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Narrow linewidth lasers and optical frequency combs generated with mode-locked lasers revolutionized optical frequency metrology. The advent of soliton Kerr frequency combs in compact crystalline or integrated ring optical microresonators…
Phononic frequency combs (PFCs) typically require nonlinear elastic media, limiting their frequency range and stability. Here, we propose a transformative approach to generate PFCs in purely linear elastic media by harnessing the magnon…
The counting and control of optical cycles of light has become common with modelocked laser frequency combs. But even with advances in laser technology, modelocked laser combs remain bulk-component devices that are hand-assembled. In…
Multimode fiber systems are desirable for industrial and scientific applications. As an interesting effect for the laser beam propagation in a multimode fiber, nonlinear Kerr beam cleanup has attracted considerable research interest due to…
We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary…
In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and…
Microresonator-based optical frequency combs emitted from high-quality-factor microresonators, also known as microcombs, have opened up new horizons to areas of optical frequency comb technology including frequency metrology, precision…
We study the analogue of optical frequency combs in driven nonlinear phononic systems, and present a new generation mechanism for phononic frequency combs via nonlinear resonances. The nonlinear resonance refers to the simultaneous…
This work explores the possibility of creating and controlling unconventional nonlinearities by periodic driving, in a broad class of systems described by the nonlinear Schr\"odinger equation (NLSE). By means of a parent quantum many-body…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
Optical frequency combs have revolutionized precision science and technology, yet their nanophotonic implementations have failed to simultaneously achieve high efficiency, power, and coherence. Optically driven microcombs provide broad and…
Optical frequency combs generated in normally dispersive Kerr microresonators have been observed to correspond to dark temporal structures, and theoretically explained as interlocked switching waves (also known as domain walls or fronts).…
Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded…
Two-photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the…
The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants.…
Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in…
Mechanical frequency combs are poised to bring the applications and utility of optical frequency combs into the mechanical domain. So far, their main challenge has been strict requirements on drive frequencies and power, which complicate…
Integrated nonlinear wavelength converters transfer optical energy from lasers or quantum emitters to other useful colors, but chromatic dispersion limits the range of achievable wavelength shifts. Moreover, because of geometric dispersion,…
The nonlinear interaction of a microresonator pumped by a laser has revealed complex dynamics including soliton formation and chaos. Initial studies of coupled-resonator systems reveal even more complicated dynamics that can lead to…
The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general, localized, response function. It is shown that there always exists a finite number of well-separated MI gain bands, with each of them…