Related papers: Non-orthogonal Transformations of Structured Light…
This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our…
At a transition in a wave-guiding structure, part of the incident energy is transmitted and part of the energy is reflected. When the waveguide has non-trivial topological properties, however, the transition may occur with no…
A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related…
It is well-known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the inhomogeneity of elastic media. However, the reported new linear elasticity equations for…
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
We present a framework for the paraxial wave equation based on propagation-dependent unitary transformations closely related to the Lewis-Ermakov invariant. This approach establishes a formal equivalence between free-space propagation and…
The coherent superposition of orthogonal modes can result in transverse offsets, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for…
The transformation media concept based on the form-invariant Maxwell's equations under coordinate transformations has opened up new possibilities to manipulate the electromagnetic fields. In this paper we report on applying the…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
While in linear optics the subject of structured light has been a fruitful field of both theoretical and applied research, its development in the arena of nonlinear optics has been underexplored. In this paper, we construct Frozen-Wave-type…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
The conformal transformations corresponding to $N$-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides…