Comb Line Spacing Research Articles

Floquet topological dissipative Kerr solitons and incommensurate frequency combs

Generating coherent optical frequency combs in micro-ring resonators with Kerr nonlinearity has remarkably advanced the fundamental understanding and applications of temporal dissipative solitons. However, the spectrum of such soliton combs is restricted to the conventional definition of combs as phase-locked, equidistant lines in frequency. Here, we introduce a new class of floquet topological soliton combs that emerge in two-dimensional arrays of strongly coupled resonators engineered using floquet topology. Specifically, we demonstrate incommensurate combs where the comb lines are not equidistant but remain phase-locked. These incommensurate combs are generated by self-organized, phase-locked floquet topological soliton molecules that circulate the edge of the array. We show that these floquet topological solitons are robust and they navigate around defects, allowing for agile tunability of the comb line spacing. Our results introduce a new paradigm in using floquet engineering to generate unconventional frequency combs beyond those achievable with single or weakly coupled resonators.

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.

Photonic Multiple Microwave Frequency Measurement System with Single-Branch Detection Based on Polarization Interference

A photonic microwave frequency measurement system with single-branch detection based on polarization interference is proposed. In this scheme, a 15-line non-flat optical frequency comb (OFC) based on sawtooth signal modulation via a Mach–Zehnder modulator is generated. The intercepted microwave signal with multiple-frequency components can be measured by frequency down-conversion with this simple structure. This system can measure the multi-tone microwave signals in real time. The single-branch detection makes the system a simple and compact structure and avoids the unbalanced variation, as in a two-branches scheme. The blind area of the system can be solved by adjusting the comb-line spacing of the OFC. A simulation is carried out and related discussion is given. The result reveals that it can measure multi-tone microwave signals with a resolution of less than 2 MHz over 0.1–12 GHz.

Measurement and analysis of instantaneous microwave frequency based on an optical frequency comb.

A microwave photonics instantaneous frequency measurement scheme with 14 channels based on an optical frequency comb (OFC) is proposed. In this scheme, a 14-line flat OFC is generated by cascading a dual-parallel Mach-Zehnder modulator (DPMZM) with a Mach-Zehnder modulator (MZM). The intercepted microwave signal with multiple-frequency components can be measured by using DPMZM, Fabry-Perot filter (FPF), wavelength division multiplexer (WDM), and optical power detector array. This scheme can measure and analyze the frequency of microwave signals in the ranges of 0.5-13.5 GHz, 13.5-26.5 GHz, and 26.5-39.5 GHz with the measurement accuracy of ±0.5GHz. The reconfigurability of the system can be realized by adjusting the comb-line spacing of the OFC and the free spectral range (FSR) of the FPF.

Coexistence of multiple microcombs in monochromatically pumped Si3N4 microresonators.

We experimentally demonstrate that multiple microcombs can coexist in monochromatically pumped Si3N4 microresonators. By pumping around the mode crossing using a CW laser with mixed polarization, three types of coherent microcombs are generated simultaneously: (i) TE-polarized soliton microcomb; (ii) TM-polarized Turing rolls microcomb; and (iii) cross-phase-modulation-induced TM-polarized microcomb. It is proved that the type-(iii) microcomb shares the same comb line spacing with the type-(i) microcomb although the free spectral ranges of TE and TM modes are different. In addition, a 22.95-GHz signal is extracted from a ∼100-GHz microresonator by heterodyning the TE and TM comb lines, and phase noise analysis reveals their coherence characteristics.

Near-octave-spanning breathing soliton crystal in an AlN microresonator.

The soliton crystal (SC) was recently discovered as an extraordinary Kerr soliton state with regularly distributed soliton pulses and enhanced comb line power spaced by multiples of the cavity free spectral ranges (FSRs), which will significantly extend the application potential of microcombs in optical clock, signal processing, and terahertz wave systems. However, the reported SC spectra are generally narrow. In this Letter, we demonstrate the generation of a breathing SC in an aluminum nitride (AlN) microresonator (FSR ∼374GHz), featuring a near-octave-spanning (1150-2200 nm) spectral range and a terahertz repetition rate of ∼1.87THz. The measured 60 fs short pulses and low intensity-noise characteristics confirm the high coherence of the breathing SC. Broadband microcombs with various repetition rates of ∼0.75, ∼1.12, and ∼1.5THz were also realized in different microresonators of the same size. The proposed scheme shows a reliable design strategy for broadband soliton generation with versatile dynamic control over the comb line spacing.

