Comb-assisted coherence transfer between laser fields
Tommaso Sala, Samir Kassi, Johannes Burkart, Marco Marangoni, Daniele Romanini
aa r X i v : . [ phy s i c s . op ti c s ] D ec Comb–assisted coherence transfer between laser fields
Tommaso Sala , Samir Kassi , , Johannes Burkart , , Marco Marangoni , Daniele Romanini , , ∗ Physics Department of Politecnico di Milano and IFN-CNR, Piazza Leonardo da Vinci 32, 20133 Milano, Italy Univ. Grenoble Alpes, LIPhy, F-38000 Grenoble, France CNRS, LIPhy, F-38000 Grenoble, France ∗ Corresponding author: [email protected]
Compiled July 23, 2018Single mode laser fields oscillate at frequencies well outside the realm of electronics, but their phase/frequencyfluctuations fall into the radio frequency domain, where direct manipulation is possible. Electro–optic deviceshave sufficient bandwidth for controlling and tailoring the dynamics of a laser field down to sub–nanosecondtime scales. Thus, a laser field can be arbitrarily reshaped and in particular its phase/frequency fluctuationscan be in principle removed. In practice, the time evolution of a reference laser field can be cloned to replacethe fluctuations of another laser field, at a close-by frequency. In fact, it is possible to exploit a partiallystabilized optical comb to perform the cloning across a large frequency gap. We realize this long–haul phasetransfer by using a fibered Mach–Zehnder single–sideband modulator driven by an appropriate mix of the beatnotes of the master and the slave laser with the comb. c (cid:13)
OCIS codes: (140.3425), (120.3930), (250.7360), (060.2390), (140.3070), (140.3490)
Frequency and time metrology foundations rest todayon optical frequency combs (OFC) working as frequencyrulers across an extremely wide spectral domain. Appli-cations range from referencing ultrastable continuous–wave (CW) laser sources [1, 2] to high precision spec-troscopy [3]. An OFC features a broad spectral envelopefilled by narrow uniformly spaced modes with frequencies f n = f + nf rep , where n is an integer. The mode spacing f rep and the comb offset f fall in the radio frequency(RF) domain and can be measured and controlled to highaccuracy [1].Mixing a CW laser with an OFC on a fast photodiodedelivers a beat note of its emission line with the closestcomb mode. Given preliminary approximate knowledgeof the laser frequency (to better than f rep / f and f rep . An ultrastablecomb can thus become a ruler for locking and narrow-ing a CW laser emitting anywhere inside its wide spec-tral envelope. However, one or even two ultrastable CWlasers are then needed to stabilize the comb [4]. In theend, such general schemes of comb–mediated coherencetransfer rely on a few high speed phase–locked loops toachieve referencing of a CW slave laser to one or two highcoherence CW master lasers across a wide spectrum andrequire full comb stabilization [5].In order to completely transfer coherence, the band-width and the control dynamic range of a servo loopmust be sufficient to handle the phase–frequency noisespectrum of the free running laser. The requirement onthe dynamic range is even stronger in a noisy environ-ment with severe 1 /f noise, i.e. outside a metrology lab-oratory. Laser setups involving high performance phaselocking loops between several lasers are expensive anddifficult to build and maintain, and demand interven-tion on the lasers to be stabilized by introducing fastfrequency control means, e.g. electro-optic or acousto- optic modulators, which may have to be installed insidethe laser cavity.So-called feed–forward (FF) schemes constitute a sim-pler approach: Phase/frequency variations derived froma fraction of the laser radiation are subtracted from themain laser beam, or else from a phase sensitive RF sig-nal generated from it. For instance, frequency mixing inthe RF domain has been used to subtract from a beatsignal the f note produced by an f − f OFC beatingsystem [6], avoiding stabilization of f . In the optical do-main, an AOM acting as a frequency shifter allowed tosubtract from an OFC beam its f fluctuations [7], or tosubtract the frequency fluctuations of a CW laser rela-tive to an OFC [8, 9]. In both applications the RF signaldriving the AOM was the beat note itself. These opticalFF approaches have a sub-MHz control bandwidth dueto the acoustic wave propagation delay in the AOM.We show here that coherence transfer between twoCW lasers lying inside the wide frequency range of anOFC can be obtained using a only one external controldevice to apply a FF phase correction to the slave laser.This correction has a double effect of eliminating at thesame time “common–mode” fluctuations of the comb atthe two lasers frequencies, as well as fluctuations of theslave with respect to the master laser. This simple FFscheme allows for larger control bandwidth and dynamicrange than any previously demonstrated approach, dueto a fibered EOM device operated as a single–sidebandmodulator [10]. It can be applied to any CW single modelaser and even used to copy complex field dynamics fromthe master to the slave laser. It does not suffer from en-vironmental perturbations, i.e. it cannot “unlock” as itmay occur to any feedback–based control loop under aviolent perturbation. Thanks to these properties it al-lows virtually instantaneous transfer of a frequency tun-ing action from the master to the slave, contrary to lockloops which can tolerate frequency changes at a given1 r:fiberComb FCFC MZMFC V-shapedreference cavity
