Experimental study on phase noise of terahertz quantum cascade laser frequency comb and dual-comb sources

Frequency combs with equally spaced frequency lines show great potentials for applications in spectroscopy,imag-ing,communications,and so on.In the terahertz frequency region,the quantum cascade laser(QCL)is an ideal radiation source for frequency comb and dual-comb operation.The systematic evaluation of phase noise characteristics of terahertz QCL frequency comb and dual-comb sources is of great importance for high precision measurements.In this work,we present detailed measurements and analysis of the phase noise characteristics of terahertz QCL frequency comb and dual-comb sources emitting around 4.2 THz with repetition frequencies of~6.2 GHz.The measurement results for the current noise of the direct current(DC)sources(that are used to electrically pump the terahertz QCLs)indicate that at 100 Hz,the current noise for DC-1 and DC-2 is 0.3895 and 0.0982 nA/Hz1/2,respectively.Such levels of current noise can be safely disregarded.The phase noise of radio frequency(RF)generators(that are employed for injection locking and phase locking),intermode beatnotes,and dual-comb signals with and without phase-locked loop(PLL)are all measured and compared.The experimental results show that in the free-running mode,the phase noise of the intermode beatnote signals is always lower than that of the dual-comb sig-nals across all frequencies.Additionally,the phase noise induced by the RF generators is negligible.By employing the phase lock-ing technique,the phase noise of the intermode beatnote and dual-comb signals in the low offset frequency band can be signifi-cantly suppressed.At an offset frequency of 100 Hz,the measured phase noise values of the dual-comb line without and with phase locking are 15.026 and-64.801 dBc/Hz,respectively.

Frequency-modulated continuous-wave multiplexed gas sensingbased on optical frequency comb calibration

Laser absorption spectroscopy has proven to be an effective approach for gas sensing, which plays an important rolein the fields of military, industry, medicine and basic research. This paper presents a multiplexed gas sensing system basedon optical frequency comb (OFC) calibrated frequency-modulated continuous-wave (FMCW) tuning nonlinearity. Thesystem can be used for multi-parameter synchronous measurement of gas absorption spectrum and multiplexed opticalpath. Multi-channel parallel detection is realized by combining wavelength division multiplexing (WDM) and frequencydivision multiplexing (FDM) techniques. By introducing nonlinear optical crystals, broadband spectrum detection is simultaneouslyachieved over a bandwidth of hundreds of nanometers. An OFC with ultra-high frequency stability is used asthe frequency calibration source, which guarantees the measurement accuracy. The test samples involve H13C14N, C_(2)H_(2)and Rb vapor cells of varying densities and 5 parallel measurement experiments are designed. The results show that themeasurement accuracies of spectral absorption line and the optical path are 150 MHz and 20 m, respectively. The schemeoffers the advantages of multiplexed, multi-parameter, wide spectrum and high resolution detection, which can realize theidentification of multi-gas components and the high-precision inversion of absorption lines under different environments.The proposed sensor demonstrates great potential in the field of high-resolution absorption spectrum measurement for gassensing applications.

Mid-infrared Optical Frequency Comb-based Fourier Transform Spectrometer for Broadband Molecular Spectroscopy

Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of precision spectroscopy and trace gas detection.Here,we report the development of a mid-infrared Fourier transform spectrometer based on an optical frequency comb combined with a Herriott-type multipass cell.Using this instrument,the broadband absorption spectra of several important molecules,including methane,acetylene,water molecules and nitrous oxide,are measured by near real-time data acquisition in the 2800-3500 cm^(-1)spectral region.The achieved minimum detectable absorption of the instrument is 4.4×10^(-8)cm^(-1)·Hz^(-1/2)per spectral element.Broadband spectra of H_(2)0 are fited using the Voigt profile multispectral fitting technique and the consistency of the concentration inversion is 1%.Our system also enables precise spectroscopic measurements,and it allows the determination of the spectral line positions and upper state constants of N_(2)O in the(0002)-(1000)band,with results in good agreement with those reported by Toth[Appl.Opt.30,5289(1991)].

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.

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.

A 23.75-GHz frequency comb with two low-finesse filtering cavities in series for high resolution spectroscopy

A laser frequency comb with several tens GHz level is demonstrated,based on a Yb-doped femtosecond fiber laser and two low-finesse Fabry-Perot cavities（FPCs） in series.The original 250-MHz mode-line-spacing of the source comb is filtered to 4.75 GHz and 23.75 GHz,respectively.According to the multi-beam interferences theory of FPC,the side-mode suppression rate of FPC schemes is in good agreement with our own theoretical results from 27 dB of a single FPC to43 dB of paired FPCs.To maintain long-term stable operation and determine the absolute frequency mode number in the23.75-GHz comb,the Pound-Drever-Hall（PDH） locking technology is utilized.Such stable tens GHz frequency combs have important applications in calibrating astronomical spectrographs with high resolution.

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.

