Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userResonant-state expansion for a simple dispersive medium
88
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is applied to media with an Ohms law dispersion, in which the frequency dependent part of the permittivity scales inversely with the frequency, corresponding to a frequency-independent conductivity. This dispersion has only a single pole at zero frequency, which is already present in the non-dispersive RSE, allowing to maintain not only the linearity of the eigenvalue problem of the RSE but also its size. Media which can be described by this dispersion over the relevant frequency range, such as optical glass or doped semiconductors, can be treated in the RSE without additional complexity. Results are presented using analytically solvable homogeneous spheres, for doped silicon and BK7 glass, both for a perturbation of the system going from non-dispersive to dispersive media and the reverse, from dispersive to non-dispersive media.
rate research
Read More
The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Greens function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method.
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Greens function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude.
A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is based on the expansion of the Greens function into the resonant states of the system. These can be calculated by any means, including the popular finite element and finite-difference time-domain methods. However, using the resonant-state expansion with a spherically-symmetric analytical basis, such as that of a homogeneous sphere, allows to determine a complete set of the resonant states of the system within a given frequency range. Furthermore, it enables to take full advantage of the expansion of the field outside the system into vector spherical harmonics, resulting in simple analytic expressions. We verify and illustrate the developed approach on an example of a dielectric sphere in vacuum, which has an exact analytic solution known as Mie scattering.
We study the guided modes in the wire medium slab taking into account both the nonlocality and losses in the structure. We show that due to the fact that the wire medium is an extremeley spatially dispersive metamaterial, the effect of nonlocality plays a critical role since it results in coupling between the otherwise orthogonal guided modes. We observe both the effects of strong and weak coupling, depending on the level of losses in the system.
The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
