Frequency Comb Research Articles

Nonlinear response of very high frequency contour mode resonators

We explore the source of nonlinearities in Aluminum Nitride (AlN) Contour Mode Resonators (CMRs) operating in the Very High Frequency (VHF) range. We demonstrate that the red-shift of the resonance frequency found in VHF CMRs when the input RF power increases is due to nonlinear stiffness appearing from self-heating, and variable damping due to geometric nonlinearities. Moreover, we find a linear relationship between the variable damping coefficient and the resonator quality factor (Q). Such nonlinear mechanisms are modeled using a spring-mass-damper physical system and, in the electrical domain, a modified Butterworth-Van Dyke (MBVD) circuit where the nonlinear stiffness and variable damping are captured by a charge-dependent motional capacitor and a charge-dependent motional resistor, respectively. Detailed guidelines are provided to accurately analyze nonlinear CMRs using full-wave numerical simulations based on a finite-element method. Such simulations allow us to isolate the influence of each independent nonlinear mechanism and establish a relation between variable damping and geometric nonlinearities. Circuit and full-wave numerical simulations are in good agreement with measured data from fabricated 225 MHz CMRs exhibiting different Q. Finally, we exploit nonlinearities in high-Q CMRs to generate frequency combs at the MHz range opening the door to new exciting applications in telecommunication and sensing.

Design and implementation of a new apparatus for astrochemistry: Kinetic measurements of the CH + OCS reaction and frequency comb spectroscopy in a cold uniform supersonic flow.

We present the development of a new astrochemical research tool, HILTRAC, the Highly Instrumented Low Temperature ReAction Chamber. The instrument is based on a pulsed form of the CRESU (Cinétique de Réaction en Écoulement Supersonique Uniforme, meaning reaction kinetics in a uniform supersonic flow) apparatus, with the aim of collecting kinetics and spectroscopic information on gas phase chemical reactions important in interstellar space or planetary atmospheres. We discuss the apparatus design and its flexibility, the implementation of pulsed laser photolysis followed by laser induced fluorescence, and the first implementation of direct infrared frequency comb spectroscopy (DFCS) coupled to the uniform supersonic flow. Achievable flow temperatures range from 32(3) to 111(9) K, characterizing a total of five Laval nozzles for use with N2 and Ar buffer gases by impact pressure measurements. These results were further validated using LIF and direct frequency comb spectroscopy measurements of the CH radical and OCS, respectively. Spectroscopic constants and linelists for OCS are reported for the 1001 band near 2890-2940cm-1 for both OC32S and OC34S, measured using DFCS. Additional peaks in the spectrum are tentatively assigned to the OCS-Ar complex. The first reaction rate coefficients for the CH + OCS reaction measured between 32(3) and 58(5) K are reported. The reaction rate coefficient at 32(3) K was measured to be 3.9(4) × 10-10cm3molecule-1s-1 and the reaction was found to exhibit no observable temperature dependence over this low temperature range.

Two-octave frequency combs from an all-silica-fiber implementation

Mid-infrared frequency-comb spectroscopy enables measurement of molecules at megahertz spectral resolution, sub-hertz frequency accuracy, and microsecond acquisition speed. However, the widespread adoption of this technique has been hindered by the complexity and alignment sensitivity of mid-infrared frequency-comb sources. Leveraging the underexplored mid-infrared window of silica fibers presents a promising approach to address these challenges. In this study, we present the first, to the best of our knowledge, experimental demonstration and quantitative numerical description of mid-infrared frequency-comb generation in silica fibers. Our all-silica-fiber frequency comb spans over two octaves (0.8 μm to 3.4 μm) with a power output of 100 mW in the mid-infrared region. The amplified quantum noise is suppressed using four-cycle (25 fs) driving pulses, with the carrier-envelope offset frequency exhibiting a signal-to-noise ratio of 40 dB and a free-running bandwidth of 90 kHz. Our developed model provides quantitative guidelines for mid-infrared frequency-comb generation in silica fibers, enabling all-fiber frequency-comb spectroscopy in diverse fields such as organic synthesis, pharmacokinetics processes, and environmental monitoring.

