Related papers: Rigorous theory of coupled resonators
We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B {\bf 76}, 155102 (2007)], allows to study…
We present analytical, numerical and experimental investigations of electromagnetic resonant modes of a compact monofilar Archimedean spiral resonator shaped in a ring, with no central part. Planar spiral resonators are interesting as…
A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the…
The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and…
The purpose of this paper is to establish several new results about the Hodge theory of Lagrangian fibrations on (not necessarily compact) holomorphic symplectic manifolds. Let $M$ be a holomorphic symplectic manifold of dimension $2n$ that…
We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity, to explore the transition between the weak, and the ultra-strong coupling regimes of light-matter interaction. We…
In anisotropic or bianisotropic waveguides, the standard coupled mode theory fails due to the broken link between the forward and backward propagating modes, which together form the dual mode sets that are crucial in constructing couple…
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…
We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott…
We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial differentiation and integration of the profile of optical beams propagating in the waveguide. The…
The number of eigenmodes in plasmonic nanostructures increases with complexity due to mode hybridization, raising the need for efficient mode characterization and selection. Here we experimentally demonstrate direct imaging and selective…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…
Rapid design and development of the emergent ultra-wide bandgap semiconductors Ga$_2$O$_3$ and Al$_2$O$_3$ requires a compact model of their electronic structures, accurate over the broad energy range accessed in future high-field,…
Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an effective alternative, which consist of…
We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…
The single-polaron band structure of the Holstein model in one and two dimensions is studied using a new form of resummed strong-coupling perturbation theory. Well converged results are obtained for phonon frequencies of the order of the…
Unlike common devices based on ring resonators, the structure in Fig. 1.a involves not only 2$\times$2 couplers but also a 3$\times$3 coupler, which means that a 3$\times$3 transfer matrix approach is required to model the system. To the…
This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the…