A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration.
ABSTRACT A 12.5 GHz-spaced optical frequency comb locked to a global positioning system disciplined oscillator for near-infrared (IR) spectrograph calibration is presented. The comb is generated via filtering a 250 MHz-spaced comb. Subsequent nonlinear broadening of the 12.5 GHz comb extends the wavelength range to cover 1380-1820 nm, providing complete coverage over the H-band transmission window of earth's atmosphere. Finite suppression of spurious sidemodes, optical linewidth, and instability of the comb has been examined to estimate potential wavelength biases in spectrograph calibration. Sidemode suppression varies between 20 and 45 dB, and the optical linewidth is approximately 350 kHz at 1550 nm. The comb frequency uncertainty is bounded by +/-30 kHz (corresponding to a radial velocity of +/-5 cm/s), limited by the global positioning system disciplined oscillator reference. These results indicate that this comb can readily support radial velocity measurements below 1 m/s in the near IR.
Book: Nonlinear Fiber Optics[show abstract] [hide abstract]
ABSTRACT: The advantages of fiber waveguides over bulk nonlinear media are demonstrated. A review is given of the main nonlinear effects which occur during propagation of laser radiation in fiber waveguides. The most interesting applications of nonlinear fiber optics are discussed.3 edited by Kelley, Paul L. and Kaminow, Ivan P. and Agrawal, Govind P., 01/2001; Academic Press., ISBN: 0120451433
A 12.5 GHz-Spaced Optical Frequency Comb Spanning >400
nm for near-Infrared Astronomical Spectrograph Calibration
F. Quinlan1,*, G. Ycas1,2, S. Osterman3, S. A. Diddams1,†
1National Institute of Standards and Technology, 325 Broadway, 80305 Boulder, CO, USA
2University of Colorado Physics Dept., Boulder, CO USA
3University of Colorado, Center for Astrophysics and Space Astronomy, Boulder, CO, USA
Abstract: A 12.5 GHz-spaced optical frequency comb locked to a Global Positioning System disciplined
oscillator for near-IR spectrograph calibration is presented. The comb is generated via filtering a 250
MHz-spaced comb. Subsequent nonlinear broadening of the 12.5 GHz comb extends the wavelength
range to cover 1380 nm to 1820 nm, providing complete coverage over the H-band transmission
window of Earth’s atmosphere. Finite suppression of spurious sidemodes, optical linewidth and
instability of the comb have been examined to estimate potential wavelength biases in spectrograph
calibration. Sidemode suppression varies between 20 dB and 45 dB, and the optical linewidth is ~350
kHz at 1550 nm. The comb frequency uncertainty is bounded by +/- 30 kHz (corresponding to a radial
velocity of +/-5 cm/s), limited by the Global Positioning System disciplined oscillator reference. These
results indicate this comb can readily support radial velocity measurements below 1 m/s in the near-IR.
High precision astronomical spectroscopy in the near infrared (IR) permits lines of scientific inquiry
unavailable in the visible and ultraviolet (UV) . For example, the higher transmission in the IR through
galactic and stellar dust allows the study of objects hidden in the visible and UV, such as young stars and
planets still embedded in the clouds from which they formed. Also, the high red shift from distant
universe objects requires IR spectroscopy to study spectra emitted in the visible and UV. Perhaps most
exciting is extrasolar planet searches around M-dwarf stars via the radial velocity (RV) method. M-
dwarfs are attractive candidates for extrasolar planet searches because they make up a large portion of
the galactic neighborhood and their lower temperatures push the habitable zone closer to the star .
The closeness of the habitable zone, in conjunction with the smaller mass of these stars, creates larger
RV signatures in a shorter time. Indeed, planet searches around M-dwarfs are a key component of the
Exoplanet task force strategy .
The growing interest in near-IR high resolution (defined as R = λ/Δλ) astronomical spectroscopy is
reflected in the number of spectrographs that have been under development in recent years, including
CRIRES (R = 100,000) , Pathfinder (R = 50,000) , APOGEE (R = 20,000)  and FIRST (R = 50,000) .
A key component in realizing the potential of these spectrographs is precision calibration. Optical
frequency combs from mode-locked lasers with multi-gigahertz spacing have recently been recognized
as near ideal standards for the calibration of astronomical spectrographs .
