the Allan deviation is close to 10-14 for integration times ranging from 0.1 s

to 1 s.