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.

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.

High-efficiency and flexible photonic microwave harmonic down-converter based on self-oscillation optical frequency combs

Photonic microwave harmonic down-converters (PMHDCs) based on self-oscillation optical frequency combs (OFCs) are interesting because of their broad bandwidth compared with plain optoelectronic oscillators. In this paper, a high-efficiency and flexible PMHDC is proposed and demonstrated. The properties of the OFC, such as the carrier-to-noise ratio (CNR),bandwidth and free spectral range (FSR), and the influence of optical injection, are investigated. The broadband OFC provides a frequency tunable and high-quality local oscillation (LO), which guarantees flexible down-conversion for the radio frequency (RF) signal. The sideband selective amplification (SSA) effect not only improves the conversion efficiency but also promotes single-sideband modulation. The conversion range can reach 100 GHz. The 12–40 GHz RF signal can be downconverted to intermediate frequency (IF) signals with a high conversion efficiency of 14.9 dB. The fixed 40-GHz RF signal is flexibly down-converted to an IF signal with the frequency from 55.4 to 2129.4 MHz. The phase noise of an IF signal at a frequency offset of 10 kHz is the same as that of the input RF signal. The PMHDC shows great performance and will find applications in radio-over-fiber (RoF) networks, electronic warfare receivers, avionics, and wireless communication systems.

Magnonic frequency combs based on the resonantly enhanced magnetostrictive effect

A magnonic counterpart to optical frequency combs is vital for high-precision magnonic frequency metrology and spectroscopy.Here,we present an efficient mechanism for the generation of robust magnonic frequency combs in a yttrium iron garnet(YIG)sphere via magnetostrictive effects.We show that magnonic and vibrational dynamics in the ferrimagnetic sphere can be substantively modified in the presence of magnetostrictive effects,which results in degenerate and non-degenerate magnonic four-wave mixing and frequency conversion.Particularly,resonantly enhanced magnetostrictive effects can induce phonon laser action above a threshold,which leads to significant magnonic nonlinearity and enables a potentially practical scheme for the generation of robust magnonic frequency combs.Numerical calculations of both magnonic and phononic dynamics show excellent agreement with this theory.These results deepen our understanding of magnetostrictive interaction,open a novel and efficient pathway to realize magnonic frequency conversion and mixing in a magnonic device,and provide a sensitive tool for precision measurement.

Generation of dual and quad‑optical frequency combs in the injected radiation free mode‑locked frequency‑shifted feedback laser

The results of an optoelectronic system—frequency-shifted feedback(FSF)laser experimental examination are presented.The considered FSF laser is seeded only with optical amplifer spontaneous emission(ASE)and operates in the mode-locked regime,whereby the output radiation is sequence of short pulses with a repetition rate determined by the delay time in its optical feedback circuit.In the frequency domain,the spectrum of such a pulse sequence is an optical frequency comb(OFC).These OFCs we call initial.We consider the possibility of tunable acousto-optic(AO)dual and quad-comb frequency spacing downconversion in the FSF laser seeded with ASE and operating in the mode-locked regime.The examined system applies a single frequency shifting loop with single AO tunable flter as the frequency shifter that is fed with several radio frequency signals simultaneously.The initial OFCs with frequency spacing of about 6.5 MHz may be obtained in the wide spectral range and their width,envelope shape and position in the optical spectrum may be tuned.The dual-combs are obtained with a pair of initial OFCs aroused by two various ultrasound waves in the acousto-optic tunable flter(AOTF).The dual-combs frequency spacing is determined by the frequency diference of the signals applied to the AOTF piezoelectric transducer and can be tuned simply.The quad-combs are obtained with three initial OFCs,forming a pair of dual-combs,appearing when three ultrasound frequencies feed the AOTF transducer.The quad-combs frequency spacing is defned by the diference between the frequency spacing of dual-combs.Quad-combs with more than 5000 spectral lines and tunable frequency spacing are observed.The successive frequency downconversion gives the possibility to reduce the OFC frequency spacing form several MHz for initial OFC to tens of kHz for quad-combs.

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.

Numerical simulation and temporal characterization of dual-pumped microringresonator-based optical frequency combs

Dual-pumped microring-resonator-based optical frequency combs(OFCs) and their temporal characteristics are numerically investigated and experimentally explored. The calculation results obtained by solving the driven and damped nonlinear Schr?dinger equation indicate that an ultralow coupled pump power is required to excite the primary comb modes through a non-degenerate four-wave-mixing(FWM) process and, when the pump power is boosted, both the comb mode intensities and spectral bandwidths increase. At low pump powers, the field intensity profile exhibits a cosine variation manner with frequency equal to the separation of the two pumps, while a roll Turing pattern is formed resulting from the increased comb mode intensities and spectral bandwidths at high pump powers. Meanwhile, we found that the power difference between the two pump fields can be transferred to the newly generated comb modes, which are located on both sides of the pump modes, through a cascaded FWM process. Experimentally, the dual-pumped OFCs were realized by coupling two self-oscillating pump fields into a microring resonator. The numerically calculated comb spectrum is verified by generating an OFC with 2.0 THz mode spacing over 160 nm bandwidth. In addition, the formation of a roll Turing pattern at high pump powers is inferred from the measured autocorrelation trace of a 10 free spectral range(FSR) OFC. The experimental observations accord well with the numerical predictions. Due to their large and tunable mode spacing, robustness,and flexibility, the proposed dual-pumped OFCs could find potential applications in a wide range of fields,including arbitrary optical waveform generation, high-capacity optical communications, and signal-processing systems.