The power of a frequency comb as a calibration source relies primarily on two properties of the comb.
First, a frequency comb consists of an array of discrete, regularly spaced frequency lines or modes
spanning hundreds of nanometers. Second, the frequency of every comb mode is traceable to the SI
second. The frequency of the nth mode of an optical frequency comb may be written as
νn = n x frep + fceo, (1)
where frep is the repetition rate or mode spacing and fceo is the carrier envelope offset frequency . The
spectrum of a frequency comb is fully determined once frep and fceo are known. Detection of frep simply
requires placing a fast photodiode in the beam path. Detecting fceo is more involved—the most
straightforward technique requires an octave-spanning spectrum and an f-2f interferometer . Once
detected, frep and fceo can be locked to oscillators traceable to the SI second, thus every mode of the
frequency comb is also traceable to the SI second. Applying this “optical frequency ruler” to the
calibration of an astronomical spectrograph would support RV measurements with cm/s precision and
accuracy . This represents more than an order of magnitude improvement over traditional calibration
sources of emission lamps and absorption cells [8-10]. Moreover, the traceability of the spectrograph
calibration allows comparisons from different instruments in different locations years or decades apart.
Also, the density of lines from a frequency comb can allow compensation for systematic shifts due to
inhomogeneity in the spectrograph that could otherwise limit RV precision [3, 11]. The high power per
combline enables improvements in spectrograph slit illumination as well. Ideally one would deliver
calibration light to the spectrograph via a uniform, isotropic source such as an integrating sphere.
Whereas the loss (10-6) of an integrating sphere is too great for traditional calibration sources, the high
power per combline (100 nW or more) of the frequency comb permits the use of such a lossy coupling
mechanism. A possible layout is shown in Fig. 1 .
FIG. 1. Frequency comb calibration setup. Light from the frequency comb is split into two fibers—calibration and reference. The
calibration fiber is fed to an integrating sphere for illumination of the spectrograph fiber. The reference fiber provides comb
light spatially offset at the spectrograph detector array. ND, neutral density; GPSDO, Global Positioning System disciplined
While frequency combs have the potential to make a significant impact, it is difficult to generate
hundreds of nanometers spectral coverage with the requisite multi-gigahertz spacing directly from a
mode-locked laser. Generally, the mode spacing from a frequency comb is limited to 1 GHz or less,
requiring a wavelength resolution well above that of current spectrographs. For example, a resolution of
50,000 at 1550 nm would require a comb spacing of at least 12 GHz to ensure modes are separated by
at least three resolution elements. A promising approach to make frequency combs available for
spectrograph calibration is to thin a lower repetition rate comb with a filter cavity that transmits only a
subset of modes [6, 11-19]. (It should be noted that the recent development of a 10 GHz Ti:Sapphire
mode-locked laser spanning a wavelength range of 470 nm to 1130 nm is also a interesting possibility
.) A filtered frequency comb has been used to simultaneously record the frequency comb and solar
spectra onto an astronomical spectrograph with state of the art performance across ~18 nm,
demonstrating the potential of this technique . In this paper, we report on a 12.5 GHz-spaced optical
frequency comb spanning over 400 nm for astronomical spectrograph calibration. The frequency comb
is obtained via cavity filtering the output of a lower repetition rate mode-locked laser. Spectral
broadening of the 12.5 GHz-spaced comb in nonlinear optical fiber yields coverage from 1380 nm to
1820 nm, supplying calibration lines across the H-band (1500 nm to 1800 nm). The mode filtering
technique can introduce small biases into spectrograph calibration, the magnitude of which depends on
the implementation. Design considerations leading to our implementation and possible wavelength
biases resulting from our setup are discussed. This discussion provides motivation for measurements
made on the optical spectrum in terms of frequency accuracy and stability, optical linewidth, and
suppression of spurious sidemodes. To our knowledge, the data presented here represent the most
comprehensive characterization of an optical frequency comb for spectrograph calibration reported to
II. 12.5 GHZ-SPACED COMB GENERATION
Generation of the 12.5 GHz-spaced optical frequency comb starts with a 250 MHz repetition rate
passively mode-locked Erbium-doped fiber laser. Part of the laser output is amplified, then passed
through highly nonlinear fiber (HNLF) to generate an octave-spanning spectrum. The broadened optical
spectrum, spanning 1 µm-2 µm, is sent to a standard f-2f interferometer for fceo detection . A separate
laser output is used for repetition rate detection. The carrier envelope offset frequency and frep are both
locked to low noise synthesizers that are referenced to a Global Positioning System disciplined oscillator
(GPSDO). Both fceo and frep stay locked for several days without intervention.