Optical feedback locking FC VCOFMaster Laser P D P D Δν slave Δν master VAVA Co rrecte d Ou t pu t Δν master - Δν slave ν master ν slave Δν master + N’f rep
N’N ν BPF
DFBSlaveLaser
0° 90°
BSDFB
Coherence bridge
Fig. 1. Experimental scheme. VCOF is the sub-kHzlinewidth master laser, DFB the slave distributed–feedback diode laser, OFC the self-referenced opticalfrequency comb, MZM the Mach-Zehnder electro–opticsingle–sideband modulator, PD1 and PD2 are photodi-odes collecting the beat notes of both lasers with theOFC, filtered by diffraction gratings (DG). FC are sin-gle mode fiber combiners/splitters, VA are RF voltageamplifiers, BPF is a bandpass RF filter.maximum rate. In fact, phase lock servo systems devel-oped in metrology laboratories to deliver high frequencystability are not intended for nor easily adapted to fre-quency agile applications. For this reason they are noteasily seen in a molecular spectroscopy laboratory. Be-sides, contrary a feedback loop, the proposed approachdoes not require acting on the slave laser, which canperturb its operation for instance by exacerbating laseramplitude noise due to laser phase–amplitude couplingsor by increasing phase noise at frequencies just outsidethe loop bandwidth. The principal drawback of our FFapproach is the low power level available in phase mod-ulation sidebands. This is not an issue for applicationssensitive to source coherence, e.g. spectroscopy in a highfinesse cavity, where the loss in total power is compen-sated by an increase of the power spectral density in thecarrier (proportional to cavity injection efficiency).This scheme of coherence transfer has high poten-tial for applications in frequency metrology, but also inhigh precision spectroscopy as it allows agile and ex-act frequency tuning.Our goal is to improve the fre-quency accuracy of ultrasensitive absorption measure-ments using fibered DFB diode lasers coupled with cav-ity ring-down spectroscopy (CRDS). Over recent years,CRDS generated refined lists of thousands spectral linesof molecules of atmospheric or planetological interest.Nonetheless, while CRDS is linear over 5 decades of theabsorption scale [11], its frequency scale is limited bythe ∼
20 MHz accuracy of the best commercial wave-length meter. Towards this goal, we recently developeda source of high coherence and stability based on a DFBdiode laser locked to an isolated high finesse V-shapedcavity by optical feedback (VCOF) [10]. Frequency tun- ing is provided by a fibered monolithic dual–parallelMach–Zehnder electro–optic modulator (MZM) used asa single–sideband modulator with excellent ( ∼
30 dB)suppression of the carrier and of other sidebands [10].We recently demonstrated coherence transfer or“phase cloning” between two CW lasers by MZM–basedFF correction applied to a DFB diode laser [12], worse–case of a noisy laser. As the beat note between slave andmaster lasers gives their instantaneous frequency differ-ence, this is subtracted from the slave laser radiationby applying the beat signal directly to the MZM single–sideband modulator, which works as a fast (GHz) fre-quency shifter: The corrected radiation is a clone of themaster laser field.That FF scheme can be extended by introducing anOFC as a coherent bridge between master and slavelasers, which scales it up from GHz to THz frequencygaps. For simplicity, let us assume we select with suit-able RF band-pass filters the beat notes of the two lasers,each with the closest lower–frequency comb modes: ∆ ν m for the master laser and ∆ ν s for the noisy slave laser. Amixer provides their difference, ∆ ν m − ∆ ν s = ν m − ( f + N f rep ) − [ ν s − ( f + N ′ f rep )] = ν m − ν s + ( N ′ − N ) f rep ,which is amplified and applied to the MZM, traversedby a fraction of the slave laser radiation. In this way,after adjusting the MZM control bias voltages to pro-duce only the upper sideband, the RF signal drivingthis sideband will subtract the slave laser frequency fluc-tuations relative to the comb modes and, at the sametime, the common–mode f frequency fluctuations ofthe comb modes relative to the master laser. In equa-tions, the MZM output shall be at frequency ν c = ν s +[ ν m − ν s +( N ′ − N ) f rep ] = ∆ ν m + N ′ f rep , thus beingat the same comb offset as the master laser but relativeto the comb mode N ′ . As the separation of slave frommaster is increased, the comb frequency fluctuations thatare not common mode at the two laser frequencies, areexpected to increase and to become a limiting factor forthe coherence transfer. This effect is small and goes un-detected in our proof-of-principle demonstration using acommercial partially stabilized OFC. It is found to benegligible in applications involving laser injection of ahigh finesse CRDS cavity, over a comb–wide frequencygap. Also, as with active servo loops, the bandwidth ofthis FF control is inversely proportional to time delaysaccumulated by both electrical and optical signals. How-ever, the latter may be used to compensate the formerprovided a fiber patch of suitable length is added to theslave propagation path upstream the MZM correctionunit [12]: To first order this leads to a zero net delay.The bandpass is then limited by photodetectors and RFcomponents used to drive the MZM.Fig.1 resumes our experimental implementation. Be-sides the VCOF source detailed elsewhere [10] and astandard fibered telecom DFB diode laser, a 100 MHzself-referenced Erbium fiber comb (Toptica FFS model)is used, with free-running mode linewidth of about10 kHz over 1 ms. This OFC is partially stabilized in2
80 500 520 540 560 580 600 620-80-60-40
Upper Sideband
Upper SidebandCoherence transfer
Carrier
Unbalanced MZM Balanced MZM R F P o w e r [ d B m ] Frequency [MHz] (a)
Lower Sideband -40 -20 0 20 40-120-100-80-60
RBW 300 kHz(b)
Relative Frequency [kHz]
RBW 24 Hz
Fig. 2. Beating of the MZM output with the VCOFmaster laser. Upper panel: Broad band view showingthe carrier and the other sideband which are stronglysuppressed after optimization of the MZM control DCbias levels. Lower panel: High resolution spectrum of thedownshifted beat note, still limited by the instrumentalresolution (24 Hz). 58% of the power is calculated to be inthe carrier, corresponding to 0.75 rad r.m.s. phase noise.the sense that moderate bandwidth control loops are ap-plied to obtain a long term stability of f and f rep : Onlythe low frequency drift and jitter of the comb modesare corrected while their short term linewidth maintainsits free–running value. Care is taken to obtain beat sig-nals with good S/N (in excess of 25 dB) for both CWlasers. The ∆ ν s beat is centered around 10-20 MHz andlow–pass filtered at 30 MHz, while ∆ ν m is kept around70 MHz at the center of a narrow bandpass filter. Thesign of the beat notes is chosen in order to use the dif-ference of these signals as the driving signal of the MZM(consistently with our equations above). RF amplifica-tion ( ∼ ν m and ∆ ν s signalsto the range where the mixer operates with negligiblenoise addition. A bandpass filter selects the difference ofthe beating notes after the mixer. A 1 Watt RF amplifierboosts this signal up to a level adequate for the MZMto deliver 2-3% of the incident optical power into thefirst sideband, and negligible power in higher order har-monics. We should note that together with the carrier,destructive interference in the dual–MZM eliminates alleven order sidebands as well [12]. The amplified signal isapplied to the MZM via a 90 ◦ RF splitter operating inthe range from 55 to 90 MHz.As a first test we use a DFB diode tunable in theproximity of the master laser (1617 nm) allowing to di-rect beating of the MZM output against the master. Theresult in the upper panel of Fig.2, shows an instrument–limited 300 kHz peak width for the upper sideband and a 4 MHz-wide peak for the lower sideband, i.e. twice aslarge as the carrier peak. In order to make this last visi-ble, the MZM must be purposely unbalanced, which al-lows to change the relative peak intensities while pre-serving their widths.To quantify the width of the coherent peak with betterresolution we downshift the beating note via a frequencymixer in order to sample the signal using a 200 MHzGAGE acquisition card (equipped with a 100 MHz lowpass filter). By Fourier transform this produces thehigher resolution spectrum in the bottom panel of Fig.2,a beat note with Fourier–transform–limited 24 Hz width,lying 57 dB above a flat pedestal. By numerical integra-tion over a span of 60 MHz, we estimate that about 58%of the power is in the carrier, corresponding to 0.75 radr.m.s. phase noise.In order to test the coherence transfer over a broadspectral range we use as an optical spectrum analyzera high finesse optical cavity whose length is linearlyscanned by a piezoelectric actuator. This is 34.5 cm long(Free Spectral Range FSR=435 MHz) and has finesse450 000 around 1610 nm, corresponding to about 1 kHzwide resonances. We add a fibered optical amplifier atthe MZM output to increase the cavity injection sig-nal, followed by an optical isolator before mode–matchedcavity injection. The cavity length is slowly (1 Hz) modu-lated over one FSR delivering the transmission transientsof the top panel of Fig.3 with the same slave laser as be-fore (1617 nm). The strong narrow peak corresponds tothe upper sideband, while