Related papers: Nonlinear eigenvalue problem for optimal resonance…
Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…
We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…
Micron-scale optical cavities are produced using a combination of template sphere self-assembly and electrochemical growth. Transmission measurements of the tunable microcavities show sharp resonant modes with a Q-factor>300, and 25-fold…
We consider the problem of enabling robust range estimation of eigenvalue decomposition (EVD) algorithm for a reliable fixed-point design. The simplicity of fixed-point circuitry has always been so tempting to implement EVD algo- rithms in…
Cavities with high quality (Q) factor and small mode-volume are crucial to realize high performance nanolasers suitable for optical interconnects. In this work, we propose a novel one-dimensional photonic crystal nanobeam cavity design with…
We demonstrate that the resonance frequencies of high-Q microcavities in two-dimensional photonic crystal membranes can be tuned over a wide range by introducing a subwavelength dielectric tip into the cavity mode. Three-dimensional…
We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency $\Omega . $ This method makes it easy to find the dominant part of the solution which…
Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for…
We study and realize asymmetric fiber-based cavities with optimized mode match to achieve high reflectivity on resonance. This is especially important for mutually coupling two physical systems via light fields, e.g. in quantum hybrid…
We present the optical and mechanical design of a mechanically compliant quasi-two-dimensional photonic crystal cavity formed from thin-film silicon in which a pair of linear nanoscale slots are used to create two coupled high-$Q$ optical…
Strong light interaction with a subwavelength object has been a long pursuing goal with difficulties mainly arising from the diffraction limit. We propose a high finesse cavity with one mirror made of a subwavelength resonant particle as a…
Small manufacturing-tolerant photonic crystal cavities are systematically designed using topology optimization to enhance the ratio between quality factor and mode volume, Q/V. For relaxed manufacturing tolerance, a cavity with bow-tie…
We study certain "geometric-invariant resonant cavitie"' introduced by Liberal et. al in a 2016 Nature Comm. paper, modeled using the transverse magnetic reduction of Maxwell's equations. The cross-section consists of a dielectric inclusion…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
We present a simple method to tune optical micro- and nanocavities with picometer precision in the resonant wavelength, corresponding to an effective sub atomic monolayer control of the cavity dimension. This is obtained through resonant…
We investigate the use of guided modes bound to defects in photonic crystals for achieving double resonances. Photoluminescence enhancement by more than three orders of magnitude has been observed when the excitation and emission…
We discuss the optimization of optical microcavity designs based on 2D photonic crystals for the purpose of strong coupling between the cavity field and a single neutral atom trapped within a hole. We present numerical predictions for the…
The nonlocal order parameter equation for nonlinear optical resonator is approximated in the limit of high Fresnel number by the Swift- Hohenberg equation. The exact soliton and periodic solutions of the Swift- Hohenberg equation for…
In this paper we obtain bounds for the decay rate in the $L^r (\rr^d)$-norm for the solutions to a nonlocal and nolinear evolution equation, namely, $$u_t(x,t) = \int_{\rr^d} K(x,y) |u(y,t)- u(x,t)|^{p-2} (u(y,t)- u(x,t)) \, dy, $$ with $ x…