With both frep and fceo locked, the frequency of the nth mode is given by
νn = n x 250 MHz – 116 MHz. (2)
For νn near 1550 nm, n ~ 773,000. The fceo value of 116 MHz was chosen for best transmission through
the mode selection filter cavity . A schematic of the 250 MHz frequency comb is shown in Fig 2.
FIG. 2. 250 MHz-spaced optical frequency comb source. frep is controlled by changes to the laser cavity length, while fceo is
controlled by changes to the laser pump power. Both frep and fceo are locked to oscillators referenced to a GPSDO. fceo is locked
via the copy of fceo at frep - fceo (134 MHz). For the fceo lock, part of the laser output is amplified with Erbium-doped fiber (EDF)
before the highly nonlinear fiber (HNLF) that broadens the spectrum to cover 1 µm - 2 µm. Light at 2 µm is frequency-doubled
in periodically-poled Lithium Niobate (PPLN). Light at 1 µm passes through the PPLN and interferes on the photodetector (PD)
with the frequency-doubled light. BPF, bandpass filter; SMF, single-mode fiber; WDM, wavelength division multiplexer; WP,
Another laser output of 40 mW is sent to the first of two mode selection filter cavities. Both filter
cavities are high finesse (2000 at 1550 nm) air-gap etalons with a free spectral range of 12.5 GHz. The
periodic transmission of the filter cavities transmits modes separated by 12.5 GHz (one mode out of
every 50) with low loss, while other modes are greatly suppressed. Both filter cavities are locked to the
frequency comb by imparting a ~50 kHz dither on the filter cavity length and locking to a peak in the
transmitted power. This lock has also shown to be robust for several days of continuous operation.
After the first cavity, the laser is sent through a system of amplifiers and dispersion compensating fiber.
Amplification and pulse compression are necessary to raise the peak power of the pulse train for
nonlinear broadening later on. The first two amplifiers are semiconductor optical amplifiers (SOAs) with
gain peaks offset by ~40 nm. This arrangement preserves the 50 nm of bandwidth after the first filter
cavity and raises the average power of the pulse train from 200 µW to 80 mW. This level is sufficient to
seed the high-power Erbium-doped fiber amplifier (HPEDFA) that follows. The average power after the
HPEDFA is ~1.4 W.
After amplification, the pulse train passes through the second filter cavity. The frequency comb is then
broadened in 50 m of low dispersion HNLF  to generate over 400 nm of 12.5 GHz-spaced modes. The
HNLF has a dispersion slope of +0.019 ps2/km/nm, a nonlinear coefficient of 30/W/km, and the zero
dispersion wavelength is 1550 nm. Losses coupling into and out of the second filter cavity as well as
insertion loss in the isolator following the HPEDFA result in ~400 mW into the HNLF. The pulse width at
the HNLF input is ~300 fs, resulting in a peak power of 100 W. The mode-locked laser and the filter
cavities rest on a vibration isolation optical table and are covered with a foamboard box to provide a
layer of vibration, acoustic and thermal isolation. A schematic showing the generation of the 12.5 GHz-
spaced comb is shown in Fig. 3.
FIG. 3. 12.5 GHz-spaced comb generation. HPEDFA, high power Erbium-doped fiber amplifier; SOA, semiconductor optical
amplifier; PZT, piezoelectric transducer; DCF, dispersion compensating fiber. All fibers are single mode at 1550 nm.
III. DESIGN CONSIDERATIONS AND WAVELENGTH BIASES
There are important limitations that must be considered when one uses a frequency comb with cavity
filtering for spectrograph calibration that warrant careful measurements of the resulting comb spectrum
[6, 13, 14]. Here we discuss the potential limitations of our particular realization of a 12.5 GHz-spaced
comb and how we have worked to mitigate these limitations.
