Related papers: Waveguide arrays interaction to second neighbors: …
We study the propagation of a compactly supported high-frequency wave through a semi-linear wave equation with a null structure. We prove that the self-interaction of the wave creates harmonics which remain close to the light-cone in the…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated via numerical simulations on the corresponding model equations. The realistic experimental setup is suggested injecting the beam in a…
The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order…
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…
The ability to navigate light signals in two-dimensional networks of waveguide arrays is a prerequisite for the development of all-optical integrated circuits for information processing and networking. In this article, we present a…
This paper presents a rigorous mathematical analysis for symmetry-based Bound States in the Continuum (BICs) in optical waveguide arrays. Different from existing research, we consider a finite system of horizontally and equidistantly…
We investigate the transport properties of a classical wave propagating through a quasi-periodic Fibonacci array of waveguide segments in the form of loops. The formulation is general, and applicable for electromagnetic or acoustic waves…
Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much…
We demonstrate that interacting spasers arranged in a 2D array of arbitrary size can be mutually synchronized allowing them to supperradiate. For arrays smaller than the free space wavelength, the total radiated power is proportional to the…
We consider light propagation above the light line in arrays of spherical dielectric nanoparticles. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…
We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical…
The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and…
We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…
The optical properties of sub-wavelength arrays of atoms or other quantum emitters have attracted significant interest recently. For example, the strong constructive or destructive interference of emitted light enables arrays to function as…
Fundamental to many applications of laser pulses in science and technology is an extended interaction length with matter that significantly exceeds the distance over which the pulse would normally diffract and transversely spread. At low…
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…