Characterizing a fiberbased frequency comb with electrooptic modulator.
ABSTRACT We report on the characterization of a commercial core fiberbased frequency comb equipped with an intracavity freespace electrooptic modulator (EOM). We investigate the relationship between the noise of the pump diode and the laser relative intensity noise (RIN) and demonstrate the use of a lownoise current supply to substantially reduce the laser RIN. By measuring several critical transfer functions, we evaluate the potential of the EOM for comb repetition rate stabilization. We also evaluate the coupling to other relevant parameters of the comb. From these measurements, we infer the capabilities of the femtosecond laser comb to generate verylowphasenoise microwave signals when phaselocked to a highspectralpurity ultrastable laser.

Conference Paper: MidIR frequency control using an optical frequency comb and a remote nearinfrared frequency reference
B. Chanteau, B. Argence, O. Lopez, W. Zhang, D. Nicolodi, M. Abgrall, F. Auguste, P. L. T. Sow, S. Mejri, S. K. Tokunaga, C. Daussy, B. Darquié, G. Santarelli, C. Chardonnet, Y. Le Coq, A. AmyKleinInternational Quantum Electronics Conference; 05/2013 
Article: Dual photodetector system for low phase noise microwave generation with femtosecond lasers.
[Show abstract] [Hide abstract]
ABSTRACT: Low phase noise microwave signals can be generated by photodetecting the pulse train of an optical frequency comb locked to a high spectral purity continuouswave optical reference. Amplitudetophase noise conversion is, however, a wellknown limitation to this technique. Great care is usually required to overcome this constraint due to its strong dependence on the impinging optical power. Here we demonstrate the combined use of "magic point" operating conditions of photodetectors, pulse repetition rate multipliers, and coherent addition of microwave signals to realize a microwave extraction device largely immune to amplitudetophase conversion effects over a large range of impinging optical powers.Optics Letters 03/2014; 39(5):12047. · 3.39 Impact Factor  SourceAvailable from: Amir Khodabakhsh[Show abstract] [Hide abstract]
ABSTRACT: Noiseimmune cavityenhanced optical frequency comb spectroscopy (NICEOFCS) is a recently developed technique that utilizes phase modulation to obtain immunity to frequencytoamplitude noise conversion by the cavity modes and yields high absorption sensitivity over a broad spectral range. We describe the principles of the technique and discuss possible combcavity matching solutions. We present a theoretical description of NICEOFCS signals detected with a Fourier transform spectrometer (FTS), and validate the model by comparing it to experimental CO2 spectra around 1575 nm. Our system is based on an Er:fiber femtosecond laser locked to a cavity and phasemodulated at a frequency equal to a multiple of the cavity free spectral range (FSR). The NICEOFCS signal is detected by a fastscanning FTS equipped with a highbandwidth commercial detector. We demonstrate a simple method of passive locking of the modulation frequency to the cavity FSR that significantly improves the long term stability of the system, allowing averaging times on the order of minutes. Using a cavity with a finesse of ~9000 we obtain absorption sensitivity of 6.4 x 10^{11} cm^{1} Hz^{1/2} per spectral element, and concentration detection limit for CO2 of 450 ppb Hz^{1/2}, determined by multiline fitting.10/2014;
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Characterizing a fiberbased frequency comb with
electrooptic modulator.
W. Zhang1, M. Lours1, M. Fischer2, R. Holzwarth2, G. Santarelli1 and Y. Le Coq1
1LNESYRTE, Observatoire de Paris, CNRS, UPMC, 61 avenue de l'Observatoire, Paris,
France
2MenloSystems GmbH, Am Klopferspitz 19a, D82152 Martinsried, , Germany
Abstract
We report on the characterization of a commercialcore fiberbased frequency comb equipped
with an intracavity electrooptic modulator (EOM). We investigate the relationship between
the noise of the pump diode and the laser relative intensity noise (RIN) and demonstrate the
use of a low noise current supply to substantially reduce the laser RIN. By measuring several
critical transfer functions, we evaluate the potential of the EOM for comb repetition rate
stabilization. We also evaluate the coupling to other relevant parameters of the comb. From
these measurements we infer the capabilities of the femtosecond laser comb to generate very
low phase noise microwave signals when phase locked to a high spectral purity ultrastable
laser.