A. Higher order spatial modes, filter cavity dispersion and finesse
Higher order spatial modes (HOMs) of the filter cavity can be excited by the comb, resulting in unwanted
laser modes transmitted with low loss . A judicious choice of curvatures in the etalon mirrors can
mitigate this effect . For the etalons presented here, there are HOMs with a frequency offset of
+1.75 GHz from the main 12.5 GHz spaced modes that are transmitted with low loss. Fortunately the
overlap between the HOM and the optical fiber spatial mode is small, and no 1.75 GHz-offset frequency
component is detectable after the second filter cavity to the -70 dB level. A larger problem stems from
dispersion in the filter cavity. Whereas the modes of the mode-locked laser are equally spaced,
dispersion in the cavity mirrors results in unequal spacing of the filter cavity transmission peaks. This
causes a walk-off between the laser modes and the etalon transmission peaks, limiting the bandwidth of
the filtered comb [6, 13, 14]. One could increase the useable bandwidth by decreasing the finesse, but
this comes at the expense of reduced sidemode suppression. For the system presented here, we have
chosen a finesse of 2000, yielding, in a single pass, ~38 dB suppression of the nearest neighbor modes
and 50 nm bandwidth.
B. Filter cavity induced wavelength biases
In addition to limiting the optical bandwidth, the shift between a laser mode and the transmission peak
of the etalon can result in an apparent wavelength shift in two ways. First, the laser modes are of finite
width and will be asymmetrically reshaped as the mode is detuned from the transmission peak of the
filter cavity. For detunings such that the mode remains within the full width at half maximum (FWHM) of
the transmission peak, as long as the linewidth is less that 1/10 of the FWHM of the etalon, the
wavelength shift should be less than 1 cm/s . Second, the shift between the laser mode and the
center of the transmission peak of the etalon will result in asymmetric suppression of the 250 MHz-
offset modes . The unequal weight of these sidemodes, unresolved by the spectrograph, will also
cause a shift in the line center. For example, consider an R = 50,000 spectrograph with a Gaussian
transfer function that is illuminated with a combline that has asymmetrically suppressed modes offset
by 250 MHz. Neglecting detector noise, for sidemodes suppressed 20 +/-1 dB, 30 +/-1 dB and 40 +/-1 dB,
the estimated RV bias from the 250 MHz-offset modes is 1.8 m/s, 0.18 m/s and 0.018 m/s, respectively
. Note that even if shifts in the observed wavelength caused by filtering are stable for long periods, it
weakens one of the major advantages of the comb, namely traceability. A frequency comb calibration
that is tied to a particular filter cavity configuration complicates comparisons with different comb
sources calibrating different spectrographs.
C. Spectral broadening in HNLF
Bandwidth limitation of the filter cavities motivated our use of HNLF to spectrally broaden the 12.5 GHz-
spaced comb to provide full H-band coverage. Nonlinear spectral broadening of a high repetition rate
pulse train comes with its own set of challenges. Because the available energy is divided into more
pulses, nonlinear spectral broadening requires a higher average power of the pulse train to achieve the
same peak power as a lower repetition rate source. For example, consider the 250 MHz pulse train used
for the f-2f interferometer and fceo detection described above. To achieve an octave of bandwidth in 50
cm of fiber, the average power of the pulse train is 100 mW. For the 12.5 GHz pulse train to have the
same peak power (assuming the pulse width is the same), the average power would need to be 50 times
higher, or 5 W. Achieving this level of output power requires amplification, but amplifying our pulse
train to several watts without spectral gain narrowing (which would broaden the pulse) or detrimental
nonlinear effects in the amplifier would be extremely challenging. Also of concern is increased noise as
the amplified comb is passed through the HNLF. The intensity noise of a pulse train is known to increase
as it passes through HNLF [24, 25]. In particular, the amplified spontaneous emission (ASE) from the
amplifiers will degrade the coherence of the optical spectrum [26, 27]. Also, four-wave-mixing (FWM)
between the 12.5 GHz-spaced modes and the suppressed 250 MHz-spaced modes can significantly
reduce the suppression ratio. We have attempted to mitigate these effects by placing a second filter
cavity just before the HNLF. The second filter cavity removes ASE between the comb modes and
increases the suppression of the 250 MHz offset sidemodes.
