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The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
Frequency combs have become a prominent research area in optics. Of particular interest as integrated comb technology are chip-scale sources, such as semiconductor lasers and microresonators, which consist of resonators embedding a…
We consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or…
Microcomb generation with simultaneous $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities brings new possibilities for ultra-broadband and potentially self-referenced integrated comb sources. However, the evolution of the intracavity field…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space…
A frequency comb generated from a phase-modulated continuous-wave laser is simultaneously subject to the temporal Talbot effect and modulational instability (MI) when propagating through a piece of optical fiber. The temporal Talbot effect…
We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…
Magnonic frequency combs have recently attracted particular attention due to their potential impact on spin-wave science. Here, we demonstrate theoretically the generation of ultra-wideband (UWB) magnonic frequency combs induced by…
Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we…
A high-power laser pulse at normal incidence onto a plane solid target will generate odd harmonics of its frequency. However, the spacing of the harmonic lines in this configuration is fixed. Here, we study harmonic generation using two…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
We investigate analytically and numerically the nonstationary circuit QED setup in which $N$ independent qubits interact with a single mode of the Electromagnetic field confined in a resonator. We consider the harmonic time modulation of…
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…
We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the…
Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially…
Modulated optical cavities have been proposed and demonstrated for applications in communications, laser frequency stabilization, microwave-to-optical conversion and frequency comb generation. However, most studies are restricted to the…
Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly…
Electromagnetic scattering from moving bodies, being inherently time-dependent phenomenon, gives rise to a generation of new frequencies, which could characterize the motion. While a standard linear path leads to a constant Doppler shift,…