Resonant state expansion applied to planar open optical systems

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 Green's 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

Resonant state expansion applied to two-dimensional open optical systems

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution

Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation

Resonant-state expansion applied to three-dimensional open optical systems

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 Green's 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

η\eta-meson in nuclear matter

The $\eta$-nucleon ($\eta$N) interactions are deduced from the heavy baryon chiral perturbation theory up to the next-to-leading-order terms. Combining the relativistic mean-field theory for nucleon system, we have studied the in-medium properties of $\eta$-meson. We find that all the elastic scattering $\eta$N interactions come from the next-to-leading-order terms. The $\eta$N sigma term is found to be about 280$\pm$130 MeV. The off-shell terms are also important to the in-medium properties of $\eta$-meson. On application of the latest determination of the $\eta$N scattering length, the ratio of $\eta$-meson effective mass to its vacuum value is near $0.84\pm0.015$, while the optical potential is about $-(83\pm5)$ MeV, at the normal nuclear density.Comment: 8 pages, 3 figures, to appear in PRC, many modification

Retardation turns the van der Waals attraction into Casimir repulsion already at 3 nm

Casimir forces between surfaces immersed in bromobenzene have recently been measured by Munday et al. Attractive Casimir forces were found between gold surfaces. The forces were repulsive between gold and silica surfaces. We show the repulsion is due to retardation effects. The van der Waals interaction is attractive at all separations. The retardation driven repulsion sets in already at around 3 nm. To our knowledge retardation effects have never been found at such a small distance before. Retardation effects are usually associated with large distances

Excitons in T-shaped quantum wires

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/Al$_{x}$Ga$_{1-x}$As and In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction $x$. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/Al$_{x}$Ga$_{1-x}$As wires we obtain an upper limit for the binding energy of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical Review

High-multipolar effects on the Casimir force: the non-retarded limit

We calculate exactly the Casimir force or dispersive force, in the non-retarded limit, between a spherical nanoparticle and a substrate beyond the London's or dipolar approximation. We find that the force is a non-monotonic function of the distance between the sphere and the substrate, such that, it is enhanced by several orders of magnitude as the sphere approaches the substrate. Our results do not agree with previous predictions like the Proximity theorem approach.Comment: 7 pages including 2 figures. Submitted to Europjysics Letter