the weaker broad peak is as-sociated with the other sideband. Smaller peaks are dueto residual transverse modes (narrow or broad, depend-ing on the sideband they correspond to). By zoomingon the narrow sideband transient, a well–known chirpedringing pattern is visible, which can occur only if the in-cident field is narrower than the cavity mode [13]. This isproduced by the intracavity field buildup at the passagethrough resonance, which then exponentially decays andbeats with the incident field that continues to weaklyfeed the cavity off-resonance. The chirp is due to the fre-quency scan of the cavity resonance. The other sidebanddoes not show any ringing, as is observed when inject-ing the uncorrected DFB laser directly into the cavity.The presence of a ringing pattern over a noisy pedestaldemonstrates that a fraction of the MZM output powerfits inside a sub–kHz bandwidth, consistently with theabove result from direct lasers beating (Fig.2).When changing DFB laser, the same cavity outputpatterns are observed up to the low wavelength edge ofour comb. In particular, the bottom panel of Fig.3 showssignals from a 1521 nm DFB laser, which are equivalentto those from the 1617 nm laser. Therefore, at the kHzlevel of the scanning cavity mode width, the coherencetransfer appears to be as good for a laser at the VCOFfrequency (186 THz) as for a laser at the comb edge(198 THz). We should underline that over this range thereflectivity of the cavity mirrors is almost constant, as isdeduced from the exponential envelope of the coherent3 .0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.00.20.40.6
Time [s] 1521nm laser C a v i t y ou t pu t [ v o l t] Fig. 3. A 450 000 finesse cavity used as an optical spec-trum analyzer. 1 s on the horizontal scale is one cavityFSR (435 MHz). Top: coherence transfer applied to aDFB laser emitting close to the master VCOF laser. Inthe insets are detailed views of the narrow coherent peakfrom the upper sideband and the broad peak from thelower sideband. Bottom: Same observations when usinga DFB laser lying at the far edge of the comb.peaks in Fig.3 which display a decay constant of about150 µ s for both frequencies. In other words, if a degrada-tion of the coherence transfer is present, it stays below1 kHz over the explored 12 THz range.This is consistent with the frequency noise analysisof Erbium combs previously reported [14], where thenoise around the optical carrier is shown to be dom-inated by environmentally–induced laser cavity lengthfluctuations. According to the elastic tape picture of thecomb noise [6], such fluctuations force the comb modesto breath around a fixed point at nearly zero frequency,making their linewidth to increase by a factor of about0.05 kHz per THz (at 1 ms observation time, longer thanthe photon decay time of our high–finesse cavity). Thus,within a 12 THz frequency span the non–common–modefrequency noise contribution of the comb can be esti-mated to about 0.6 kHz.In conclusion, we demonstrate a simple and robustFF approach for phase locking two CW single modelasers beating with the same OFC, with a fast side-band modulator as the only optical control element. Aswe demonstrate, this can be applied to high precisioncavity–enhanced spectroscopy over the 12 THz spectralrange of an Erbium fiber comb. A set of cost–effectivewidely tunable telecom lasers can thus be used to in-terrogate molecular absorption in a high finesse cavitywithout any trade off in terms of precision, sensitivityand spectral resolution, these being inherited from a sin-gle high coherence master (e.g. our VCOF system). Inour experimental conditions the coherence transfer washampered by a comb mode spacing of 100 MHz: This forced the comb–DFB beat note to be singled out fromthe replicas due to the adjacent comb modes by meansof a relatively tight bandpass filter, slicing off a portionof the DFB noise spectrum. Using a comb with widermode spacing, effective control bandwidths exceeding100 MHz are within reach as recently demonstrated bydirect FF lock of a DFB laser against a VCOF laser [12].While we used a commercial comb with standard low–bandwidth controls of f and f rep , for demanding ap-plications where the contribution from the f rep noise isinacceptable, only this comb parameter would need tobe stabilized by a high–bandwidth servo control system.Even though at present the technique works in the tele-com range where fibered MZM modulators are readilyavailable, it will eventually become exploitable in thevisible or mid–infrared regions thanks to progress withguided optics devices based on lithium–niobate or silicontechnologies, respectively.The authors recognize financial support by: Polo diLecco - Politecnico di Milano, Institute of Photonics andNanotechnology of CNR, LabexOSUG@2020 project(ANR10 LABX56), Pˆole SMINGUE (Universit´e JosephFourier), Femto network of CNRS. References
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