Giant enhancement of nonlinear harmonics of an optical-tweezer phonon laser

Phonon lasers, as mechanical analogues of optical lasers, are unique tools for not only fundamental studies of the emerging field of phononics but also diverse applications such as deep-ocean monitoring, force sensing, and biomedical ultrasonics. Recently, nonlinear phonon-lasing effects were observed in an opto-levitated micro-sphere, i.e., the spontaneous emerging of weak signals of high-order phonon harmonics in the phonon lasing regime. However, both the strengths and the quality factors of the emerging phonon harmonics are very poor, thus severely hindering their potential applications in making and utilizing nonlinear phonon-laser devices. Here we show that, by applying a single-colour electronic injection to this levitated system, giant enhancement can be achieved for all higher-order phonon harmonics, with more than 3 orders enhanced brightness and 5 orders narrowed linewidth. Such an electronically-enhanced phonon laser is also far more stable, with frequency stability extended from a dozen of minutes to over 1 h. More importantly, higher-order phonon correlations, as an essential lasing feature, are confirmed to be enhanced by the electronic injection as well, which as far as we know, has not been reported in previous works using this technique. This work, providing much stronger and better-quality signals of coherent phonon harmonics, is a key step towards controlling and utilizing nonlinear phonon lasers for applications such as phonon frequency combs, broadband phonon sensors, and ultrasonic bio-medical diagnosis.

Full-Scale Readout Electronics for the ECHo Experiment

Recent advances in the development of cryogenic particle detectors such as magnetic microcalorimeters allow the fabrication of sensor arrays with an increasing number of pixels. Since these detectors must be operated at the lowest temperatures, the readout of large detector arrays is still quite challenging. This is especially true for the ECHo experiment, which presently aims to simultaneously run 6,000 two pixel detectors to investigate the electron neutrino mass. For this reason, we developed a readout system based on a microwave SQUID multiplexer (μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}MUX) that is operated by a custom software-defined radio (SDR) at room-temperature. The SDR readout electronics consist of three distinct hardware units: a data processing board with a Xilinx ZynqUS+ MPSoC; a converter board that features DACs, ADCs, and a coherent clock distribution network; and a radio frequency front-end board to translate the signals between the baseband and the microwave domains. Here, we describe the characteristics of the full-scale SDR system. First, the generated frequency comb for driving the μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}MUX was evaluated. Subsequently, by operating the SDR in direct loopback, the crosstalk of the individual channels after frequency demultiplexing was investigated. Finally, the system was used with a 16-channel μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}MUX to evaluate the linearity of the SDR, and the noise contributed to the overall readout setup.

Generation of Soliton Frequency Combs in NEMS.

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

12.1 terabit/second data center interconnects using O-band coherent transmission with QD-MLL frequency combs

Most current Data Center Interconnects (DCI) use intensity modulation direct detection (IMDD) configurations due to their low complexity and cost. However, significant scaling challenges allow coherent solutions to become contenders in these short reach applications. We present an O-band coherent optical fiber transmission system based on Quantum Dot—Mode Locked Lasers (QD-MLLs) using two independent free-running comb lasers, one each for the carrier and the Local Oscillator (LO). Using a comb-to-comb configuration, we demonstrate a 10 km single mode fiber, O-band, coherent, heterodyne, 12.1 Tbps system operating at 0.47 Tbps/λ using 26 λs. We used fewer comb lines (26 λs), faster symbol rate (56 GBaud) and higher constellation cardinality (32 QAM) relative to the highest capacity C-band systems reported to date. Through design, analysis, and experimentation, we quantify the optimum comb line spacing for this use case. We compare potential configurations for increasing data center interconnect capacities whilst reducing power consumption, complexity, and cost.