Tunable and broadband microwave frequency combs based on a semiconductor laser with incoherent optical feedback

Based on a semiconductor laser （SL） with incoherent optical feedback, a novel all-optical scheme for generating tunable and broadband microwave frequency combs （MFCs） is proposed and investigated numerically. The results show that, under suitable operation parameters, the SL with incoherent optical feedback can be driven to operate at a regular pulsing state, and the generated MFCs have bandwidths broader than 40 GHz within a 10 dB amplitude variation. For a fixed bias current, the line spacing （or repetition frequency） of the MFCs can be easily tuned by varying the feedback delay time and the feedback strength, and the tuning range of the line spacing increases with the increase in the bias current. The linewidth of the MFCs is sensitive to the variation of the feedback delay time and the feedback strength, and a linewidth of tens of KHz can be achieved through finely adjusting the feedback delay time and the feedback strength. In addition, mappings of amplitude variation, repetition frequency, and linewidth of MFCs in the parameter space of the feedback delay time and the feedback strength are presented.

Recent progress in integrated electro-optic frequency comb generation

Optical frequency combs have emerged as an important tool enabling diverse applications from test-and-measurement,including spectroscopy,metrology,precision distance measurement,sensing,as well as optical and microwave waveform synthesis,signal processing,and communications.Several techniques exist to generate optical frequency combs,such as mode-locked lasers,Kerr micro-resonators,and electro-optic modulation.Important characteristics of optical frequency combs include the number of comb lines,their spacing,spectral shape and/or flatness,and intensity noise.While mode-locked lasers and Kerr micro-resonators can be used to obtain a large number of comb lines compared to electro-optic modulation,the latter provides increased flexibility in tuning the comb spacing.For some applications in optical communications and microwave photonics,a high degree of integration may be more desirable over a very large number of comb lines.In this paper,we review recent progress on integrated electro-optic frequency comb generators,including those based on indium phosphide,lithium niobate,and silicon photonics.

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.

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.

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.

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.

Broadband Frequency Comb for Calibration of Astronomical Spectrographs

We present our state-of-the-art version of a frequency comb for calibration of astronomical spectrographs. The mode spacing of the frequency comb can be designed to match the resolution of a spectrograph. Combined with its excellent accuracy and stability, the spectral coverage of more than 70% of the whole visible spectrum range makes the frequency comb an ideal calibration source. In addition, the new version introduces the automatic start-up function that brings convenience to the astronomers.

Relative phase locking of a terahertz laser system configured with a frequency comb and a single-mode laser

Stable operation is one of the most important requirements for a laser source for high-precision applications.Many efforts have been made to improve the stability of lasers by employing various techniques,e.g.,electrical and/or optical injection and phase locking.However,these techniques normally involve complex experimental facilities.Therefore,an easy implementation of the stability evaluation of a laser is still challenging,especially for lasers emitting in the terahertz(THz)frequency range because the broadband photodetectors and mature locking techniques are limited.In this work,we propose a simple method,i.e.,relative phase locking,to quickly evaluate the stability of THz lasers without a need of a THz local oscillator.The THz laser system consists of a THz quantum cascade laser(QCL)frequency comb and a single-mode QCL.Using the single-mode laser as a fast detector,heterodyne signals resulting from the beating between the singlemode laser and the comb laser are obtained.One of the heterodyne beating signals is selected and sent to a phase-locked loop(PLL)for implementing the relative phase locking.Two kinds of locks are performed by feeding the output error signal of the PLL,either to the comb laser or to the single-mode laser.By analyzing the current change and the corresponding frequency change of the PLL-controlled QCL in each phase-locking condition,we,in principle,are able to experimentally compare the stability of the emission frequency of the single-mode QCL(f s)and the carrier envelope offset frequency(f CEO)of the QCL comb.The experimental results reveal that the QCL comb with the repetition frequency injection locked demonstrates much higher stability than the single-mode laser.The work provides a simple heterodyne scheme for understanding the stability of THz lasers,which paves the way for the further locking of the lasers and their high-precision applications in the THz frequency range.

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.

High-Resolution Rb Two-Photon Transition Spectroscopy by a Femtosecond Frequency Comb via Pulses Control

We experimentally observe the high resolution direct frequency comb spectroscopy using counter-propagating broadband femtosecond pulses on two-photon transitions in room-temperature ^87 Rb atoms. The Doppler broad- ened background is effectively eliminated with the pulse shaping method and the spectrum modulation technique. The combination of the pulse shaping method and the spectra modulation technique provides a potential approachto reduce background of at least 99%.

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.

Pump-induced carrier envelope offset frequency dynamics and stabilization of an Yb-doped fiber frequency comb

In this paper, we demonstrate a carrier envelope phase-stabilized Yb-doped fiber frequency comb seeding by a nonlinear-polarization-evolution（NPE） mode-locked laser at a repetition rate of 60 MHz with a pulse duration of 191 fs.The pump-induced carrier envelope offset frequency（ f0） nonlinear tuning is discussed and further explained by the spectrum shift of the laser pulse. Through the environmental noise suppression, the drift of the free-running f0 is reduced down to less than 3 MHz within an hour. By feedback control on the pump power with a self-made phase-lock loop（PLL）electronics the carrier envelope offset frequency is well phase-locked with a frequency jitter of 85 m Hz within an hour.

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.