Related papers: Extending completeness of the eigenmodes of an ope…
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…
We generalize normal mode expansion of Green's tensor $\bar{\bar{G}}(\bf{r},\bf{r}')$ to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to…
A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the…
We establish high energy $L^2$ estimates for the restriction of the free Green's function to hypersurfaces in $\mathbb{R}^d$. As an application, we estimate the size of a logarithmic resonance free region for scattering by potentials of the…
We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations…
The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…
We give details on how to calculate spectral functions and Green's functions for finite systems using the Chebyshev polynomial expansion method. We apply the method to a finite Anderson impurity system, and furthermore give details on how…
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering at all frequencies via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE…
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is formulated for Transverse Electrodynamic modes of an effectively $2$-dimensional system. The RSE is a perturbation theory based on the Lippmann…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
This paper develops a finite-difference analogue of the boundary integral/element method for the numerical solution of two-dimensional exterior scattering from scatterers of arbitrary shapes. The discrete fundamental solution, known as the…
We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems.…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the…
A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…
We calculate the Green's functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green's functions which describe scattering or bound states (depending…
We uncover a novel mechanism for superscattering of subwavelength resonators closely associated with the physics of bound states in the continuum. We demonstrate that superscattering occurs as a consequence of constructive interference…
Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a…