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We derive a spatiotemporal equation describing nonlinear optical dynamics in Fabry-Perot (FP) cavities containing a Kerr medium. This equation is an extension of the equation that describes dynamics in Kerr-nonlinear ring resonators,…
We analyse the nonlinear dynamics of Fabry-Perot cavities of arbitrary finesse filled by a dispersive Kerr medium, pumped by a continuous wave laser or a synchronous train of flat-top pulses. The combined action of feedback, group velocity…
Nonlinear frequency combs, including electro-optic and Kerr combs, have become central platforms for chip-scale frequency synthesis. Recent breakthroughs in strong-coupling electro-optic modulation further expanded their accessible…
The model, that is usually called Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and…
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser within an optical microresonator. It has been observed that…
Optical frequency combs allow for precise measurement of optical frequencies and are used in a growing number of applications beyond spectroscopy and optical frequency metrology. A class of compact microresonator based frequency comb…
Optical frequency combs are crucial for both fundamental science and applications demanding wide frequency spanning and ultra-precision resolutions. Recent advancements of nonlinear Kerr effect based optical frequency combs in microcavities…
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and…
Lugiato-Lefever equation (LLE) is a nonlinear Schr\"odinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonators and more recently, in the form of a variant, in…
Kerr microresonators driven in the normal dispersion regime typically require the presence of localized dispersion perturbations, such as those induced by avoided mode crossings, to initiate the formation of optical frequency combs. In this…
Microresonator Kerr frequency combs, which rely on third-order nonlinearity ($\chi^{(3)}$), are of great interest for a wide range of applications including optical clocks, pulse shaping, spectroscopy, telecommunications, light detection…
The aim of this work is to theoretically investigate the possibility of Kerr frequency combs in mechanical systems. In particular, whether microelectrome-chanical devices (MEMS) can be used to generate frequency combs in a manner that is…
Laser-driven high-Q Kerr-nonlinear optical microresonators enable parametric oscillation with low-power continuous-wave lasers and host a variety of coherent dissipative structures, including dissipative Kerr solitons and switching waves.…
Kerr optical frequency combs generated in a coherently driven Kerr nonlinear resonator has the potential for a wide range of applications. However, in a single cavity which is a widely adopted configuration for Kerr optical frequency combs…
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over…
Kerr frequency comb generation relies on dedicated waveguide platforms that are optimized towards ultralow loss while offering comparatively limited functionality restricted to passive building blocks. In contrast to that, the…
Optical frequency combs are indispensable links between the optical and microwave domains, enabling a wide range of applications including precision spectroscopy, ultrastable frequency generation, and timekeeping. Chip-scale integration…
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 Schr\"odinger equation with a phase potential. In…
We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the normal dispersion regime. We analyze the spatial bifurcation structure of the…
Frequency-modulated (FM) laser combs, which offer a periodic quasi-continuous-wave output and a flat-topped optical spectrum, are emerging as a promising solution for wavelength-division multiplexing applications, precision metrology, and…