Optical frequency comb technology: from ground to space

Optical frequency combs,as powerful tools for precision spectroscopy and research into optical frequency standards,have driven continuous progress and significant breakthroughs in applications such as time-frequency transfer,measurement of fundamental physical constants,and high-precision ranging,achieving a series of milestone results in ground-based environments.With the continuous maturation and evolution of femtosecond lasers and related technologies,optical frequency combs are moving from ground-based applications to astronomical and space-based applications,playing an increasingly important role in atomic clocks,exoplanet observations,gravitational wave measurements,and other areas.This paper,focusing on astronomical and space-based applications,reviews research progress on astronomical frequency combs,optical clock time-frequency networks,gravitational waves,dark matter measurement,dual-comb large-scale absolute ranging,and high-resolution atmospheric spectroscopy.With enhanced performance and their gradual application in the field of space-based research,optical frequency combs will undoubtedly provide more powerful support for astronomical science and cosmic exploration in the future.

Equal-amplitude optical comb generation using multi-frequency phase modulation in optical fibers

We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n-1 equalamplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the odd harmonic frequencies, and 2n＋1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the even harmonic frequencies. Then, we numerically simulate the spectra of 5, 7, 9, and 11 equal-amplitude spectral lines, respectively, which are also obtained in experiments with frequency separation of 30 MHz and flatness of better than 0.3 dB.

Hybrid Optical Comb Filter with Multi-Port Fiber Coupler for DWDM Optical Network

Optical comb filters based on multi-port fused fiber couplers are proposed and numerically analyzed, 3-arm MZI composed by 1×7 fiber splitter and 3×3 fiber coupler, and 2-stage cascaded FIR type MZI interleave filter.

10-GHz broadband optical frequency comb generation at 1550/1310 nm

The generation of high-repetition rate(frep≥10 GHz)ultra-broadband optical frequency combs(OFCs)at 1550 nm and 1310 nm is investigated by seeding two types of highly nonlinear fibers(HNLFs)with 10 GHz picosecond pulses at the pump wavelength of 1550 nm.When pumped near the zero dispersion wavelength(ZDW)in the normal dispersion region of a HNLF,10 GHz flat-topped OFC with 43 nm bandwidth within 5 dB power variation is generated by self-phase modulation(SPM)-based OFC spectral broadening at 26.5 dBm pump power,and 291 fs pulse trains with 10 GHz repetition rate are obtained at 18 dBm pump power without complicated pulse shaping methods.Furthermore,when pumped in the abnormal dispersion region of a HNLF,OFCs with dispersive waves around 1310 nm are studied using a common HNLF and fluorotellurite fibers,which maintain the good coherence of the pump light at 1550 nm.At the same time,sufficient tunability of the generated dispersive waves is achieved when tuning the pump power or ZDW.

A long-term frequency-stabilized erbium-fiber-laser-based optical frequency comb with an intra-cavity electro-optic modulator

We demonstrate an optical frequency comb based on an erbium-doped-fiber femtosecond laser with the nonlinear polarization evolution scheme. The repetition rate of the laser is about 209 MHz. By controlling an intra-cavity electro- optic modulator and a piezo-transducer, the repetition rate can be stabilized with a high-bandwidth servo in a frequency range of 3 kHz, enabling long-term repetition rate phase-locking. The in-loop frequency stability of repetition rate is about 1.6× 10-13 in an integration time of 1 s, limited by the measurement system; and it is inversely proportional to integration time in the short term. Furthermore, using a common path f-2f interferometer, the carrier envelope offset frequency of the comb is obtained with a signal-to-noise ratio of 40 dB in a 3-MHz resolution bandwidth. Stabilized cartier envelope offset frequency exhibits a deviation of 0.6 mHz in an integration time of 1 s.