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1.Introduction.
Femtosecond lasers have revolutionized the field of time and frequency metrology by
providing a phase coherent link between a large span of optical and microwave frequencies
[17]. These so called optical frequency combs are widely used for optical frequency
measurements with uncertainty close to the limitations of the caesium fountain clocks [811],
as well as frequency comparisons between different optical frequency standards [12,13]. By
transferring the spectral purity of ultra stable cwlasers [1418] to the microwave domain with
minute excess added noise [1921], they also provide ultralow phase noise microwave signals
[2224]. Such signals may be of wide technological application in fields such as radar,
telecommunications, deep space navigation systems, timing distribution and synchronization
[25]. They have proven to be suitable as interrogation signal for atomic fountain clocks at the
quantum projection noise limit [26,27].
Among the different modelocked laser technologies available, the Titanium Sapphire (Ti:S)
laser has traditionally been the workhorse of most optical metrology laboratories. Now
Erbiumdoped fiberbased systems are currently evolving into very serious contenders,
especially when high reliability and very long term operation (several days or weeks of
operatorfree continuous measurements) are crucial aspects. The main drawbacks of Erbium
doped fiberbased systems, when compared to Ti:S lasers, have been the higher noise and
lower control bandwidth available. Laboratory systems with an intracavity ElectroOptic
Modulator (EOM) for improved control bandwidth have been demonstrated [2830]. Highly
reliable systems, including an EOM actuator and exhibiting the high repetition rates suitable
for optical frequency metrology, are now available commercially with a builtin self
referencing unit [31]. We present in this paper several characterizations of such a commercial
core laser and demonstrate how we have used this information to understand and minimize
the residual noise of the system when phase locked to an ultrastable cavity stabilized cw
laser, with a strong emphasis on low phase noise microwave signal generation. We start by
presenting the various parameters and actuators of the commercialcore optical frequency
comb. We proceed with a description of the methods used to measure actuators response
(transfer functions) and the relevant noise properties of our comb. We conclude by applying
these studies to the low phase noise microwave generation.
2. Optical frequency comb
A self referenced optical frequency comb is characterized, in the frequency domain by a set of
phase coherent optical frequencies νN=N×frep+f0, where N is the index of the mode, frep the
repetition rate (typically hundreds of MHz) and f0 the carrierenvelope offset frequency [1]. A
freerunning optical frequency comb exhibits fluctuations of both frep and f0, as well as of its
average amplitude A. The state of the laser at a given time is therefore characterized by these
three distinct parameters. Note that, in principle, beyond these three “global parameters” one
could imagine that the phase and amplitude relation between the different spectral
components of the comb could also be changing over time. Due to the nonlinear effects
responsible for the modelocking mechanism, such variations have been shown to be minute
and, at best, have a very slow evolution [32]. We will therefore not take such effect into
account in this paper. A full characterization of the comb’s noise properties therefore requires
the measurement of three power spectral densities (PSD), of either phase or frequency noise
for f0 and frep, and of amplitude noise for A. Note that the effect of parameter A is usually
neglected in optical frequency metrology. In the context of low phase noise microwave signal
generation, where amplitudetophase coupling in the photodetection process is a strong
limitation [33,34], characterizing the amplitude fluctuations of the laser is however of utmost
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interest.
These three parameters (f0, frep and A), can be controlled via multiple actuators. In this paper,
we characterize a femtosecond comb system which possesses a piezo electric actuator (PZT,
whose purpose is to change the laser cavity length), allows fine tuning of the laser pumping
via adjustment of the current which drives the pump laser diodes, and has an EOM in the
cavity. The latter element operates mainly as a very fast voltagecontrolled group delay
element in the femtosecond laser’s cavity. It therefore changes the repetition rate, although
with unavoidable coupling to the other two parameters (f0 and A). Ideally, the PZT modifies
only frep. However it is well known that a tiny misalignment of the laser cavity may influence
both f0 and A. Changing the pump power of the laser comb (via the current driving the pump
diode lasers) obviously impacts A, as well as both f0 and frep via complex modelocked laser
dynamics [3537]. A full characterization of the response of the comb to the various actuators
therefore requires the measurement of the nine transfer function matrix elements (three
actuators for three comb’s parameters) as shown by the following equation:
(
(
(
where Ipump is the pump diode current VPZT is the voltage driving the PZT and VEOM is the
voltage driving the EOM crystal. We have measured the nine transfer functions of this matrix
but we will focus on the subset which impact optical frequency metrology and opticalto
microwave division process.
