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The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show…
Highly lossy nature of metals has severely limited the scope of practical applications of plasmonics. The conventional approach to circumvent this limitation has been to search for new materials with more favorable dielectric properties…
A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc.…
A generalized dispersion equation is derived featuring coupled mode theory, parity-time symmetry, and leaky wave antennas of arbitrary periodic modulation. It can be specialized to each of these cases individually or can describe a…
We investigate the spontaneous emission of light in three-dimensional (3D) photonic crystals through theoretical calculations and simulations. It is well known that spontaneous emission depends on the radiative local density of states…
Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling the optical response of materials and resulting structures. In the…
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
In this study, we present several improvements of the non-relativistic Friedrichs-Lee model with multiple discrete and continuous states and still retain its solvability. Our findings establish a solid theoretical basis for the exploration…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties…
Random optical-pulse polarization switching along an active optical medium in the $\Lambda$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable…
Material susceptibilities govern interactions between electromagnetic waves and matter and are of a crucial importance for basic understanding of natural phenomena and for tailoring practical applications. Here we present a new…
We present here a study of the radial modes for infinitely long cylinders and cylindrical shells of general anisotropic crystals. The elastic coefficients matrix includes twenty-one independent constants. We obtain expressions in closed…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
We present a numerical model which describes the propagation of a single femtosecond laser pulse in a medium of which the optical properties dynamically change within the duration of the pulse. We use a Finite Difference Time Domain (FDTD)…