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
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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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) , high resolution spectroscopy ,
optical tracking oscillator (including phase coherent tracking of optical signal from a satellite
), heterodyne high resolution optical spectrum analyzer, optical processing of radio-
frequency signals , coherent manipulation of atoms for quantum information storage ,
low noise interferometric sensors  or optical frequency-modulated continuous-wave
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 . 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
Fourier frequency (normalized by 1/τ)
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[
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
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 (
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 . 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.
1/2, while the error signal scales as L0. Consequently, a longer fiber makes
FM: Faraday Mirror
( ) t
Fig. 2. Experimental setup frame scheme: VCO (Voltage Controlled Oscillator), AOM
(Acousto-Optical Modulator), PD (photodiode), PI (proportional-integral control system), PZT
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  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
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  is frequency-to-voltage
converted and analyzed by a fast Fourier transform analyzer. Frequency noise measurements
are presented in Fig. 3.
Frequency noise PSD [Hz
Fourier frequency [Hz]
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 . 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 , 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  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.