We proceed with a description of the methods we developed to measure these transfer
functions, as well as several noise properties of the femtosecond laser.
2. Transfer functions and noise measurements techniques.
Our commercialcore fiberbased frequency comb has a repetition rate near frep~250MHz,
which can be coarsely adjusted to within +/ 1MHz using a motorized translation stage on one
of the cavity mirrors. The available optical output power is about 130 mW. The laser has a
builtin f2f interferometer unit which generates the offset frequency signal f0. A motorized
double wedge [37] allows coarse frequency adjustment of this quantity, which we maintain
near 70 MHz. To measure transfer functions, we use a two channel vector signal analyzer
(VSA  Agilent 89410A) which can operate up to 10 MHz Fourier frequency and has a with
builtin programmable source voltage output. The applied modulation is directed
simultaneously to the Channel 1 input of the VSA and the actuators of the laser which we
want to characterize (PZT, pump diode current or EOM) via a suitable actuator driver. Note
that these drivers need to be independently characterized, to insure they don’t impose
bandwidth limitation to the measurement. The quantity to characterize (frep, f0 or A) is
transformed into a voltage signal and fed to Channel 2 of the VSA. By programming the VSA
source output to generate a chirped sine wave, we measure the transfer function from Ch1 to
Ch2.
This allows obtaining the transfer function from the actuator to the comb parameter. The set
up schematic is depicted in figure 1.
)
)
)
()()()
()()()
()()()
(
(
(
)
)
)
=
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
ω
j
V
V
I
HHH
HHH
HHH
f
f
A
EOM
PZT
pump
fVfVfI
fVfVfI
AVAVAI
rep
EOMPZTpump
repEOMrep PZTreppump
EOM PZTpump
000
,,,
,,,
,,,
0
(1)
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Fig 1: Setup schematic used to measure transfer functions of amplitude, f0 and frep vs laser pump current, intra
cavity EOM voltage and PZT voltage, as well as power spectral densities of the same quantities. fto2f: builtin
selfreferencing unit, LNA: low noise amplifier, VSA: vector signal analyzer.
The key part of such an experiment is to design ways to transform frep, f0 and A into a voltage
signal with high sensitivity and minimal cross talk from the other two parameters of the comb.
Measuring A is quite straightforward. We inject a few milliwatts of light from the
femtosecond laser output (30 nm bandwidth around 1.55 µm) onto a fiberpigtailed InGaAs
photodiode. The output of the photodiode is low pass filtered to remove the harmonics of the
repetition rate and, after low noise amplification, the output voltage is fed to the VSA. To
measure f0 fluctuations, we process this signal with a homemade fast tracking oscillator filter.
This device is composed of a voltagecontrol oscillator (VCO), which is phase locked to the
input signal with more than 3 MHz of bandwidth. At Fourier frequencies lower than this
bandwidth, the correction signal of the tracking oscillator (i.e. the voltage which controls the
VCO when the phase lock loop is operating) is proportional to the frequency fluctuations of f0
(the free running VCO noise is negligible compared to that of f0). To measure frep fluctuations,
it is convenient to increase the sensitivity by measuring N×frep, with N a large integer. By
beating the comb output with an ultra stable laser (linewidth<1Hz) [17] of optical frequency
νcw (near the 1.55 µm central wavelength of the comb), we have access to fb =N×frep +f0  νcw.
This radiofrequency (RF) signal mixed with f0 leads to two sidebands, highly sensitive to frep
fluctuations (because of the large multiplicative factor N). We select, with a bandpass filter,
the sideband which is independent from f0 (since fbf0 = N×frepνcw). Locking a tracking
oscillator to this signal therefore leads to a voltage correction signal proportional to the
fluctuations of frep.
We use these techniques to transform A, f0 and frep into voltage signals to measure the nine
transfer functions and the noise power spectral densities of the optical frequency comb.