Precise determination of characteristic laser frequencies by an Er-doped fiber optical frequency comb

Femtosecond optical frequency combs correlate the microwave and optical frequencies accurately and coherently.Therefore,any optical frequency in visible to near-infrared region can be directly traced to a microwave frequency.As a result,the length unit“meter”is directly related to the time unit“second”.This paper validates the capability of the national wavelength standards based on a home-made Er-doped fiber femtosecond optical frequency comb to measure the laser frequencies ranging from visible to near-infrared region.Optical frequency conversion in the femtosecond optical frequency comb is achieved by combining spectral broadening in a highly nonlinear fiber with a single-point frequencydoubling scheme.The signal-to-noise ratio of the beat notes between the femtosecond optical frequency comb and the lasers at 633,698,729,780,1064,and 1542 nm is better than 30 d B.The frequency instability of the above lasers is evaluated by using a hydrogen clock signal with a instability of better than 1×10^(-13)at 1-s averaging time.The measurement is further validated by measuring the absolute optical frequency of an iodine-stabilized 532-nm laser and an acetylenestabilized 1542-nm laser.The results are within the uncertainty range of the international recommended values.Our results demonstrate the accurate optical frequency measurement of lasers at different frequencies using the femtosecond optical frequency comb,which is not only important for the precise and accurate traceability and calibration of the laser frequencies,but also provides technical support for establishing the national wavelength standards based on the femtosecond optical frequency comb.

A diode laser spectrometer at 634 nm and absolute frequency measurements using optical frequency comb

This paper reports that two identical external-cavity-diode-laser （ECDL） based spectrometers are constructed at 634nm referencing on the hyperfine B-X transition R（80）8-4 of 127I2. The lasers are stabilized on the Doppler-free absorption signals using the third-harmonic detection technique. The instability of the stabilized laser is measured to be 2.8 × 10^-12 （after 1000 s） by counting the beat note between the two lasers. The absolute optical frequency of the transition is, for the first time, determined to be 472851936189.5 kHz by using an optical frequency comb referenced on the microwave caesium atomic clock. The uncertainty of the measurement is less than 4.9 kHz.

Coherence transfer from 1064 nm to 578 nm using an optically referenced frequency comb

A laser at 578 nm is phase-locked to an optical frequency comb（OFC） which is optically referenced to a subhertzlinewidth laser at 1064 nm. Coherence is transferred from 1064 nm to 578 nm via the OFC. By comparing with a cavitystabilized laser at 578 nm, the absolute linewidth of 1.1 Hz and the fractional frequency instability of 1.3 × 10^-15 at an averaging time of 1 s for each laser at 578 nm have been determined, which is limited by the performance of the reference laser for the OFC.

Photonic radio frequency channelizers based on Kerr optical micro-combs

We review recent work on broadband RF channelizers based on integrated optical frequency Kerr micro-combs combined with passive micro-ring resonator filters,with microcombs having channel spacings of 200 and 49 GHz.This approach to realizing RF channelizers offers reduced complexity,size,and potential cost for a wide range of applications to microwave signal detection.

Two-Photon Transitions of ^(85)Rb 5D_(5/2) State by Using an Optical Frequency Comb and a Continuous-Wave Laser

A high-resolution two-photon spectrum of 5S1/2 → 5P3/2 → 5D5/2 transitions in a thermal SSRb vapor cell is presented by using an optical frequency comb and a cw laser. The fluorescence of 6P3/2 → 5S1/2 spontaneous emission is detected when the cw laser frequency is scanned from the 5S1/2 ground state to 5P3/2 hyperfine levels and the optical frequency comb repetition rate is fixed. The hyperfine splittings （Ff = 2-5） of the 5D5/2 excited state are well resolved. The dependences of fluorescence intensities on the cw laser intensity and temperature of SSRb vapor eel1 are studied, respectively. The experimental results are in good agreement with the theoretical analyses.

Precision Frequency Measurement of ^(87)Rb 5S_(1/2)(F=2)→5D_(5/2)(F″=4)Two-Photon Transition through a Fiber-Based Optical Frequency Comb

The absolute frequency of 87Rb 5S1/2 （F=2）→5D5/2 （F＂ = 4） two-photon transition at 778nm is measured in an accuracy of 44kHz. A home-made erbium-doped fiber laser frequency comb with frequency stability of 5.0 × 10-13@1 s is employed for the light source. By using a periodically poled lithium niobate, the femtosecond pulse operating in 1556 nm is frequency-doubled to 778 nm to obtain the direct two-photon transition spectroscopy of thermal rubidium vapor. Through sweeping the carrier envelope offset frequency （fceo）, the 5S1/2 （F=2）→5D5/2 （F＂ = 4） two-photon transition line is clearly resolved and its absolute frequency is determined via the peak-finding of the fitting curve. After the frequency correction, the measured result agrees well with the previous experiment on this transition. The entire potential candidate of optical frequency standard for system configuration is compact and robust, providing a telecommunication applications.

