Related papers: Geometrical optics in nonlinear media and integrab…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
We briefly tackle the following concepts in the Demkov-Ostrovsky (DO) nodeless sector: (i) orbital impedance, (ii) orbital capacity, (iii) closeness to reflectionlessness. Moreover, using previous supersymmetric results for the DO problem,…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
The applied method of the amplitude envelopes give us the possibility to describe a new class of amplitude equations governing the propagation of optical pulses in media with dispersion, dispersionless media and vacuum. We normalized these…
Rheological properties, especially 'shear-thinning', of dense colloidal dispersions are discussed on three different levels. A generalized phenomonological Maxwell model gives a broad framework connecting glassy dynamics to the linear and…
The nonlinear optical response of materials to exciting light is enhanced by resonances between the incident laser frequencies and the energy levels of the excited material. Traditionally, in molecular nonlinear spectroscopy one tunes the…
Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases,…
This paper establishes a comprehensive mathematical framework connecting optical physics equations to generative models, demonstrating how light propagation dynamics inspire powerful artificial intelligence approaches. We analyze six…
Propagation of light through media with a complex refractive index in which gain and loss are engineered to be $PT$ symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the…
The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics…
We study the Gevrey character of a natural parameterization of one dimensional invariant manifolds associated to a parabolic direction of fixed points of analytic maps, that is, a direction associated with an eigenvalue equal to $1$. We…
We discuss optical chirality in different types of gyrotropic media. Our analysis is based on the formalism of nongeometric symmetries of Maxwell's equations in vacuum generalized to material media with given constituent relations. This…
There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear…
The mechanism of wavefront reconstruction by a geometric-optical reflection of reconstructing light from surfaces with constant phase differences between the object and reference waves used to record the interference fringe structure in the…
We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding…
This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
We demonstrate that laser beam collapse in highly nonlinear media can be described, for a large number of experimental conditions, by the geometrical optics approximation within high accuracy. Taking into account this fact we succeed in…