Self-Injection Locking of a Gain-Switched Laser Diode

We experimentally observed self-injection locking regime of the gain-switched laser to high-Q optical microresonator. We revealed that comb generated by the gain-switched laser experiences a dramatic reduce of comb teeth linewidths in this regime. We demonstrated the Lorentzian linewidth of the comb teeth of sub-kHz scale as narrow as for non-switched self-injection locked laser. Such setup allows generation of high-contrast electrically-tunable optical frequency combs with tunable comb line spacing in a wide range from 10 kHz up to 10 GHz. The characteristics of the generated combs were studied for various modulation parameters - modulation frequency and amplitude, and for parameters, defining the efficiency of the self-injection locking - locking phase, coupling efficiency, pump frequency detuning.

Optical Frequency Comb Generation via Cascaded Intensity and Phase Photonic Crystal Modulators

Nanophotonics, driven by low processing power and high density integration, is appearing as the next logical step for microwave photonics. Optical frequency combs (OFCs), which play a vital role in integrated microwave photonics, have not yet generated using nano-structured devices. In this paper, we propose OFC generation based on all-optical modulation of nanophotonic structures. A theoretical model based on temporal coupled mode theory is developed to describe cascaded all-optical photonic crystal intensity and phase modulators. Using a modulation light with a sinusoidal waveform, a separate carrier light is modulated to generate an OFC. By manipulating the modulation power and device dimensions, a flat OFC that spans over a 600 GHz is delivered. The proposed system offers OFC generation with tunable comb line spacing using devices with high density integration capabilities.

Broadband high-resolution molecular spectroscopy with interleaved mid-infrared frequency combs

Traditionally, there has been a trade-off in spectroscopic measurements between high resolution, broadband coverage, and acquisition time. Originally envisioned for precision spectroscopy of the hydrogen atom in the ultraviolet, optical frequency combs are now commonly used for probing molecular ro-vibrational transitions throughout broad spectral bands in the mid-infrared providing superior resolution, speed, and the capability of referencing to the primary frequency standards. Here we demonstrate the acquisition of 2.5 million spectral data points over the continuous wavelength range of 3.17–5.13 µm (frequency span 1200 cm−1, sampling point spacing 13–21 MHz), via interleaving comb-tooth-resolved spectra acquired with a highly-coherent broadband dual-frequency-comb system based on optical subharmonic generation. With the original comb-line spacing of 115 MHz, overlaying eight spectra with gradually shifted comb lines we fully resolve the amplitude and phase spectra of molecules with narrow Doppler lines, such as carbon disulfide (CS2) and its three isotopologues.

Microwave frequency comb generation through optical double-locked semiconductor lasers

A microwave frequency comb (MFC) consists of equally spaced discrete microwave frequency components that have small magnitude variations across its bandwidth. In this work, a scheme comprising of a slave laser that is optically injected by a strongly intensity-modulated master laser is proposed and numerically investigated to generate MFCs. Based on the double-locking characteristics of the periodic oscillations induced by strong intensity-modulated optical injection, locked comb structures are invoked when the modulation frequency is at a submultiple frequency of the period-one oscillation frequency. Furthermore, broad microwave frequency comb bandwidths are achieved through the bandwidth enhancement effect of optically injected lasers at appropriate operating conditions. The demonstrated MFC source has a continuously tunable comb-line spacing between 1–10 GHz reaching bandwidths that are six times the relaxation resonance frequency of the free-running semiconductor laser.

Harmonic and rational harmonic driving of microresonator soliton frequency combs

With demonstrated applications ranging from metrology to telecommunications, soliton microresonator frequency combs have emerged over the past decade as a remarkable new technology. However, standard implementations allow only for the generation of combs whose repetition rate is tied closely to the fundamental resonator free-spectral range (FSR), offering little or no dynamic control over the comb line spacing. Here we propose and experimentally demonstrate harmonic and rational harmonic driving as novel techniques that allow for the robust generation of soliton frequency combs with discretely adjustable frequency spacing. By driving an integrated Kerr microresonator with a periodic train of picosecond pulses whose repetition rate is set close to an integer harmonic of the 3.23 GHz cavity FSR, we deterministically generate soliton frequency combs with frequency spacings discretely adjustable between 3.23 GHz and 19.38 GHz. More remarkably, we also demonstrate that driving the resonator at rational fractions of the FSR allows for the generation of combs whose frequency spacing corresponds to an integer harmonic of the pump repetition rate. By measuring the combs’ radio-frequency spectrum, we confirm operation in the low-noise soliton regime with no supermode noise. The novel techniques demonstrated in our work provide new degrees of freedom for the design of synchronously pumped soliton frequency combs.