Kerr frequency combs in large-size,ultra-high-Q toroid microcavities with low repetition rates [Invited]

By overcoming fabrication limitations, we have successfully fabricated silica toroid microcavities with both large diameter(of 1.88 mm) and ultra-high-Q factor(of 3.3 × 10~8) for the first time, to the best of our knowledge. By employing these resonators, we have further demonstrated low-threshold Kerr frequency combs on a silicon chip,which allow us to obtain a repetition rate as low as 36 GHz. Such a low repetition rate frequency comb can now bedirectly measured through a commercialized optical-electronic detector.

Robust generation of frequency combs in a microresonator with strong and narrowband loss

Octave-spanning frequency comb generation in microresonators is promising, but strong spectral losses caused by material absorption and mode coupling between two polarizations or mode families can be detrimental. We examine the impact of the spectral loss and propose robust comb generation with a loss of even 300 dB/cm.Cavity nonlinear dynamics show that a phase change associated with spectral losses can facilitate phase matching and Kerr comb generation. Given this unique capability, we propose a novel architecture of on-chip spectroscopy systems.

Fiber-delay-line-referenced optical frequency combs:three stabilization schemes

We demonstrate the stabilization of an optical frequency comb(OFC) using a segment of fiber delay line as a reference. A mode-locked Er-doped fiber laser is phase locked to a kilometer-long fiber delay line using three different schemes. The short-term stability of the comb modes in the OFC stabilized by these schemes is obviously enhanced, down to the 10;level at millisecond average time. Among these three schemes, phase locking two bunches of comb modes in the OFC to the same fiber delay line exhibits the lowest residual phase noise. Fiber-delay-line-referenced OFCs can provide reliable laser sources in precise metrology owing to the advances of low cost, compactness, and high integration.

Silicon nitride-based Kerr frequency combs and applications in metrology

Kerr frequency combs have been attracting significant interest due to their rich physics and broad applications in metrology,microwave photonics,and telecommunications.In this review,we first introduce the fundamental physics,master equations,simulation methods,and dynamic process of Kerr frequency combs.We then analyze the most promising material platform for realizing Kerr frequency combs—silicon nitride on insulator(SNOI)in comparison with other material platforms.Moreover,we discuss the fabrication methods,process optimization as well as tuning and measurement schemes of SNOI-based Kerr frequency combs.Furthermore,we highlight several emerging applications of Kerr frequency combs in metrology,including spectroscopy,ranging,and timing.Finally,we summarize this review and envision the future development of chip-scale Kerr frequency combs from the viewpoint of theory,material platforms,and tuning methods.

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.

Stretching the spectra of Kerr frequency combs with self-adaptive boundary silicon waveguides

Dispersion engineering of optical waveguides is among the most important steps in enabling the realization of Kerr optical frequency combs.A recurring problem is the limited bandwidth in which the nonlinear phase matching condition is satisfied,due to the dispersion of the waveguide.This limitation is particularly stringent in high-index-contrast technologies such as silicon-on-insulator.We propose a general approach to stretch the bandwidth of Kerr frequency combs based on subwavelength engineering of single-mode waveguides with self-adaptive boundaries.The wideband flattened dispersion operation comes from the particular property of the waveguide optical mode that automatically self-adapts its spatial profile at different wavelengths to slightly different effective spatial spans determined by its effective index values.This flattened dispersion relies on the squeezing of small normal-dispersion regions between two anomalous spectral zones,which enables it to achieve two Cherenkov radiation points and substantially broaden the comb,achieving a bandwidth between 2.2 and 3.4μm wavelength.This strategy opens up a design space for trimming the spectra of Kerr frequency combs using high-index-contrast platforms and can provide benefits to various nonlinear applications in which the manipulation of energy spacing and phase matching are pivotal.

On-chip multiphoton Greenberger-Horne Zeilinger state based on integrated frequency combs

One of the most important multipartite entangled states,Greenberger-Horne-Zeilinger state(GHZ),serves as a fundamental resource for quantum foundat ion test,quantum communication and quantum computation.To increase the number of entangled particles,significant experimental efforts should been invested due to the complexity of optical setup and the difficulty in maintaining the coherence condition for high-fidelity GHZ state.Here,we propose an ultra-integrated scalable on-chip GHZ state generation scheme based on frequency combs.By designing several microrings pumped by different lasers,multiple partially overlapped quantum frequency combs are generated to supply as the basis for on-chip polarization-encoded GHZ state with each qubit occupying a certain spectral mode.Both even and odd numbers of GHZ states can be engineered with constant small number of integrated components and easily scaled up on the same chip by only adjusting one of the pumnp wavelengths.In addition,we give the on-chip design of projection measurement for characterizing GHZ states and show the reconfigurability of the state.Our proposal is rather simple and feasible within the existing fabrication technologies and we believe it will boost the development of multiphoton technologies.

Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains

Frequency-comb emission via high-order harmonic generation(HHG)provides an alternative method for the coherent vacuum ultraviolet(VUV)and extreme ultraviolet(XUV)radiation at ultrahigh repetition rates.In particular,the temporal and spectral features of the HHG were shown to carry profound insight into frequency-comb emission dynamics.Here we present an ab initio investigation of the temporal and spectral coherence of the frequency comb emitted in HHG of He atom driven by few-cycle pulse trains.We find that the emission of frequency combs features a destructive and constructive coherences caused by the phase interference of HHG,leading to suppression and enhancement of frequency-comb emission.The results reveal intriguing and substantially different nonlinear optical response behaviors for frequency-comb emission via HHG.The dynamical origin of frequency-comb emission is clarified by analyzing the phase coherence in HHG processes in detail.Our results provide fresh insight into the experimental realization of selective enhancement of frequency comb in the VUV–XUV regimes.

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.

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.

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.

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.