D. Accuracy and stability of reference oscillator
Finally we note that the accuracy and stability of a frequency comb are ultimately determined by its
frequency reference. We have chosen a GPSDO as the frequency reference for our frequency comb as it
provides transportable, long term accuracy at a reasonable cost. While the GPSDO frequency is expected
to track UTC(USNO) in the long term (accuracy better than 10-12 in a day), short term fluctuations on the
order of a few parts in 10-10 are possible. The performance among different GPSDOs can vary
significantly , therefore measurements of the GPSDO are warranted, as well as confirming the comb
tracks it after the filter cavities, amplifiers and HNLF.
As these concerns indicate, the comb must be measured in detail to confirm spectrograph calibration at
the cm/s level. In the next section we report on measurements of 250 MHz-offset sidemode
suppression, optical frequency accuracy and stability, and optical linewidth.
A. Optical spectrum and sidemode suppression
The optical spectra for various points along the lightpath are shown in Fig. 4. Immediately after the first
filter cavity, a reduction in the wings of the spectrum is evident—a result of the walk-off between the
filter cavity transmission peaks and the laser modes. At the center of the spectrum, the loss from
coupling to the filter cavity and single mode fiber is ~4dB. The optical spectrum after the SOAs maintains
the spectral FWHM while the power per mode increases more than a factor of 100. The spectrum after
the second filter cavity is also shown. Note the bandwidth reduction due to gain narrowing in the
HPEDFA. This represents the optical spectrum of the pulse train into the HNLF. The optical spectrum
following the HNLF is shown in Fig. 5. The comb extends from 1380 nm to 1820 nm, spanning the H-
band. From 1300 nm to 1700 nm, the spectrum was measured with a high resolution (R = 77,000) optical
spectrum analyzer. For wavelengths longer than 1700 nm, the spectrum was measured with a much
lower resolution monochromator, thus only the spectral envelope is available for λ > 1700 nm. Shorter
lengths of the same HNLF were also tested where it was observed that the peak near 1820 nm moved to
shorter wavelengths. This is consistent with a soliton self-frequency shift . The power of the 12.5
GHz-spaced comblines varies about 15 dB from 10 µW per mode to 320 µW per mode.
15501575 16001625 1650
Power per mode (dBm)
High res close-in
After 1st cavity
After 2nd cavity
FIG. 4. Power per optical mode at different stages of comb filtering and amplification. The inset is a high resolution close-in view
of the spectrum after the SOAs.
130014001500 1600 1700 18001900
Power per mode (dBm)
FIG. 5. Power per optical mode after nonlinear broadening. The inset is a high resolution close-in view around 1600 nm. The
comb signal-to-noise is limited by the grating-based optical spectrum analyzer employed for this measurement. The asymmetry
of the modes in the inset is also due to the optical spectrum analyzer.
The level of suppression of the 250 MHz-offset modes, asymmetry in mode suppression and how mode
suppression varies with wavelength were measured. These measurements were performed by optically
heterodyning the 12.5 GHz-spaced comb with a tunable continuous-wave (CW) laser. The microwave
spectrum of the photodetected beat between the CW laser and the frequency comb directly gives the
optical sidemode suppression. An example microwave spectrum trace of a CW-comb beat is shown in
Fig. 6(a). Two tunable lasers, spanning 1380 nm to 1490 nm and 1520 nm to 1630 nm, respectively, were
tuned across the comb spectra in 10 nm steps. For measurements on the comb after the HNLF, the
measurement span was limited by the tuning range of our tunable lasers. The results of all the beats
measured are summarized in Fig. 6(b). Immediately after the first filter cavity, the suppression is ~38 dB
in the center of the spectrum and ~31 dB at 1525 nm. This is consistent with the reflectively of the
mirror coatings: 99.89 % from 1550 nm to 1600 nm but dropping to ~99.85 % at 1510 nm. After the
SOAs, the suppression is reduced considerably, likely due to FWM in the SOAs. Also note the asymmetry
as great as 7 dB in the sidemodes, particularly at 1580 nm and 1590 nm. The second filter cavity
increases the suppression of the sidemodes to around 60 dB and no asymmetry was detected within the
measurement uncertainty of +/-1 dB. The level of suppression changes again after the HNLF, ranging
from 20 dB at 1380 nm to 45 dB at 1570 nm. Again, no asymmetry in the sidemode strength was
observed within +/-1 dB.
