Related papers: Perfectly matched layer method for optical modes i…
Localized-surface plasmon resonance is of importance in both fundamental and applied physics for the subwavelength confinement of optical field, but realization of quantum coherent processes is confronted with challenges due to strong…
We discuss how the Perfectly Matched Layer (PML) can be adapted to numerical simulations of nonlinear and matter wave systems, such as Bose-Einstein condensates. We also present some examples which illustrate the benefits of using the PML…
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonators arrays in two dimensions. The resonator geometry is…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
A new variational theory is presented for beam loading in microwave cavities. The beam--field interaction is formulated as a dynamical interaction whose stationarity according to Hamilton's principle will naturally lead to steady-state…
Harnessing the full complexity of optical fields requires complete control of all degrees-of-freedom within a region of space and time -- an open goal for present-day spatial light modulators (SLMs), active metasurfaces, and optical phased…
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are…
We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser and the optical cavity mode…
Multimode cavity optomechanical systems allow light to couple otherwise non-interacting mechanical resonators, enabling non-Hermitian phenomena such as exceptional points, where eigenfrequencies and eigenvectors of coupled modes coalesce.…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
Quasi-phase-matching (QPM) is a widely adopted technique for mitigating stringent momentum conservation in nonlinear optical processes such as second-harmonic generation (SHG). It effectively compensates for the phase velocity mismatch…
Image-amplifying optical cavities offer an intriguing platform for nonlinear optical processing of two-dimensional signals, with potential applications in optical information processing and optically implemented artificial neural networks.…
Applications of cavity optomechanics span from gravitational wave detection to the study of quantum motion states in mesoscopic mechanical systems. The engineering of resonators supporting strongly interacting mechanical and optical modes…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the evolution and its asymptotic state. Laboratory experiments…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…