All polarization-maintaining Er:fiber-based optical frequency comb for frequency comparison of optical clocks

We demonstrate an optical frequency comb(OFC)based on a turnkey mode-locked laser with a figure-9-shape structure and polarization-maintaining fibers,for the comparison of frequency among optical clocks with wavelengths of 698 nm,729 nm,1068 nm,and 1156 nm.We adopt a multi-branch approach in order to produce high power OFC signals at these specific wavelengths,enabling the signal-to-noise ratio of the beatnotes between the OFC and the clock lasers to exceed30 d B at a resolution bandwidth of 300 k Hz.This approach makes the supercontinuum spectra much easier to be generated than a single branch OFC.However,more out-of-loop fibers degrade the long-term frequency instability due to thermal drift.To minimize the thermal drift effect,we set the fiber lengths of different branches to be similar,and we stabilize the temperature as well.The out-of-loop frequency instability of the OFC due to the incoherence of the multi-branch is about5.5×10^(19) for 4000 s,while the in-loop frequency instability of fceo and that of fbeat are 7.5×10^(18) for 1 s and 8.5×10^(18) for 1 s,respectively.The turnkey OFC meets the requirement for the comparison of frequency between the best optical clocks.

Mid-infrared supercontinuum and optical frequency comb generations in a multimode tellurite photonic crystal fiber

We numerically investigate the mid-infrared(MIR)supercontinuum(SC)and SC-based optical frequency comb(OFC)generations when the three optical modes(LP_(01),LP_(02),and LP_(12))are considered in a multimode tellurite photonic crystal fiber(MM-TPCF).The geometrical parameters of the MM-TPCF are optimized to support the multimode propagation and obtain the desired dispersion characteristics of the considered three optical modes.When the pump pulse with center wavelengthλ=2.5μm,width T=80 fs,and peak power P=18 kW is coupled into the anomalous dispersion region of the LP_(01),LP_(02),and LP_(12)modes of the MM-TPCF,the-40-dB bandwidth of the generated MIR SCs can be up to 2.56,1.39,and 1.12 octaves,respectively,along with good coherence.Moreover,the nonlinear dynamics of the generated SCs are analyzed.Finally,the MIR SCs-based OFCs are demonstrated when a train of 50 pulses at 1-GHz repetition rate is used as the pump source and launched into the MM-TPCF.

Two-photon spectrum of^(87) Rb using optical frequency comb

The high precision two-photon excitation measurements for 5S1/2 （Fg = 2） to 5D5/2 （Fe = 4 to 1） of 87Rb are per- formed by using an optical frequency comb. The two counter-propagating femtosecond pulses （5S1/2 →5P3/2 at 780 nm, and 5P3/2→5D5/2 at 776 nm） act on 87Rb vapor, and the Doppler broadened background signal is effectively eliminated. The temperature and power dependences of the two-photon spectrum are studied in this paper.

Optical Frequency Comb-Based Cavity-Enhanced Fourier-Transform Spectroscopy:Application to Collisional Line-Shape Study

Direct-comb spectroscopy techniques uses optical frequency combs(OFCs)as spectroscopic light source.They deliver high sensitivity,high frequency resolution and precision in a broad spectral range.Due to these features,the field has burgeoned in recent years.In this work we constructed an OFC-based cavity-enhanced Fourier-transform spectrometer in the nearinfrared region and used it for a line-shape study of rovibrational transitions of CO perturbed by Ar.The highly sensitive measurements spanned the wavenumber range from 6270 cm^-1 to 6410 cm^-1,which covered both P and R branch of the second overtone band of CO.The spectrometer delivers high-resolution surpassing the Fourier-transform resolution limit determined by interferogram length,successfully removing ringing and broadening effects caused by instrumental line shape function.The instrumental-line-shape-free method and high signal-to-noise ratio in the measurement allowed us to observe collisional effects beyond those described by the Voigt profile.We retrieved collisional line-shape parameters by fitting the speed-dependent Voigt profile and found good agreement with the values given by precise cavity ring-down spectroscopy measurements that used a continuous-wave laser referenced to a stabilized OFC.The results demonstrate that OFC-based cavity-enhanced Fouriertransform spectroscopy is a strong tool for accurate line-shape studies that will be crucial for future spectral databases.