FIG. 6. 250 MHz-offset mode suppression measurements. (a) Example heterodyne measurement where the higher and lower
frequency sidemodes are suppressed 34 dB. (b) Summary of all sidemode suppression measurements. Circles: after the 1st filter
cavity, showing higher (blue) and lower(red) frequency sidemode suppression. Crosses: after the SOAs, showing higher and
lower frequency sidemode suppression. Squares: after the second filter cavity, where no asymmetry in sidemodes was
detected. Black diamonds: after HNLF where no asymmetry was detected.
Ideally, the sidemode suppression on every 12.5 GHz-spaced combline would be measured. From 1380
to 1630 nm the measurements are representative, for we consider it unlikely that the suppression ratio
changes more than a few dB in 10 nm. Less certain is the sidemode suppression beyond 1630 nm. Other
possible techniques to measure suppression on every 12.5 GHz-spaced combline over the entire
wavelength range are two comb spectroscopy , or a high resolution Fourier transform spectrometer.
The use of these measurement techniques is currently under investigation.
Another method that has been reported in the literature to calculate the sidemode suppression ratio is
to photodetect the filtered comb and measure the sidemode strength in the photodetected microwave
spectrum [13, 18, 19]. We find this method unreliable for the following reasons. First, no information
about asymmetry of sidemode suppression or variations of suppression with wavelength can be
obtained. Second, using the photodetected pulse train to measure optical sidemode suppression
requires assumptions about the relative phase among the optical modes. As an example of how such
assumptions can be misleading, consider the photodetected spectrum of the pulse train after the SOAs,
shown in Fig. 7(a). This spectrum shows 250 MHz offset spurs are >57 dB below the 12.5 GHz carrier. If
we make the assumption that all modes are in phase, we would predict an optical sidemode suppression
of 63 dB. However, as shown in Fig. 7(b), an optical heterodyne measurement at 1560 nm reveals the
optical sidemode suppression after the SOAs of 27 dB.
> 57 dB
FIG. 7. (a) Microwave spectrum of the photodetected pulse train after the SOAs. Sidemodes offset by 250 MHz from the 12.5
GHz carrier are 57 dB below the carrier. (b) optical heterodyne measurement at 1560 nm where only 27 dB suppression is
observed. This heterodyne measurement is also represented in Fig. 6.
B. Frequency accuracy and stability
Frequency accuracy and stability of the 12.5 GHz-spaced comb were measured. These measurements
made use of frequency counters referenced to a 10 MHz Hydrogen-Maser signal, traceable to the SI
second, with stability near 1·10-13 in one second. For all measurements, the frequency counter gate time
was one second. The 10 MHz reference from the GPSDO, frep, fceo and a comb mode at 1550 nm (n =
773,587) were simultaneously measured. Measurements were made along the lightpath to see the
effects, if any, of the filter cavities, amplifiers and HNLF.
Because the frequency of the mode near 1550 nm is not directly countable, a separate reference
frequency comb was used to generate a beat tone that could be counted. The setup for generating the
beat tone between the reference comb and the mode near 1550 nm is shown in Fig. 8. The reference
comb is an octave-spanning, 1 GHz repetition rate Ti:sapphire laser with both frep and fceo frequencies
referenced to the H-Maser . A CW fiber laser at 1550 nm is frequency-doubled to 775 nm and beat
against the reference comb. The beat signal between the reference comb and the frequency-doubled
fiber laser is then used to lock the frequency of the fiber laser to the reference comb. A beat signal
between the fiber laser output at 1550 nm and the comb for spectrograph calibration is then
photodetected and counted. In this way the stability and accuracy of a mode near 1550 nm can be
measured against the H-Maser.
FIG 8. Setup for measuring the frequency stability, accuracy and linewidth of an optical mode. Light from the Ti:Sapphire
frequency comb is combined with the frequency-doubled light from the CW laser via a polarization beam splitter (PBS) and
polarizer (Pol.). Half-wave plates (λ/2) control the polarization into the PBS. For frequency accuracy and stability
measurements, the 1 GHz Ti:Sapphire reference comb is locked to the H-Maser and the beat frequency, fbeat, is sent to the
frequency counter. For linewidth measurements the reference comb is locked to an ultrastable optical reference and fbeat is
sent to an rf spectrum analyzer (RFSA). EDFA, erbium-doped fiber amplifier.
