Related papers: Nonlinear eigenvalue problem for optimal resonance…
Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are…
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound…
Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly…
Optical cavities operating in the near-concentric regime are the fundamental tools to perform high precision experiments like cavity QED applications. A strong focusing regime unfortunately is prone to excite higher-order modes.…
Subwavelength dielectric structures offer an attractive low loss alternative to plasmonic structures for the development of resonant optics functionality such as metamaterials. Nonspherical like rectangular structures are of most interest…
In electrical engineering, for example during the design of superconducting radio-frequency cavities, eigenmodes must be identified based on their field patterns. This allows to understand the working principle, optimize the performance of…
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions,…
We develop a theory for non-degenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a…
This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…
We present a unified description of extremal metrics for the Laplace and Steklov eigenvalues on manifolds of arbitrary dimension using the notion of $n$-harmonic maps. Our approach extends the well-known results linking extremal metrics for…
The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic…
Modal volumes at the nano-scale, much smaller than the "diffraction-limit", with appreciable quality factors, are calculated for a dielectric cavity embedded in a space between metal plates. The modal field is bounded between the metal…
Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads…
This work deals with theoretical and numerical aspects related to the behavior of the Steklov-Lam\'e eigenvalues on variable domains. After establishing the eigenstructure for the disk, we prove that for a certain class of Lam\'e…
The capacitance of arbitrarily shaped objects is reformulated in terms of the Neumann-Poincar\'{e} operator. Capacitance is simply the dielectric permittivity of the surrounding medium multiplied by the area of the object and divided by the…
Radio frequency (RF) cavities are commonly used to accelerate charged particle beams. The shape of the RF cavity determines the resonant electromagnetic fields and frequencies, which need to satisfy a variety of requirements for a stable…
The concern of this paper is to clarify a relationship between the curvatures at infinity and the spectral structure of the Laplacian. In particular, this paper discusses the question of whether there is an eigenvalue of the Laplacian…
We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on…
We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-\Delta + V - i\epsilon x^2$, $|V(x)|\leq C…
Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in…