Related papers: Nonlinear Spectral Singularities and Lasing Thresh…
We report on the stationary and robust propagation of light beams with rather arbitrary and controllable intensity and dissipation transverse patterns in self-focusing Kerr media with nonlinear absorption. When nonlinear absorption is due…
We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts…
Probabilistic amplitude shaping (PAS) is a practical means to achieve a shaping gain in optical fiber communication. However, PAS and shaping in general also affect the signal-dependent generation of nonlinear interference. This provides an…
In this Letter, we present a rigorous method to study the stability of periodic lasing systems. In a linear model, the presence of a continuum of modes (with arbitrarily close lasing thresholds) gives the impression that stable single-mode…
When supersymmetry is spontaneously broken it will be generically non-linearly realized. A method to describe the non-linear realization of supersymmetry is with constrained superfields. We discuss the basic features of this description and…
We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved…
This paper studies singularity structures of the linear inviscid damping of two-dimensional Euler equations in a finite periodic channel. We introduce a recursive definition of singularity structures which characterize the singularities of…
Brane-world singularities are analysed, emphasizing the case of supergravity in singular spaces where the singularity puzzle is naturally resolved. These naked singularities are either time-like or null, corresponding to the finite or…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
Chirality is an important concept that describes the asymmetry property of a system, which usually emerges spontaneously due to mirror symmetry breaking. Such spontaneous chirality manifests predominantly as parity breaking in modern…
In this paper we report on the details of the derivation of approximate closed-form results related to the coherence effect in non-linear noise accumulation, in the context of the GN-model of fiber non-linearity. The coherence effect is…
We deal with the problem of existence of periodic solutions for the scalar differential equation x" + f (t, x) = 0 when the asymmetric nonlinearity satisfies a one-sided superlinear growth at infinity. The nonlinearity is asked to be next…
Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…
We present a method to measure the spectral density of in-band optical transmission impairments without coherent electrical reception and digital signal processing at the receiver. We determine the method's accuracy by numerical simulations…
We show that optical nonlinearities allow sub-wavelength beams to propagate in circular trajectories without being attenuated in spite of their partially evanescent spectrum. Such beams are exact solutions to Maxwell's equations with Kerr…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
In an earlier work (R. Bhandari, Phys. Lett. A 204 (1995) 188), it was shown that, contrary to the property of achromaticity (independence of wavelength) usually associated with topological phases, topological phases encountered in…
We study a nonlinear wave for a system of balance laws in one space dimension, which describes combustion for two-phase (gas and liquid) flow in porous medium. The problem is formulated for a general $N$-component liquid for modeling the…
We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As…
We present a general analysis for finding and characterizing nonlinear exceptional point (EP) lasers above threshold, using steady-state ab-initio Maxwell-Bloch equations. For a system of coupled slabs, we show that a nonlinear EP is…