3. Results and applications
Once the comb is characterized, by the 3x3 transfer functions matrix, we can use this
information to improve the comb’s properties. Our work puts a strong focus on the context of
low phase noise microwave signal generation by photodetection of the repetition rate’s
harmonics when the comb is phase locked to an ultra stable cw laser [23,24,27,38]. However,
the use of the transfer functions matrix goes well beyond what as appears in the following.
A first example of the use of the transfer function/noise characterization is illustrated in fig.2.
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0
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10
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(2)
(1)
Frequency [Hz]
Laser pump diode current noise [A/Hz1/2]
early (noisy) pump laser current supply
low noise pump laser current supply
(a)
10
0
10
1
10
Frequency [Hz]
2
10
3
10
4
10
5
160
140
120
100
(3)
(2)
(4)
(1)
RIN [dBc/Hz]
Predicted for noisy pump laser current supply
Measured fo pump laser noisy current supply
Measured for low noise pump laser current supply
Predicted for low noise pump laser current supply
(b)
Fig 2: Plot (a): measured a spectral density of current noise for early noisy (1) (blue line) and low noise (2)
(black line) current supply. Plot (b): RIN of the femtosecond laser output with two different current supplies for
the pump lasers diodes. Curve (1) red (measured) and (2) black (predicted) are for the early (noisy) current
supply. Curve (3) green (measured) and curve (4) blue (predicted) are for the low noise current supply.
The first comb was equipped with a relatively noisy pump diode lasers current supply (Fig. 2
plot (a), blue curve (1)). By plugging the current noise of this current supply to the transfer
function we measured from the pump diodes’ current to the amplitude of the laser, we obtain
a predicted relative intensity noise (RIN) of the comb which matches very well the actual
measurement (Fig 2 plot (b), red curve (1) & black curve (2)). We can conclude from this that
the rather important noise of the early prototype current supply originates the excessive RIN
of the laser comb. Indeed, by using a low noise current supply as a replacement (Fig. 2 plot
(a), black curve (2)), we obtained a very substantial improvement of the RIN. Furthermore, by
comparing, for the low noise current supply, the predicted RIN (Fig. 2 plot (b), green curve
(3)) to the new RIN measurement (Fig. 2 plot (b), blue curve (4)), we can conclude that the
new current supply is not a limiting factor anymore.
10
3
10
4
10
5
10
6
10
1
10
0
0
30
60
90
120
150
180
Phase [degree]
Transfer function HEOM,frep [Hz/V]
Frequency [Hz]
Fig 3: Transfer function
repEOMfV
H
,
from EOM voltage to repetition rate frep. Black is amplitude (left axis), red
plot is phase (right axis). The ultimate bandwidth available with such actuator is limited by the strong narrow
resonances near 900 kHz Fourier frequency.
By studying the RIN of the pump laser diode itself (when driven by the lownoise current
supply), we observed a RIN higher than expected from the current supply’s characteristic
alone. This excess noise explains the comb’s RIN for Fourier frequencies lower than 30
50 kHz. Improving the performance may require to handselect lower RIN pump laser diodes
and/or actively servo their output power. For Fourier frequencies higher than 3050 kHz, the
RIN of the pump diode lasers does not explain RIN of the comb. Understanding this excess
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noise at high Fourier frequencies would necessitate further theoretical and experimental
studies.
A second example of transfer function application is to optimize the feedback loop when
phase locking the comb to an external reference (an ultra stable 1.542 µm laser in our
case).We give, in fig 3 and 6, the three transfer functions from the EOM control voltage to,
respectively frep, f0 and A.
From Fig 3, we deduce that the maximum available servo bandwidth when using the EOM as
an actuator to control frep is limited by sharp resonances observed around 900 kHz. As a
matter of facts, they produce rapid large phase shifts so large that they cannot be easily
compensated by control circuit design. We use proportional and multiple integration control
which acts on both the EOM and the PZT actuators (both act mainly on frep) to phase lock frep
to a cw ultra stable laser near 1.55 µm. Similarly to the technique we previously described for
measuring frep fluctuations, the beatnote between the cw laser and one nearby tooth of the
comb is mixed with f0 to provide a signal of frequency Nxfrepνcw, independent of f0. By
mixing it with a reference from a fixed synthesizer, we produce an error signal which is sent
to a proportionalintegral (PI) controller. This PI controller directly steers the EOM. The
EOM control voltage is further integrated and fed to the PZT. In this way frep is phaselocked
to the optical frequency νcw, with the EOM acting for Fourier frequencies larger than 6
10 kHz, while the PZT controls the laser for low Fourier frequencies. Fig. 4 (a) shows the in
loop error spectral density and Fig. 4 (b) the correction voltage spectral density applied to the
EOM when the phaselock loop is running.