A Microwave Photonic Channelized Receiver Based on Polarization-Division Multiplexing of Optical Signals

Aimed at the problems of optical frequency combs, such as their large number of comb lines, their high flatness, and their lack of ease in generating, as well as the fact that the channelization efficiency of the scheme based on optical frequency combs is low, we proposed a microwave photonic channelization receiver based on signal polarization multiplexing. Using two-line local optical frequency combs with different frequencies to demodulate the RF signal in the orthogonal polarization state, 16 sub-channels with a bandwidth of 1 GHz can be received simultaneously. The experimental results show that the image rejection ratio can reach 28 dB, and the third-order spurious-free dynamic range of the system can reach 96.8 dB·Hz2∕3. This scheme has the advantages of a large number of sub-channels and a high channelization efficiency; it has great application potential in broadband wireless communication, radar, and electronic warfare systems.

165 MHz highly stable femtosecond Er:ZBLAN fiber laser operating at 2.8 µm.

Three-micrometer mid-infrared (MIR) femtosecond pulse sources with a high repetition rate (HRR) have potential applications in a number of fields such as biological imaging, optical frequency combs, and gas detection. In this paper, by optimizing the fiber length and the cavity structure, we demonstrated a highly stable, self-starting mode-locked fluoride fiber laser (MLFFL) with a fundamental repetition rate of ∼165 MHz and a signal-to-noise ratio (SNR) of 90 dB. As far as we know, this stands as the highest fundamental repetition rate ever acquired directly from an ultrafast MLFFL in the >2.5 µm MIR region. Stable 352-fs pulses at 2795 nm with an average output power of 392 mW and a low integrated relative intensity noise (RIN) of 0.018% [10 Hz, 10 MHz] were generated. The root mean square (RMS) power fluctuation is 0.17% over 2 h, which indicates excellent oscillator stability. This high-performance laser offers a practicable scheme both for scaling the repetition frequency in MIR MLFFLs and high-precision ultrafast applications at longer wavelengths.

Ultraviolet astronomical spectrograph calibration with laser frequency combs from nanophotonic lithium niobate waveguides

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants on cosmological scales. Laser frequency combs can provide the required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this challenging. Here, we demonstrate astronomical spectrograph calibration with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and could contribute to unlock the full potential of next-generation ground-based and future space-based instruments.

Octave-spanning Kerr soliton frequency combs in dispersion- and dissipation-engineered lithium niobate microresonators

Dissipative Kerr solitons from optical microresonators, commonly referred to as soliton microcombs, have been developed for a broad range of applications, including precision measurement, optical frequency synthesis, and ultra-stable microwave and millimeter wave generation, all on a chip. An important goal for microcombs is self-referencing, which requires octave-spanning bandwidths to detect and stabilize the comb carrier envelope offset frequency. Further, detection and locking of the comb spacings are often achieved using frequency division by electro-optic modulation. The thin-film lithium niobate photonic platform, with its low loss, strong second- and third-order nonlinearities, as well as large Pockels effect, is ideally suited for these tasks. However, octave-spanning soliton microcombs are challenging to demonstrate on this platform, largely complicated by strong Raman effects hindering reliable fabrication of soliton devices. Here, we demonstrate entirely connected and octave-spanning soliton microcombs on thin-film lithium niobate. With appropriate control over microresonator free spectral range and dissipation spectrum, we show that soliton-inhibiting Raman effects are suppressed, and soliton devices are fabricated with near-unity yield. Our work offers an unambiguous method for soliton generation on strongly Raman-active materials. Further, it anticipates monolithically integrated, self-referenced frequency standards in conjunction with established technologies, such as periodically poled waveguides and electro-optic modulators, on thin-film lithium niobate.

