Unifying Frequency Combs in Active and Passive Cavities: Temporal Solitons in Externally Driven Ring Lasers

Driven bright solitons on a mid-infrared laser chip

Despite the continuing progress in integrated optical frequency comb technology1, compact sources of short, bright pulses in the mid-infrared wavelength range from 3 to 12 μm so far remain beyond reach. The state-of-the-art ultrafast pulse emitters in the mid-infrared are complex, bulky and inefficient systems based on the downconversion of near-infrared or visible pulsed laser sources. Here we show a purely DC-driven semiconductor laser chip that generates 1-ps solitons at the centre wavelength of 8.3 μm at GHz repetition rates. The soliton generation scheme is akin to that of passive nonlinear Kerr resonators2. It relies on a fast bistability in active nonlinear laser resonators, unlike traditional passive mode-locking, which relies on saturable absorbers3, or active mode-locking by gain modulation in semiconductor lasers4. Monolithic integration of all components-drive laser, active ring resonator, coupler and pump filter-enables turnkey generation of bright solitons that remain robust for hours of continuous operation without active stabilization. Such devices can be readily produced at industrial laser foundries using standard fabrication protocols. Our work unifies the physics of active and passive microresonator frequency combs while simultaneously establishing a technology for nonlinear integrated photonics in the mid-infrared5.

Phase-locking characteristics and dynamics of the subharmonic entrainment of breathing temporal solitons

Subharmonic entrainment (SHE) of the breathing solitons, an intriguing resonance phenomenon, arises from frequency locking between the breathing frequency and the cavity repetition frequency. This study investigates the phase-locking characteristics and dynamics of the SHE of breathing temporal cavity solitons. We reveal that the breathing solitons arise from the periodic enhancement and depletion of coherence between solitons and pump light, achieving SHE locking across various periods within the stringent parameter ranges of driving intensity, detuning, and cavity finesse. Furthermore, we summarize the excitation condition of SHE within the phase-locking region, enhancing the understanding of the dynamics of SHE. Our research could provide valuable insights into the generation and regulation of SHE.

Multistable Kuramoto Splay States in a Crystal of Mode-Locked Laser Pulses

We demonstrate the existence of coexisting frequency combs in a harmonically mode-locked laser that we link to the splay phases of the Kuramoto model with short range interactions. These splay states are multistable and the laser may wander between them under the influence of stochastic forces. Consequently, the many pulses circulating in the cavity are not necessarily coherent with each other. As these partially disordered states for the phase of the field still feature regular intensity pulses, we term them as incoherent crystals of optical pulses. We provide evidence that the notion of coherence should be interpreted by comparing the duration of the measurement time with the Kramers' escape time of each splay state. Our theoretical results are confirmed experimentally by performing high resolution spectral measurements via a heterodyne technique of a passively mode-locked vertical external-cavity surface-emitting laser.

Theory and application of cavity solitons in photonic devices

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed. Cavity solitons in the plane perpendicular to light propagation find application in optical information processing, while cavity solitons in the longitudinal direction produce high-quality frequency combs with applications in optical communications, frequency standards, optical clocks, future GPS, astronomy and quantum technologies.This article is part of the theme issue 'The quantum theory of light'.

Normal dispersion Kerr cavity solitons: beyond the mean-field limit

We predict the existence of a novel type of temporal localized structure in injected Kerr-Gires-Tournois interferometers (KGTI). These bright pulses exist in the normal dispersion regime, yet they do not correspond to the usual scenario of domain wall locking that induces complex shape multistability, weak stability, and a reduced domain of existence. The new states are observed beyond the mean-field limit and out of the bistable region. Their shape is uniquely defined, with peak intensities beyond that of the upper steady state, and they are stable over a broad range of the injection field, highlighting their potential for optical frequency comb (OFC) generation.

Theoretical model of passive mode-locking in terahertz quantum cascade lasers with distributed saturable absorbers

In research and engineering, short laser pulses are fundamental for metrology and communication. The generation of pulses by passive mode-locking is especially desirable due to the compact setup dimensions, without the need for active modulation requiring dedicated external circuitry. However, well-established models do not cover regular self-pulsing in gain media that recover faster than the cavity round trip time. For quantum cascade lasers (QCLs), this marked a significant limitation in their operation, as they exhibit picosecond gain dynamics associated with intersubband transitions. We present a model that gives detailed insights into the pulse dynamics of the first passively mode-locked QCL that was recently demonstrated. The presence of an incoherent saturable absorber, exemplarily realized by multilayer graphene distributed along the cavity, drives the laser into a pulsed state by exhibiting a similarly fast recovery time as the gain medium. This previously unstudied state of laser operation reveals a remarkable response of the gain medium on unevenly distributed intracavity intensity. We show that in presence of strong spatial hole burning in the laser gain medium, the pulse stabilizes itself by suppressing counter-propagating light and getting shortened again at the cavity facets. Finally, we study the robustness of passive mode-locking with respect to the saturable absorber properties and identify strategies for generating even shorter pulses. The obtained results may also have implications for other nanostructured mode-locked laser sources, for example, based on quantum dots.

Backscattering-Induced Dissipative Solitons in Ring Quantum Cascade Lasers

Ring quantum cascade lasers have recently gained considerable attention, showing ultrastable frequency comb and soliton operation, thus opening a way to integrated spectrometers in the midinfrared and terahertz fingerprint regions. Thanks to a self-consistent Maxwell-Bloch model, we demonstrate, in excellent agreement with the experimental data, that a small but finite coupling between the counterpropagating waves arising from distributed backscattering is essential to stabilize the soliton solution.

