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.

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.

Semiconductor-based terahertz frequency combs

Frequency combs[1, 2] consisting of equally-spaced frequencylines can be fully described by two frequencies, i.e., carrieroffset (fCEO) and repetition rate (frep). Once the two frequenciesare stabilized, the frequency comb is well defined. Frequencycombs can be used for various applications, i.e., metrology,spectroscopy, timing, communications, absolute distancemeasurements, and so on, due to their two importantcharacteristics, i.e., stabilized frequency lines and ultra-shortoptical pulses (if the mode-locking is obtained) as shown inFig. 1.

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.

Combs钻速法检测地层压力的原理及应用

Combs法检测地层压力消除了钻井参数及钻头磨钝对钻速的影响,精度高。可以随钻测量和录井评价,不必要建立正常趋势线,作图简化,解释工作量也减少。

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.

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.

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.

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.

Generation of polarization-multiplexed terahertz orbital angular momentum combs via all-silicon metasurfaces

Electromagnetic waves carrying orbital angular momentum(OAM),namely OAM beams,are important in various fields including optics,communications,and quantum information.However,most current schemes can only generate single or several simple OAM modes.Multi-mode OAM beams are rarely seen.This paper proposes a scheme to design metasurfaces that can generate multiple polarization-multiplexed OAM modes with equal intervals and intensities(i.e.,OAM combs)working in the terahertz(THz)range.As a proof of concept,we first design a metasurface to generate a pair of polarization-multiplexed OAM combs with arbitrary mode numbers.Furthermore,another metasurface is proposed to realize a pair of polarization-multiplexed OAM combs with arbitrary locations and intervals in the OAM spectrum.Experimental results agree well with full-wave simulations,verifying a great performance of OAM combs generation.Our method may provide a new solution to designing high-capacity THz devices used in multi-mode communication systems.

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.

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.

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.

Fabrication of the high-Q Si_(3)N_(4) microresonators for soliton microcombs

The microresonator-based soliton microcomb has shown a promising future in many applications.In this work,we report the fabrication of high quality[Q]Si_(3)N_(4)microring resonators for soliton microcomb generation.By developing the fabri-cation process with crack isolation trenches and annealing,we can deposit thick stoichiometric Si3N4 film of 800 nm without cracks in the central area.The highest intrinsic Q of the Si_(3)N_(4)microring obtained in our experiments is about 6×10^(6),corresponding to a propagation loss as low as 0.058 dBm/cm.With such a high Q film,we fabricate microrings with the anomalous dispersion and demonstrate the generation of soliton microcombs with 100 mW on-chip pump power,with an optical parametric oscillation threshold of only 13.4 mW.Our Si_(3)N_(4)integrated chip provides an ideal platform for researches and applications of nonlinear photonics and integrated photonics.

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.

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.

Self-mode-locking optoelectronic oscillator with ultrashort time delay

The optoelectronic oscillator(OEO)is a typical time-delay system with rich nonlinear dynamical characteristics.Most of the previous research on OEOs has been focused on analyzing the properties of OEOs with a long time delay,which makes it difficult to realize mode locking without additional phaselocking mechanisms.We have achieved,for the first time to our knowledge,a self-mode-locking OEO and generated stable microwave frequency combs by analyzing the characteristics of OEOs with an ultrashort time scale.In the experiment,the self-mode-locking OEOs with fundamental mode,second-order harmonic,and sixth-order harmonic were realized by adjusting the system parameters,all of which produced uniform square wave signals with tunable duty cycles,steep rising and falling edges,and periods of less than 20 ns.The self-fundamental-mode-locking OEOs with different time delays were also implemented and experimentally realized.Furthermore,the experiment revealed the self-hybrid mode-locking OEO,which is the coexistence and synchronization of the three measured self-locking modes in one OEO cavity,demonstrating the complex nonlinear dynamical behaviors of the OEO system and enabling the generation of periodic nonuniform hybrid square wave signals.The realization of the self-mode-locking OEO and the generation of flexible and stable square wave signals at ultrashort time scales enrich the study of OEO nonlinear dynamics in the realm of complex microwave waveform generation,offering promising applications in areas such as atomic clocks,radars,communications,and optoelectronic neural networks.