Perfect Soliton Crystals on Demand

AbstractRecent advances in of soliton microcombs have shown great promise to revolutionize many important areas such as optical communication, spectroscopic sensing, optical clock, and frequency synthesis. A largely tunable comb line spacing is crucial for the practical application of soliton microcombs, which unfortunately is challenging to realize for an on‐chip monolithic microresonators. The recently discovered perfect soliton crystal (PSC) offers a convenient route to tune the comb line spacing. However, excitation of a PSC is generally stochastic by its nature and accessing a certain PSC state requires delicate tuning procedure. Here the on‐demand generation of PSCs in a lithium niobate microresonator is demonstrated. The unique device characteristics allow to produce a variety of PSCs and to switch between different PSC states, deterministically and repetitively. The device is utilized to show arbitrary dialing of the comb line spacing from 1 to 11 times of the free‐spectral range of the resonator. The demonstration of PSCs on demand may now open up a great avenue for flexibly controlling the repetition rate of soliton pulses, which would significantly enhance and extend the application potential of soliton microcombs for communication, signal processing, and sensing.

Kerr frequency comb with varying FSR spacing based on Si3N4 micro-resonator

In this paper, we experimentally investigate a novel feedback loop scheme to generate optical frequency comb with varying free spectral range (FSR) spacing in a high-Q silicon nitride (Si$_3$N$_4$) micro-ring resonator. By selecting and amplifying different feedback sidebands, comb line spacing varying from 1-fold to 6-fold FSRs is successfully achieved. This approach could be beneficial to tune the comb repetition rate which is an important parameter for many applications, such as optical coherent communications, optical metrology and arbitrary waveform generation.

Emergence of microfrequency comb via limit cycles in dissipatively coupled condensates

Self-sustained oscillations, limit cycles, are a fundamental phenomenon unique to nonlinear dynamic systems of high-dimensional phase space. They enable understanding of a wide range of cyclic processes in natural, social and engineering systems. Here we show that limit cycles form in coupled polariton cavities following the breaking of Josephson coupling, leading to frequency-comb emission. The limit cycles and destruction of Josephson coupling both appear due to interplay between strong polariton-polariton interaction and a dissipative contribution to the cavity coupling. The resulting nonlinear dynamics of the condensates is characterized by asymmetric population distribution and nontrivial average phase difference between the two condensates, and by time-periodic modulation of their amplitudes and phases. The latter is manifested by coherent emission of new equidistant frequency components. The emission spectrum resembles that of a micro-frequency comb, but originates from a fundamentally different mechanism than that of existing frequency combs. It allows non-resonant excitation with a power input much below the conventional semiconductor laser threshold. The comb line spacing is determined by the interaction and coupling strengths, and is adjustable up to multi-terahertz frequency. The work establishes coupled polariton cavities as an experimental platform for rich nonlinear dynamic phenomena.

Microfluidic mid-infrared spectroscopy via microresonator-based dual-comb source.

Over the past decade, microresonator-based soliton combs based on photonic integration have broadened the scope of applications in sensing, ranging, and imaging. The large comb line spacing on the order of hundreds of gigahertz allows for rapid acquisition of absorption spectra in the condensed matter phase without aliasing via a dual-comb interferometer. We present a proof-of-principle demonstration of high-throughput label-free microresonator-based dual-comb spectroscopy in a microfluidic chip that dynamically probes the linear absorption of liquid acetone in the mid-infrared wavelength regime. We measure the flow dynamics of an acetone droplet with a spectral acquisition rate of 25kHz (40μs per spectrum) covering a spectral range from 2900 to 2990nm. Combining microfluidics and silicon-photonic technology would potentially enable a compact time-resolved spectroscopy system for a wide range of applications such as chemical synthesis, biological cell-sorting, and lab-on-a-chip.

Laser Frequency Combs for Coherent Optical Communications

Laser frequency combs with repetition rates on the order of 10 GHz and higher can be used as multi-carrier sources in wavelength-division multiplexing (WDM). They allow replacing tens of tunable continuous-wave lasers by a single laser source. In addition, the comb's line spacing stability and broadband phase coherence enable signal processing beyond what is possible with an array of independent lasers. Modern WDM systems operate with advanced modulation formats and coherent receivers. This introduces stringent requirements in terms of signal-to-noise ratio, power per line, and optical linewidth which can be challenging to attain for frequency comb sources. Here, we set quantitative benchmarks for these characteristics and discuss tradeoffs in terms of transmission reach and achievable data rates. We also highlight recent achievements for comb-based superchannels, including >10 Tb/s transmission with extremely high spectral efficiency, and the possibility to significantly simplify the coherent receiver by realizing joint digital signal processing. We finally discuss advances with microresonator frequency combs and compare their performance in terms of flatness and conversion efficiency against state-of-the-art electro-optic frequency comb generators. This contribution provides guidelines for developing frequency comb sources in coherent fiber-optic communication systems.

Broadband near-infrared astronomical spectrometer calibration and on-sky validation with an electro-optic laser frequency comb.