From the frequency counter record, the fractional frequency offset was determined by subtracting the
nominal frequency, as determined by the H-Maser, and normalizing the frequency to its carrier.
Fractional frequency offset measurements for GPSDO, frep, fceo and a comb mode after the HNLF are
shown in Fig. 9. Note the fractional frequency of frep, fceo and the comb mode at 1550 nm all track the
GPSDO reference and are on the order of a few parts in 10-10. Since the fractional frequency instability is
clearly dominated by the GPSDO reference, it is interesting to examine the difference in the fractional
frequency offset of the comb mode [Fig. 9(d)] and the GPSDO [Fig. 9(a)]. As shown in Fig. 10, this
difference is bounded by +/- 1 10-11 with a standard deviation 6.4 10-13, indicating significantly improved
performance should be possible with a better reference oscillator.
FIG. 9. Fractional frequency offset of (a) the GPSDO, (b) fceo, (c) frep and (d) an optical mode near 1550 nm.
Residual Frequency Fluctuation x10 -11
Standard deviation: 6.4x10 -13
FIG. 10. Residual fractional frequency offset of the 1550 nm mode relative to the GPSDO.
Similar measurements were made to examine the comb mode directly from the 250 MHz laser, after the
first filter cavity, and after the second filter cavity. In all cases the optical mode tracked the GPSDO as in
Fig. 9. Fig. 11 shows the stability and accuracy of the comb mode in both frequency and RV units along
the lightpath. For all measurements, obtained over a one week period, RV offsets are mostly bound
between +/- 5 cm/s. There are a few momentary (less than 3 s duration) excursions approaching 10
cm/s originating from the GPSDO. Depending upon the integration time of the spectrograph detector
array, these short term excursions may be averaged over. Note that these measurements only track the
instability of one of the 12.5 GHz-spaced modes—any constant offset due to asymmetry in suppressed
sidemodes is not taken into account.
Frequency Offset (kHz)
Time (5 hrs/div)
Residual Velocity (cm/s)
After 1st cavityAfter 2nd cavityAfter HNLF 250 MHz comb
FIG. 11. Frequency and radial velocity bias of an optical mode near 1550 nm measured along the lightpath. Zero offset is
determined by the H-Maser. For the measurement after the HNLF, the mode number n and frequency were determined to be
773587 and 193.9966 THz, respectively. For all measurements the accuracy and stability is dominated by the GSPDO.
C. Optical linewidth
As noted above, a broad optical linewidth can introduce a bias into spectrograph calibration if the mode
is asymmetrically shaped by one of the filter cavities. Because the finesse of 2000 for our filter cavities
corresponds to a transmission peak FWHM of 6.25 MHz, the optical linewidth into the filter cavities
should be less than 625 kHz to avoid any significant wavelength biasing due to line reshaping. The
linewidth from a mode-locked laser comb source is largely determined by the short term stability (<1 s)
of its reference, although the free running linewidth, and the frep and fceo locking electronics also have an
effect. As shown above, it is the fractional frequency noise of the reference that will be transferred to
the comblines, therefore the noise of the reference signal must be multiplied by the frequency ratio of
the combline to the reference. Thus a mode near 1550 nm can have a linewidth of 100s of kHz when the
10 MHz reference signal linewidth is sub-Hertz. Aside from the 10 MHz reference, the components used
to generate the 12.5 GHz comb can also affect the linewidth, most notably the HNLF. The optical
linewidth for a mode near 1550 nm was measured along the lightpath. The setup for measuring the
optical linewidth is nearly identical to that of the frequency accuracy and stability measurements. The
only difference is the H-Maser frequency reference is replaced with a sub-Hertz linewidth optical
reference . The stability of the optical reference is transferred to the reference comb and the 1550
nm CW laser . The heterodyne beat between the CW laser and the spectrograph comb was
measured with a microwave spectrum analyzer to determine the linewidth. The optical linewidth at
various points along the lightpath is shown in Fig. 12. Fig. 12(a) shows the linewidth measurement on a
linear scale with a 1 MHz span. There is no significant change in the ~340 kHz FWHM linewidth as the
comb passes through the filter cavities and the HNLF. The linewidth differences are more apparent in
Fig. 12(b), where the intensity is plotted on a log scale and the span increased to 50 MHz. Note the high
noise floor of the measurement after the HPEDFA, resulting from ASE from the amplifiers. This floor
reduces dramatically as the ASE is filtered by the second filter cavity. After the HNLF, skirts appear
staring 25 dB below the peak and drop to 60 dB below the peak at 25 MHz offset. The origins of these
skirts could be the nonlinear increase of technical intensity noise on the pulse train and ASE that
survives the second filter cavity parametrically mixing with the comb [22, 24-26].
