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Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances whilst simultaneously being physically compact.…
Open-access microcavities are emerging as a new approach to confine and engineer light at mode volumes down to the $\lambda^3$ regime. They offer direct access to a highly confined electromagnetic field while maintaining tunability of the…
Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide,…
We construct a model which describes a recently performed experiment (Phys. Rev. A 64, 050301(R) (2001)) in which an entangled state between two modes of a single cavity is built. Environmental effects are taken into account and the results…
We present the results of experimental and theoretical study of irregular, tetrahedral microwave networks consisting of coaxial cables (annular waveguides) connected by T-joints. The spectra of the networks were measured in the frequency…
We derive relationships between various types of small misalignments on a triangular Fabry-Perot cavity and associated geometrical eigenmode changes. We focus on the changes of beam spot positions on cavity mirrors, the beam waist position,…
The spontaneous emission spectrum for a three level cascade configuration atom in a single mode high-Q cavity coupled to a zero temperature reservoir of continuum external modes is determined from the atom-cavity mode master equation using…
We have developed the mode matching technique that is based on the using the eigenmodes of circular cavities and the eigenwaves of circular waveguides as the basic functions for calculation the properties of nonuniform disc-loaded…
A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between…
We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…
Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
Despite the moduli space of triangles being three dimensional, we prove the existence of two triangles which are not isometric to each other for which the first, second and fourth Dirichlet eigenvalues coincide, establishing a numerical…
We have developed a circularly polarized dielectric rutile (TiO$_2$) cavity with a high quality-factor that can generate circularly polarized microwaves from two orthogonal linearly polarized microwaves with a phase difference of $\pm…
We study photon creation in a cavity with two perfectly conducting moving mirrors. We derive the dynamic equations of the modes and study different situations concerning various movements of the walls, such as translational or breathing…
We prove sharp spectral gap estimates on compact manifolds with integral curvature bounds. We generalize the results of Kr\"oger (Kr\"oger '92) as well as of Bakry and Qian (Bakry-Qian '00) to the case of integral curvature and confirm the…
In the past years quasi-conformal mapping has been typically used to design broadband electromagnetic cloaks. However, this technique has some inherit practical limitations such as the lateral beam shift, rendering the device visible or…
The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we…
We use public V-band imaging data from the wide-angle surveys conducted by the ESO Imaging Survey project (EIS) to further investigate the nature of the EIS galaxy cluster candidates. These were originally identified by applying a…
It has been proposed that microwave cavities can be used in a photon regeneration experiment to search for hidden sector photons. Using two isolated cavities, the presence of hidden sector photons could be inferred from a 'light shining…