We report a theoretical investigation of quadratic frequency combs in a dispersive second-harmonic generation cavity system. We identify different dynamical regimes and demonstrate that the same system can exhibit both bright and dark localized cavity solitons in the absence of a temporal walk-off.

This review describes recent theoretical and experimental advances in the area of multimode solitons, focusing primarily on multimode fibers. We begin by introducing the basic concepts such as the spatial modes supported by a multimode fiber and the coupled mode equations for describing the different group delays and nonlinear properties of these modes. We review several analytic approaches used to understand the formation of multimode solitons, including those based on the 3D+1 spatiotemporal nonlinear Schrödinger equation (NLSE) and its approximate 1D+1 representation that has been found to be highly efficient for studying the self-imaging phenomena in graded-index multimode fibers. An innovative Gaussian quadrature approach is used for faster numerical simulations of the 3D+1 NLSE. The impact of linear mode coupling is discussed in a separate section using a generalized Jones formalism because of its relevance to space-division multiplexed optical communication systems. The last section is devoted to the relevant experimental studies involving multimode solitons.

Optical frequency combs are one of the most remarkable inventions in recent decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we present a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its subharmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.

Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for optical frequency combs in a dissipative and nonlinear χ⁽³⁾-based cavity system with parametric coupling between fundamental and third-harmonic waves. We investigate temporally dispersive dual-comb generation of phase-matched combs with broad bandwidth and anomalous dispersion of the fundamental field, individuating conditions for accessing a multistable regime that simultaneously supports two types of coupled bright cavity solitons. These bistable cavity solitons coexist for the same pump power and frequency detuning, while featuring dissimilar amplitudes of their individual field components. Third-harmonic generation frequency combs grant telecom pump laser sources a simultaneous and direct access to both the near-infrared and the visible regions, which may prove advantageous for the development of optical clocks and sensing applications.

Optical frequency comb synthesizers with a wide spectral range are an essential tool for many research areas such as spectroscopy, precision metrology, optical communication, and sensing. Recent studies have demonstrated the direct generation of frequency combs, via second-order processes, that are centered on two different spectral regions separated by an octave. Here, we present the capability of optical quadratic frequency combs for broad-bandwidth spectral emission in unexplored regimes. We consider comb formation under phase-matched conditions in a continuous-wave pumped singly resonant second-harmonic cavity, with large intracavity power and control of the detuning over several cavity linewidths. The spectral analysis reveals quite distinctive sidebands that arise far away from the pump, singularly or in a mixed regime together with narrowband frequency combs. Notably, by increasing the input power, the optical frequency lines evolve into widely spaced frequency clusters, and at maximum power, they appear in a wavelength range spanning up to 100 nm. The obtained results demonstrate the capacity of second-order nonlinearities to produce direct comb within a wide range of wavelengths.

Optical frequency combs currently represent enabling components in a wide number of fast-growing research fields, from frequency metrology to precision spectroscopy, from synchronization of telecommunication systems to environmental and biomedical spectrometry. As recently demonstrated, quadratic nonlinear media are a promising platform for optical frequency combs generation, through the onset of an internally pumped optical parametric oscillator in cavity enhanced second-harmonic generation systems. We present here a proposal for quadratic frequency comb generation in AlGaAs waveguide resonators. Based on the crystal symmetry properties of the AlGaAs material, quasi-phase matching can be realized in curved geometries (directional quasi-phase matching), thus ensuring efficient optical frequency conversion. We propose a novel design of AlGaAs waveguide resonators with strongly reduced total losses, compatible with long-path, high-quality resonators. By means of a numerical study, we predict efficient frequency comb generation with threshold powers in the microwatt range, paving the way for the full integration of frequency comb synthesizers in photonic circuits. © (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.