Active mid-infrared ring resonators

High-quality optical ring resonators can confine light in a small volume and store it for millions of roundtrips. They have enabled the dramatic size reduction from laboratory scale to chip level of optical filters, modulators, frequency converters, and frequency comb generators in the visible and the near-infrared. The mid-infrared spectral region (3-12 μm), as important as it is for molecular gas sensing and spectroscopy, lags behind in development of integrated photonic components. Here we demonstrate the integration of mid-infrared ring resonators and directional couplers, incorporating a quantum cascade active region in the waveguide core. It enables electrical control of the resonant frequency, its quality factor, the coupling regime and the coupling coefficient. We show that one device, depending on its operating point, can act as a tunable filter, a nonlinear frequency converter, or a frequency comb generator. These concepts extend to the integration of multiple active resonators and waveguides in arbitrary configurations, thus allowing the implementation of purpose-specific mid-infrared active photonic integrated circuits for spectroscopy, communication, and microwave generation.

Nozaki-Bekki solitons in semiconductor lasers

Optical frequency-comb sources, which emit perfectly periodic and coherent waveforms of light1, have recently rapidly progressed towards chip-scale integrated solutions. Among them, two classes are particularly significant-semiconductor Fabry-Perót lasers2-6 and passive ring Kerr microresonators7-9. Here we merge the two technologies in a ring semiconductor laser10,11 and demonstrate a paradigm for the formation of free-running solitons, called Nozaki-Bekki solitons. These dissipative waveforms emerge in a family of travelling localized dark pulses, known within the complex Ginzburg-Landau equation12-14. We show that Nozaki-Bekki solitons are structurally stable in a ring laser and form spontaneously with tuning of the laser bias, eliminating the need for an external optical pump. By combining conclusive experimental findings and a complementary elaborate theoretical model, we reveal the salient characteristics of these solitons and provide guidelines for their generation. Beyond the fundamental soliton circulating inside the ring laser, we demonstrate multisoliton states as well, verifying their localized nature and offering an insight into formation of soliton crystals15. Our results consolidate a monolithic electrically driven platform for direct soliton generation and open the door for a research field at the junction of laser multimode dynamics and Kerr parametric processes.

Mode-locking induced by coherent driving in fiber lasers

Mode-locking is a broad concept that encompasses different processes enabling short optical pulse formation in lasers. It typically requires an intracavity mechanism that discriminates between single and collective mode lasing, which can be complex and sometimes adds noise. Moreover, known mode-locking schemes do not guarantee phase stability of the carrier wave. Here, we theoretically propose that injecting a detuned signal seamlessly leads to mode-locking in fiber lasers. We show that phase-locked pulses, akin to cavity solitons, exist in a wide range of parameters. In that regime the laser behaves as a passive resonator due to the non-instantaneous gain saturation.

A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers

We elucidate the mechanisms that underlay the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first-principles model based upon delay algebraic equations to a minimal pattern formation scenario. It consists in a real cubic Ginzburg-Landau equation modified by high-order effects such as third-order dispersion and nonlinear drift, which are responsible for generating localized states via the locking of domain walls connecting the high and low intensity levels of the injected micro-cavity. We interpret the effective parameters of the normal form in relation with the configuration of the optical setup. Comparing the two models, we observe an excellent agreement close to the onset of bistability.

Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states

Frequency-modulated (FM) combs with a linearly-chirped frequency and nearly constant intensity occur naturally in certain laser systems; they can be most succinctly described by a nonlinear Schrödinger equation with a phase potential. In this work, we perform a comprehensive analytical study of FM combs in order to calculate their salient properties. We develop a general procedure that allows mean-field theories to be constructed for arbitrary sets of master equations, and as an example consider the case of reflective defects. We derive an expression for the FM chirp of arbitrary Fabry-Perot cavities-important for most realistic lasers-and use perturbation theory to show how they are affected by finite gain bandwidth and linewidth enhancment in fast gain media. Lastly, we show that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all of the stable states of the laser: the fundamental comb, the continuous-wave solution, and the harmonic states.

Operating regimes of cavity solitons by virtue of a graphene flake saturable absorber

Exploiting the. broadband operating frequency regimes of a graphene flake saturable absorber (GFSA), a cavity soliton (CS) is excited in heretofore unexplored ultraviolet and visible regions. A broad-area device, namely, a vertical cavity surface emitting laser (VCSEL) is taken as a host of CSs; a two-dimensional (2D) transverse soliton, which is quite different from the conventional propagating one. The VCSEL with an embedded 2D homogeneous transverse layer of a GFSA is coupled with a frequency selective feedback. A CS is also generated in the infrared region, especially at the optical communication wavelength. Spontaneous dynamics and interaction behavior of CSs as well as generation of CS molecules and the push-broom effect are reported in this broad cross-sectional device. In comparison with other existing and potential models, the proposed VCSEL with GFSA model shows greater efficiency.

Frequency Comb Generation by Bloch Gain Induced Giant Kerr Nonlinearity

Optical nonlinearities are known to coherently couple amplitude and phase of light, which can result in the formation of periodic waveforms. Such waveforms are referred to as optical frequency combs. Here we show that Bloch gain-a nonclassical phenomenon that was first predicted in the 1930s-can play an essential role in comb formation. We develop a self-consistent theoretical model that considers all aspects of comb dynamics: band structure, electron transport, and cavity dynamics. In quantum cascade lasers, Bloch gain gives rise to a giant Kerr nonlinearity, which enables frequency modulated combs and serves as the physical origin of the linewidth enhancement factor. Bloch gain also triggers the formation of solitonlike structures in ring resonators, paving the way toward electrically driven Kerr combs.