The quest for extrasolar planets and their characterization as well as studies of fundamental physics on cosmological scales rely on capabilities of high-resolution astronomical spectroscopy. A central requirement is a precise wavelength calibration of astronomical spectrographs allowing for extraction of subtle wavelength shifts from the spectra of stars and quasars. Here, we present an all-fiber, 400 nm wide near-infrared frequency comb based on electro-optic modulation with 14.5 GHz comb line spacing. Tests on the high-resolution, near-infrared spectrometer GIANO-B show a photon-noise limited calibration precision of < 10 cms as required for Earth-like planet detection. Moreover, the presented comb provides detailed insight into particularities of the spectrograph such as detector inhomogeneities and differential spectrograph drifts. The system is validated in on-sky observations of a radial velocity standard star (HD221354) and telluric atmospheric absorption features. The advantages of the system include simplicity, robustness and turn-key operation, features that are valuable at the observation sites.

Calibration Tests of a 25-GHz Mode-spacing Broadband Astro-comb on the Fiber-fed High Resolution Spectrograph (HRS) of the Chinese 2.16-m Telescope

A 25-GHz mode-spacing astro-comb with 470–720 nm wavelength coverage has been installed as the calibration source on the fiber-fed High Resolution Spectrograph (HRS) of the Chinese 2.16-m telescope at Xinglong Observatory. The calibration tests were carried out based on the single-channel system of HRS. The results have achieved a 2–8 times (for different orders) higher wavelength solution accuracy than the thorium argon (ThAr) lamp, and a short-term repeatability of 0.1 m s−1, which is around the photon noise limit. It proved that the coupling system linking the astro-comb to HRS successfully suppressed the negative effects of laser speckles. The comb-line overlapping exists in the acquired spectrum of the astro-comb on HRS. We demonstrated that when determining the comb-line center, the comb-line overlapping leads to a systematic bias, which is caused by asymmetrical sampling, and meanwhile a larger uncertainty. The correction for the systematic bias is feasible by simulating the overlapping comb lines according to actual comb-line spacing and pixel phase and then calculating the difference of the fitted line center with the true line center. A higher accuracy of wavelength solution has been achieved after correction.

Generating orthogonally polarized dual frequency combs with slow megahertz repetition rates by a low-nanowatt-level pump

Dual frequency comb generation has been the focus of many recent research efforts owing to its viability in a myriad of applications, ranging from precision measurement to high-speed optical communications. Here, with the state of the art of a single quantum dot (QD) coupled to a pillar microcavity [Nat. Nanotechnol. 12, 663 (2017)], we put forward an alternative setup for the generation of orthogonally polarized dual frequency combs and their corresponding control by using coherent two-tone cavity driving, i.e., a control laser and a probe laser. The present QD-pillar microcavity system operates in the weak-coupling regime, and this makes the experimental realization of the scheme easy. The underlying nonlinear process of the system, thanks to the QD-pillar interaction, for example, degenerate and nondegenerate four-wave mixing, results in efficient frequency comb formation. The dual combs consist of equidistant spectral lines whose spectral spacing coincides with the frequency difference between the control and probe lasers. So, programming this frequency difference between them enables us to tune both the comb-line spacing (i.e., repetition rate) and comb-line number in both vertical ($V$) and horizontal ($H$) polarizations. As compared with the previous approaches for dual microcomb generation, the present scheme has attractive features such as a tunable, slow repetition rate (as slow as a few megahertz), low input power (as low as a few nanowatts), and integrated compact nature in experimentally realistic operating regimes. The achievable low repetition rates are desirable to resolve narrower spectral lines and to enable use of low-power signal processing electronics.

Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs.

We propose and characterize experimentally a new source of optical frequency combs for performing multi-heterodyne spectrometry. This comb modality is based on a frequency-shifting loop seeded with a continuous-wave (CW) monochromatic laser. The comb lines are generated by successive passes of the CW laser through an acousto-optic frequency shifter. We report the generation of frequency combs with more than 1500 mutually coherent lines, without resorting to non-linear broadening phenomena or external electronic modulation. The comb line spacing is easily reconfigurable from tens of MHz down to the kHz region. We first use a single acousto-optic frequency comb to conduct self-heterodyne interferometry with a high frequency resolution (500 kHz). By increasing the line spacing to 80 MHz, we demonstrate molecular spectroscopy on the sub-millisecond time scale. In order to reduce the detection bandwidth, we subsequently implement an acousto-optic dual-comb spectrometer with the aid of two mutually coherent frequency shifting loops. In each architecture, the potentiality of acousto-optic frequency combs for spectroscopy is validated by spectral measurements of hydrogen cyanide in the near-infrared region.