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A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for…
Coupled-mode theory (CMT) is a powerful tool for simulating near-harmonic systems. In telecommunications, variations of the theory have been used extensively to study waveguides, both analytically and through numerical modelling. Analogous…
Confined geometries, such as optical waveguides, support a discrete set of eigen-modes. In multimoded structures, depending on the boundary conditions, superposition states can propagate. Characterization of these states is a fundamental…
We have obtained an analytical solution for the dispersion relation of the light field modes in the nanowaveguide structure. The solution has been analyzed for the planar waveguide with metamaterial claddings and dielectric core. The…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves…
We analytically derive a rigorous expression for the relative impedance ratio between two photonic structures based on their electromagnetic interaction. Our approach generalizes the physical meaning of the impedance to a measure for the…
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic…
Rayleigh-Bloch waves are guided acoustic waves propagating along a periodic line of inclusions placed inside an open, infinite medium. Below the sound cone, they are transversely evanescent on both sides of the line of inclusions. Guidance…
Some rigorous results can be derived using a very simple approach to hadron spectroscopy, in which a static potential is associated with non-relativistic kinematics. Several regularities of the experimental spectrum are explained by such…
We adapt the resonant state expansion to optical fibers such as capillary and photonic crystal fibers. As a key requirement of the resonant state expansion and any related perturbative approach, we derive the correct analytical…
Acoustic propagation models are widely used in numerous oceanic and other underwater applications. Most conventional models are approximate solutions of the acoustic wave equation, and require accurate environmental knowledge to be…
Models of light-matter interactions typically invoke the dipole approximation, within which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes that they interact with. However, when the…
One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
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…
Light's spatial degree of freedom is emerging as a potential resource for a myriad of applications, in both classical and quantum domains, including secure communication, sensing and imaging. However, it has been repeatedly shown that a…
Optical fibres constitute an exceptional sensing platform. However, standard fibres present an inherent sensing challenge: they confine light by design to an inner core. Consequently, nearly all distributed fibre sensors are restricted to…
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an…
The purpose of this paper is to present the derivation and mathematical analysis of a new asymptotic model that describes the evolution of medium amplitude internal waves propagating between a flat rigid-lid and a highly variable…