Frequency pushing and pulling in semiconductor lasers subject to optical frequency comb injection

We theoretically investigate the frequency shift of a free-running semiconductor laser when optically injected by an optical frequency comb. By numerical integration of the laser rate equations, we have identified two types of frequency shifts, frequency pulling, and frequency pushing. The free-running slave laser seems to switch between pulling and pushing in a regular manner. We have systematically determined the dependence of these shifts on comb parameters, including comb spacing and number of lines. We have found that the occurring frequency pushing seems to be almost independent of comb signals and comb spacing, while in contrast, the frequency pulling shows weak dependence on comb signals but largely affected by comb spacing. We have also shown that carrier density dynamic is the origine of these phenomena.

Polarized Frequency Combs in a Mode-Locked VECSEL

Polarized Frequency Combs in a Mode-Locked VECSEL

Hybrid Patterns and Solitonic Frequency Combs in Non-Hermitian Kerr Cavities.

We unveil a new scenario for the formation of dissipative localized structures in nonlinear systems. Commonly, the formation of such structures arises from the connection of a homogeneous steady state with either another homogeneous solution or a pattern. Both scenarios, typically found in cavities with normal and anomalous dispersion, respectively, exhibit unique fingerprints and particular features that characterize their behavior. However, we show that the introduction of a periodic non-Hermitian modulation in Kerr cavities hybridizes the two established soliton formation mechanisms, embodying the particular fingerprints of both. In the resulting novel scenario, the stationary states acquire a dual behavior, playing the role that was unambiguously attributed to either homogeneous states or patterns. These fundamental findings have profound practical implications for frequency comb generation, introducing unprecedented reversible mechanisms for real-time manipulation.

Frequency comb generation from the ultraviolet to mid-infrared region based on a three-stage cascaded PPLN chain

Optical frequency combs (OFCs) have enabled significant opportunities for high-precision frequency metrology and high-resolution broadband spectroscopy. Although nonlinear photonics chips have the capacity of frequency expansion for OFCs, most of them can only access the limited bandwidths in the partial infrared region, and it is still hard to satisfy many measurement applications in the ultraviolet-to-visible region. Here, we demonstrate a compact broadband OFC scheme via the combination of three χ(2) nonlinearities in a three-stage periodically poled lithium niobate (PPLN) chain. With a supercontinuum spectrum OFC delivered into the PPLN chain, the intra-pulse diffidence frequency generation, optical parametric amplification, and high-order harmonic generation were carried out in sequence. It is crucial that the harmonics of the 1st–10th orders are simultaneously obtained with an offset-free OFC spectrum from 0.35 to 4.0 μm. In view of the great potential for integration and spectral expansion, this wideband frequency comb source will open a new insight for the valuable applications of two-dimensional material analysis, biofluorescence microscopy, and nonlinear amplitude-phase metrology.

Optical frequency comb significantly spanned to broadband by an optomechanical resonance

An optical frequency comb, as a spectrum made of discrete and equally spaced spectral lines, is a light source with essential applications in modern technology. Cavity optomechanical systems were found to be a feasible candidate for realizing an on-chip frequency comb with low repetition rate. However, it was difficult to increase the comb line numbers of this type of frequency combs because the mechanical oscillation amplitude of such a system, which determines the frequency comb bandwidth, cannot quickly increase with pump laser power. Here, we develop a new approach to generate a broadband optomechanical frequency comb by employing a different mechanism to enhance the mechanical oscillation. Two pump tones with their frequency difference matching the mechanical frequency will drive the system into a self-organized nonlinear resonance and thus tremendously transfer the energy to the mechanical resonator. As a result, more than 10,000 or even more comb lines become available under the pump laser power of the order of milliwatts. A unique feature of the self-organized resonance is the mechanical frequency locking so that, within a certain range of the frequency difference between two drive tones, the distance between comb teeth can be locked by the two drive tones and becomes independent of any change of pump power. This property guarantees a stable repetition rate of the generated frequency comb.

