Related papers: Optics in nonuniform media and Lagrange geometry
We present an analytical description of the nonlocal optical response of plasmonic nanowire metamaterials that enable negative refraction, subwavelength light manipulation, and emission lifetime engineering. We show that dispersion of…
The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…
Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…
New propagation regimes for light arise from the ability to tune the dielectric permittivity to extremely low values. Here we demonstrate a universal approach based on the low linear permittivity values attained in the epsilon-near-zero…
We study the Euler-Lagrange equations for a parameter dependent $G$-invariant Lagrangian on a homogeneous $G$-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group $G$, emphasizing the special invariance…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was…
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature.…
The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for…
The influence of the medium on the gravitational deflection of light rays is widely discussed in literature for the simplest non-trivial case: cold non-magnetized plasma. In this article, we generalize these studies to the case of an…
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many…
Relativistic aberration influences apparent luminosities of objects moving with relativistic relative velocities. The superluminosity or dimming of incoming or receding jets ejected from Active Galactic Nuclei is believed to be the…
The dynamics of light beams in the nonlinear optical media with periodically modulated in the longitudinal direction parity-time distribution of the complex refractive index is investigated. The possibility of dynamical stabilization of…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
Relativistic flying mirrors in plasmas are realized as thin dense electron (or electron-ion) layers accelerated by high-intensity electromagnetic waves to velocities close to the speed of light in vacuum. The reflection of an…
In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is…
Light propagation is investigated in the context of local anisotropic nonlinear dielectric media at rest with the dielectric coefficients $\epsilon^\mu{}_\nu = \epsilon^\mu{}_\nu (\vec{E},\vec{B})$ and constant $\mu$, in the limit of…