10
4
10
5
10
6
0
2x10
4
4x104
0
1x10
1
2x10
1
Frequency [Hz]
In loop error [rad/Hz
1/2]
Integrated inloop error [rad]
(a)
10
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6
0
1x10
3
2x10
3
3x10
3
4x10
3
0,0
0,5
1,0
1,5
2,0Integrated EOM voltage [Vrms]
1.7Vrms
Frequency [Hz]
EOM corr. voltage [Vrms/Hz
1/2]
(b)
Fig 4: Plot (a): Inloop residual phase error signal when phase locking the comb to a continuous ultra stable laser
near 1.55 µm. In red (right axis) the integrated phase error signal. Plot (b): rms correction voltage applied to the
EOM when the phase lock loop is running. In red (right axis), the integrated rms voltage applied to the EOM.
The decrease of the correction voltage below 6 kHz is due to the use of the PZT controlling the laser for low
Fourier frequencies (in lieu of the EOM).
The inloop error exhibits a resonance around 900 kHz and a servo bump near 400 kHz,
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consistent with the transfer function presented in fig. 3. By integrating the inloop error up to
1 MHz, the total phase error is about 0.21 rad rms, resulting in 96.7% energy in the carrier. As
the total phase error is much lower than 1 rad rms, the comb is in the so called “ultrastable
regime”, where each tooth of the comb has nearly the same spectral purity as the ultrastable
cw laser used as a reference for the lock (once f0 is removed).
4030 20 10010 20 3040
50
40
30
20
10
0
Beatnote signal power spectrum [dB]
νν0 [Hz]
Fig 5: Radio frequency spectrum of the beat note signal between the stabilized comb and an ultrastable laser
near 1062.5 nm (Span 80 Hz, RBW 1Hz, 10 averages)
This was confirmed independently by beating the comb output near 1062.5 nm (obtained from
the same highly nonlinear fiber used in the builtin f2f unit) with a second ultra stable laser
(see Fig. 5)[39,40]. The integrated correction voltage is 1.7 Vrms (~6 Vpp maximum, verified
with an oscilloscope). When comparing to the 25 V output range of our fast control
electronics, this leaves room to optimize the EOM dimensions, using shorter crystals with
lower dispersion and, potentially, higher resonances which may allow larger control
bandwidths. A third example of the use of the transfer function is directly related to the
coupling transfer functions that are presented in Fig. 6. This figure represents the unavoidable
cross talks to, respectively, f0 and A, when we act on the EOM to control frep (and, ideally, frep
only). Understanding the dynamics of these two crosstalk responses (enhanced responses at
high Fourier frequencies in particular) is not straightforward. We believe them to be caused
by minute misalignments of the EOM crystal, which couples, via complex laser dynamics, to
the polarization and amplitude of the pulse in the femtosecond laser’s cavity. Verifying this
hypothesis would require a thorough theoretical and experimental analysis which is well
beyond the scope if this paper. The measured transfer functions of Fig. 6 provide some useful
information about the limit of the EOM (in its current implementation) as an actuator to phase
lock frep.