Although these measurements were performed on only one comb mode, they do provide information
on the linewidth of other modes. The linewidth varies with frequency, but for a spectrum spanning less
than an octave, the linewidth will vary by less than a factor of 2 across the spectrum. Since the
wavelength band through the filter cavities is narrow, the linewidths of the modes passing through the
filter cavities are relatively constant at 340 kHz. This is below our 625 kHz criterion, therefore
wavelength bias due to line reshaping should not be a concern. Again we note that with a better
reference oscillator the linewidth can be reduced. After the HNLF, the linewidth FWHM should vary
according to the mode frequency. Further investigation is required to determine how the magnitude of
the skirts varies across the spectrum.
Frequency (200 kHz/div)
250 MHz comb
after 2 cavities
after 2 cavities
FIG. 12. Linewidth of an optical mode near 1550 nm. (a) Linear scale measurement of the linewidth along the lightpath. For
each trace the spectrum analyzer sweep time is 5 msec and averaged 100 times. (b) Log scale measurement of the linewidth
after the HPEDFA, after the second filter cavity and after the HNLF. For each trace the spectrum analyzer sweep time is 113
msec and averaged 100 times. Note the difference in frequency scales for (a) and (b).
With growing interest in near-IR high resolution astronomical spectroscopy, precise spectrograph
calibration becomes vital. To this end, a 12.5 GHz-spaced optical frequency comb spanning 1380 nm to
1820 nm has been built and characterized. The comb spacing was chosen for R = 50,000 spectrograph,
placing one combline every 3 resolution elements. Measurements on sidemode suppression, optical
mode frequency accuracy, stability and linewidth indicate sub-m/s calibration should be possible across
the H-band. The frequency stability of the frequency comb is currently limited by the GPSDO to ~ +/- 5
cm/s. Higher performance GPSDOs are commercially available, therefore improvements on the comb
frequency stability are likely. If calibration across a smaller wavelength span is required, the setup can
be simplified by removing the HPEDFA and the HNLF. Measurements on this simplified setup
demonstrated 60 dB sidemode suppression in a 50 nm FWHM bandwidth and more than -17 dBm (20
µW) per mode. Although the comb developed here is targeted for R = 50,000 in the H-band, the
techniques used to characterize the comb should be applicable to frequency combs developed for other
wavelength bands and other spectrograph resolutions as well.
In the hunt for exoplanets, precision calibration with a frequency comb is only one element necessary to
measure a star’s radial velocity with cm/s precision. Intrinsic limitations such as density of features in
the stellar spectrum and stellar rotations, as well technical limitations such as signal-to-noise ratio on
the spectrograph detector and pointing stability of the telescope will all affect the final RV precision
. However, spectrograph calibration is currently the dominating uncertainty, limiting RV precision in
the H-band to ~10 m/s [3, 10]. Calibrating the spectrograph with a frequency comb should help facilitate
RV precision limited by the intrinsic properties of the starlight.
We thank T. Fortier for the use of the Ti:sapphire reference comb, Y. Jiang for supplying the sub-Hertz
optical reference, Y. Jiang and D. Braje for contributions in building the 250 MHz comb source, M.
Lombardi and A. Novick for assistance with the GPSDO, and M. Hirano of Sumitomo Electric Industries
for use of the HNLF. Financial support is provided by NIST and the NSF. F. Quinlan is supported as an
NRC/NAS postdoctoral fellow. This work is a contribution of an agency of the US government and is not
subject to copyright in the US.
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