Numerical study of converting beat-note signals of dual-frequency lasers to optical frequency combs by optical injection locking of semiconductor lasers

The optical injection locking of semiconductor lasers to dual-frequency lasers is studied by numerical simulations.The beat-note signals can be effectively transformed to optical frequency combs due to the effective four wave-mixing in the active semiconductor gain medium. The low-noise Gaussian-like pulse can be obtained by locking the relaxation oscillation and compensating the gain asymmetry. The simulations suggest that pulse trains of width below 30 ps and repetition rate in GHz frequency can be generated simply by the optical injection locking of semiconductor lasers. Since the optical injection locking can broaden the spectrum and amplify the optical power simultaneously, it can be a good initial stage for generating optical frequency combs from dual-frequency lasers by multi-stage of spectral broadening in nonlinear waveguides.

Attosecond-Resolution Er:Fiber-Based Optical Frequency Comb

Highly stable frequency-controlled optical frequency combs axe key elements of many applications in time- frequency and optical-metrology domains. In this work, we demonstrate a highly stable frequency-controlled erbium-fiber-based optical frequency comb system. Its repetition rate is phase-stabilized to a continuous-wave laser with both an intra-cavity electro-optic modulator and a piezo-transducer; while the carrier-envelope-offset frequency is phase-locked to a radio-frequency signal generator by controlling the pump power. In-loop relative frequency stabilities of the comb are below 1 ×10-16 at I s, and integrate down to low 10-2o level at 104 s. The corresponding timing uncertainties are 100-200 as over the full measurement range.

Sub-femtometer-resolution absolute spectroscopy with sweeping electro-optic combs

Optical frequency comb with evenly spaced lines over a broad bandwidth has revolutionized the fields of optical metrology and spectroscopy.Here,we propose a fast interleaved dual-comb spectroscopy with sub-femtometer-resolution and absolute frequency,in which two electro-optic frequency combs are swept.Electrically-modulated stabilized laser enables ultrahigh resolution of 0.16 fm(or 20 k Hz in optical frequency)and single-shot measurement in 90 ms.Total 20 million points are recorded spanning 3.2 nm(or 400 GHz)bandwidth,corresponding to a spectral sampling rate of 2.5×10^(8)points/s under Nyquist-limitation.Besides,considering the trade-off between the measurement time and spectral resolution,a fast single-shot measurement is also realized in 1.6 ms with 8 fm(or 1 MHz)resolution.We demonstrate the 25-averaged result with 30.6 d B spectral measurement signal-to-noise ratio(SNR)by reducing the filter bandwidth in demodulation.The results show great prospect for precise measurement with flexibly fast refresh time,high spectral resolution,and high SNR.

Raman lasing and other nonlinear effects based on ultrahigh-Q CaF_(2)optical resonator

The calcium fluoride(CaF_(2))whispering gallery mode crystalline resonator is an excellent platform for nonlinear optical applications because of the decreasing in threshold caused by ultrahigh quality(Q)factor.In this paper,we achieved the observation of Raman lasing,first-order Raman comb,and second-order Raman lasing in a CaF_(2)disk resonator with a diameter of 4.96 mm and an ultrahigh-Q of 8.43×10^(8)at 1550-nm wavelength.We also observed thermal effects in CaF_(2)disk resonator,and the threshold of thermo-optical oscillation is approximately coincident with Raman lasing,since the intracavity power increases rapidly when the power reaches the threshold,and higher input pump power results in longer thermal drift and higher Raman emission power.With a further increase in pump power,the optical frequency combs range is from 1520 nm to 1650 nm,with a wavelength interval of 4×FSR.It is a promising candidate for optical communication,biological environment monitoring,spectral analysis,and microwave signal sources.

Monolithic CEO-stabilization scheme-based frequency comb from an octave-spanning laser

We demonstrate a carder-envelope phase-stabilized octave-spanning oscillator based on the monolithic scheme. A wide output spectrum extending from 480 nm to 1050 nm was generated directly from an all-chirped mirror Ti：sapphire laser. After several improvements, the carder-envelope offset （CEO） beat frequency accessed nearly 60 dB under a reso- lution of 100 kHz. Using a feedback system with 50-kHz bandwidth, we compressed the residual phase noise to 55 mrad （integrated from 1 Hz to 1 MHz） for the stabilized CEO, corresponding to 23-as timing jitter at the central wavelength of 790 nm. This is, to the best of our knowledge, the smallest timing jitter achieved among the existing octave-spanning laser based frequency combs.