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Frequency [Hz]
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(b)
Transfer function HVEOM,A [W/V]
10
3
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4
10
5
Transfer function HVEOM, f0 [Hz/V]
(a)
Fig 6: Plot (a) transfer function
0
, fVEOM
H
(EOM voltage to f0 ). Plot (b)
amplitude)
0
,AVEOM
H
(EOM voltage to comb’s
By combining the correction voltage spectral density applied to the EOM when the servo loop
operating (Fig. 4(b)) to the transfer functions of Fig 6, we can deduce the EOM control
induced fluctuations of f0 and A. The fluctuations of f0 are not important in the context of our
scheme, where f0 is uncontrolled and simply removed from fb by frequency mixing. Other f0
removal techniques, including the one presented in [41], are likewise inherently immune to
such cross talk. Note that in experiments which independently phase lock frep and f0 as in Refs
[8,42,43]) may however need to account for those effects. On the other hand, the crosstalk
induced fluctuations of A are of preeminent importance in the context noise microwave
signal extraction by photodetection of the femtosecond pulses. Indeed, amplitudetophase
conversion which occurs in the photodetection process limits the achievable performance of
low phase noise microwave generation experiments [33, 34]. From the predicted crosstalk
induced fluctuations of A, and a given amplitudetophase conversion factor related to the
photodetection process, one can deduce the achievable level of residual microwave phase
noise. For instance, in our case, for a microwave signal at 12 GHz generated from a 250 MHz
repetition rate laser, we assume a dφ/(dP/P)~0.03 rad amplitudetophase conversion factor of
the photodetection process. Here, φ is the phase of the microwave compared to that of the
pulse train and P is the average optical power on the photodetector. Note that substantially
higher conversion factors are normally without the fine adjustment of the experimental
parameters [33,34].
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120
(d)
(b)
(a)
Frequency [Hz]
Sφ(f ) [dB rad2/Hz] @12 GHz
(c)
Fig. Residual phase noise for opticaltomicrowave frequency division operation of the frequency comb at
12 GHz. Curve (a) (red line): detection noise floor limit (shot noise at high Fourier frequencies) from ref [44],
plot (b) (black line): phase noise induced by EOM inloop error (i.e. due to limited bandwidth of the EOM
actuator).Plot (c) (green line) : RINinduced phase noise. Plot (d) (blue line): EOM voltage to amplitude induced
phase noise. To obtain curves (c) and (d), we assumed typical 0.03 rad per relative amplitude change of the
amplitudetophase conversion factor in the photodetection process.
Fig. 7 presents the predicted residual phase noise limits obtained from RINinduced phase
noise (in green) and EOM crosstalkinduced phase noise (in blue) value of the amplitude
phase conversion factor. When comparing these predictions to the best noise floor limit we
measured for such a system with a repetition rate multiplication technique detailed in [44], it
appears that the crosstalk is not a limiting factor at the present level of noise floor limit. Note
however that if the amplitudephase conversion factor were equal to 1 rad (typical worst case
scenario observed from [38]), it would constitute a limitation for Fourier frequencies in the
10 kHz1 MHz range substantially higher than the measured noise floor limit. Furthermore,
the RINinduced residual phase noise is also lower than the noise floor limit. Similarly, an
amplitudephase conversion factor higher than 0.1 rad would induce a substantial limitation to
the performances of the system. On the other hand, it also appears from Fig. 7 that the main
limitation in the 100 kHz1 MHz Fourier frequencies range is due to the residual inloop error
of the phase lock loop (black line). This limitation is ultimately linked to the still limited
actuation bandwidth achievable with the EOM. Further improvement of the EOM actuator
would therefore be necessary to achieve residual phase noise limits in the 160 dB(rad2/Hz).
Note that recently a 1.2 MHz bandwidth was achieved with a waveguide EOM [45] and we
could therefore expect a similar result for the future prototypes.
4. Conclusions
We have presented in detail the techniques used to measure the various transfer functions
which characterize an optical frequency comb equipped with various actuators. We have
shown some examples of how to use such characterization to deduce the performance limits
of the comb and improve its performance. When phase locking the repetition rate of the comb
to an ultra stable cw laser optical frequency, we reached the “ultrastable regime”, where the
linewidth of each comb tooth is limited by that of the cw laser reference (and not the phase
lock loop performances). In the context of low phase noise microwave generation by
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photodetecting the pulse train, we have made a prediction of the achievable minimum phase
noise from different possible noise sources. These prediction make us confident that we can
achieve residual phase noise in the 160 dB(rad2/Hz) level, close to the shot noise limit, with a
slightly improved EOM actuator. In addition we have shown how to use the dynamic
characterization of a frequency comb (via its actuators transfer functions) to understand and
improve an optical frequency comb’s performance.
5. Acknowledgments
We want to thanks J. Pinto for the valuable work for the electronic sub systems, and John Mc
Ferran for careful reading of the manuscript.
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