Quantum dot fourth-harmonic colliding pulse mode-locked laser for high-power optical comb generation

Quantum-dot mode-locked lasers have advantages such as high temperature stability, large optical bandwidth, and low power consumption, which make them ideal optical comb sources, especially for wavelength-division multiplexing (WDM) telecommunications, and optical I/O applications. In this work, we demonstrate an O-band quantum dot colliding pulse mode-locked laser (QD-CPML) to generate optical frequency combs with 200 GHz spacing with maximum channels of 12 within 3 dB optical bandwidth. To achieve the high output power of individual comb lines, four channel conditions are implemented at central wavelength of 1310 nm for WDM transmission experiments. Each channel exhibits more than 10 dBm output power with 200 Gb/s PAM-4 and 270 Gb/s PAM-8 modulation capability via thin-film LiNbO3 Mach–Zehnder interferometer modulator without the requirement of any optical amplifications. This high-order QD-CPML is an ideal comb source for power-efficient optical interconnects and large bandwidth optical data transmission.

Picosecond Ultrasonics in Magnetic Topological Insulator MnBi2Te4.

MnBi2Te4 is a magnetic topological insulator with layered A-type antiferromagnetic order. It exhibits a rich layer- and magnetic-state dependent topological phase diagram; however, much about the coupling between spin, charge, and lattice remains to be explored. In this work, we report that MnBi2Te4 is an excellent acoustic phonon cavity by realizing phonon frequency combs using picosecond ultrasonics. With the generated acoustic phonon wavepackets, we demonstrate that the timing and phase of acoustic echoes can be used to detect the presence of stacking faults between van der Waals layers buried deep within the crystal. Furthermore, by implementing this nondestructive ultrafast optical measurement in conjunction with time-resolved magneto-optical Kerr effect experiments, we uncover that out-of-plane vibrations in MnBi2Te4 do not couple to the magnetic order, i.e. there is no appreciable magnetostriction. Our work points out how a well-developed technique can probe the structural defects and phonon pulse engineering in layered topological insulators.

Heterodyne coherent detection of the electric field temporal trace emitted by frequency-modulated comb lasers

Frequency-modulated (FM) combs are produced by mode-locked lasers in which the electric field has a linearly chirped frequency and nearly constant amplitude. This regime of operation occurs naturally in certain laser systems and constitutes a valuable alternative to generate spectra with equidistant modes. Here, we use a low-noise fs-pulse comb as the local oscillator and combine dual comb heterodyne detection with time domain analysis of the multi-heterodyne signal to reveal the temporal trace of both amplitude and phase quadratures of FM comb lasers’ electric field. This technique is applied to both a dense and a harmonic mid-infrared free-running quantum cascade laser frequency comb and shows direct evidence of the FM behavior together with the high degree of coherence of these sources. Our results furnish a deeper insight on the origin of the FM combs and pave the way to further improvement and optimization of these devices.

Hybrid integrated GaSb/Si3N4 narrow linewidth (<50 kHz) distributed Bragg reflector laser

A narrow linewidth hybrid integrated distributed Bragg reflector (DBR) laser platform operating at 2 μm wavelength region is demonstrated. The laser architecture comprises AlGaInAsSb/GaSb type-I quantum well reflective semiconductor optical amplifiers butt-coupled to a Si3N4 photonic integrated circuit (PIC), incorporating a narrow-band DBR. The DBR is realized with a long spiral-shaped waveguide structure with periodic circular posts placed adjacent to the waveguide. At room temperature operating conditions, the laser exhibits a maximum continuous wave output power of more than 17 mW for emission near 2 μm. Linewidth properties are analyzed with a heterodyne measurement technique, involving the mixing of the laser signal with a frequency comb phase-locked to an ultra-stable laser. The hybrid laser exhibits a narrow linewidth of ∼8 kHz in 1 ms timescale and ∼50 kHz in 10 ms timescale.