Related papers: Nonlinear Spectral Singularities and Lasing Thresh…
Onset of the instability of a multiple-scattering speckle pattern in a random medium with Kerr nonlinearity is significantly affected by the noninstantaneous character of the nonlinear medium response. The fundamental time scale of the…
It is shown that two fundamentally different phenomena, the bound states in continuum and the spectral singularity (or time-reversed spectral singularity), can occur simultaneously. This can be achieved, in particular, in a rectangular core…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can…
Photonic crystal fibers doped with silver nanoparticles exhibit the Kerr nonlinearity that can be positive or negative depending on wavelength and vanishes at a specific wavelength. We study numerically how the simultaneous presence of a…
We investigate numerically the effect of Kerr nonlinearity on the transmission spectrum of a one dimensional $\delta$-function photonic crystal. It is found that the photonic band gap (PBG) width either increases or decreases depending on…
The directionality and polarization of light show peculiar properties when the scattering by a dielectric sphere can be described exclusively by electric and magnetic dipolar modes. Particularly, when these modes oscillate in-phase with…
In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
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…
Recently an analytical model was presented that treats the nonlinear signal distortion from the Kerr nonlinearity in optical transmission systems as additive white Gaussian noise. This important model predicts the impact of the Kerr…
The effects of coherence of quantum transitions and the interference of resonant nonlinear optical processes on the spectra of absorption, amplification, and nonlinear-optical generation are considered. The most favorable conditions are…
Using sum rules and a new dipole-free sum-over-states expression, we calculate the fundamental limits of the dispersion of the real and imaginary parts of all electronic nonlinear-optical susceptibilities. As such, these general results can…
We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all $t>0$. The singularity of these solutions is of the same type as the singularity of…
A simple method is proposed for inclusion of inelastic effects (electron absorption) in computations of low-energy electron reflectivity (LEER) spectra. The theoretical spectra are formulated by matching of electron wavefunctions obtained…
Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which…
Singular Spectrum Analysis and many other subspace-based methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of…
We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We…
Nonlinear optical media of Kerr type are described by a particular version of an anharmonic quantum harmonic oscillator. The dynamics of this system can be described using the Moyal equations of motion, which correspond to a quantum phase…
We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the…