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Surface spontaneous parametric down-conversion is predicted as a consequence of continuity requirements for electric- and magnetic-field amplitudes at a discontinuity of chi2 nonlinearity. A generalization of the usual two-photon spectral…
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two \chi^2 level oscillation…
The rotational echo response of molecules is found to strongly depend on the delay between the two ultrashort laser pulses, as opposed to two-level systems. We study this dependence experimentally and theoretically and show that by…
Microresonator frequency combs based on the $\chi^{(3)}$ nonlinearity are nowadays well understood and making their way into different applications. Recently, microresonator frequency combs based on the $\chi^{(2)}$ nonlinearity are…
Discrete nonlinear systems support a rich variety of localized and extended wave phenomena, with their dynamics sensitively dependent on the symmetries of the underlying interaction forces within the lattice. Odd elasticity, emerging in…
We report the soliton frequency comb generation in microring optical parametric oscillators operating in the down-conversion regime and with the simultaneous presence of the $\chi^{(2)}$ and Kerr nonlinearities. The combs are studied…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
We consider Euler flows on two-dimensional (2D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2D Taylor-Green vortex. As the first main result, numerical evidence is…
Second-harmonic generation in resonant structures is commonly evaluated in terms of intracavity field enhancement at the fundamental and harmonic frequencies. Here, we formulate nonlinear frequency conversion within a symmetry-resolved…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
G\"ortler vortices developing over a concave wall support rapidly oscillating wavelike disturbances through secondary instabilities. Although experiments indicate that the finite-amplitude evolution of these waves acts as a precursor to…
Self-steepening of optical pulses arises due the dispersive contribution of the $\chi^{(3)}(\omega)$ Kerr nonlinearity. In typical structures this response is on the order of a few femtoseconds with a fixed frequency response. In contrast,…
We study the local dynamics of $L^{2}\left(\mathbb{R}\right)$-perturbations to the zero solution of spatially $2\pi$-periodic coefficient reaction-diffusion systems. In this case the spectrum of the linearization about the zero solution is…
We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the…
In this paper, we propose a microcavity supported by a designed photonic crystal structure (PhC) that supplies both tunability of cavity modes and quality factor of cavity. Low symmetric defect region provides a trigger effect for the…
Mid-infrared laser frequency combs are compelling sources for precise and sensitive metrology with applications in molecular spectroscopy and spectro-imaging. The infrared atmospheric window between 3-5.5 $\mu$m in particular provides vital…
A general electrodynamic theory of a grating coupled two dimensional electron system (2DES) is developed. The 2DES is treated quantum mechanically, the grating is considered as a periodic system of thin metal strips or as an array of…
Shear to longitudinal mode conversion via second harmonic generation is studied theoretically and computationally for plane waves in a two-dimensional, adhesive, hexagonally close-packed microscale granular medium. The model includes…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
Nonlinear wave-induced perturbations are discussed within the framework of the second-order theory. Due to the slow attenuation of the long perturbations with depth, they modulate motions beneath surface waves down to the bottom and can…