相关论文: Resonant modes in triangular dielectric cavities
An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum…
Topological insulators (TIs) are quantum materials combining insulating bulk properties with conductive surface states protected by time-reversal symmetry. Their unique electromagnetic behavior originates from the topological…
We investigate the internal observability of the wave equation with Dirichlet boundary conditions in a triangular domain. More precisely, the domain taken into exam is the half of the equilateral triangle. Our approach is based on Fourier…
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…
We study the laser regime of terahertz (THz) emission from a semiconductor microcavity in the strong coupling regime, where optical transitions between upper and lower exciton-polariton modes are allowed due to the mixing of the upper mode…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
We demonstrate harmonic mode-locking in a semiconductor VCSEL using polarization-controlled delayed feedback. By integrating a rotatable $\lambda$/2-plate within an external cavity, we achieve precise control over pulse multiplicity and…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
Exterior Dirichlet problems for two-dimensional lattice waves on the semi-infinite triangular lattice are considered. Namely, we study Dirichlet problems for the two-dimensional discrete Helmholtz equation in a plane with a hole. New…
Self-complementary metasurfaces have gained significant attention due to their unique frequency-independent transmission and reflection properties and the possibility of the polarization transformation of plane waves. In this paper, we…
Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite, and challenging for iterative solvers, particularly at high…
The resemblance between electrons and optical waves has strongly driven the advancement of mesoscopic physics. However, electron waves have yet to be understood in open cavity structures which have provided contemporary optics with rich…
A rigorous analytical approach is applied to solve the eigenvalue problem for a pair of circular dielectric cylinders with complex permittivity. This approach relies on field expansion in terms of two sets of orthogonal azimuthal modes,…
We develop a non-perturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory allowing to include accurately…
Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index $n>1$. The outer resonances can be verified as the resonances which survive only outside the cavity in the small…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
Radiative emission from an open-ended unflanged planar dielectric waveguide is studied for the case of TM polarization on the basis of an iterative scheme. The first step of the scheme leads to approximate values for the reflection…
We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…