Related papers: Perfectly matched layer method for optical modes i…
In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function $f$ has decay $f=O(r^{-1-\varepsilon}) $ for…
We develop a generalized non-Hermitian Hamiltonian formalism for guided resonances in photonic crystal slabs, derived directly from Maxwell's equations through a systematic guided-mode expansion. By expanding the electromagnetic fields over…
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard type one dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time independent classical Hamiltonian is of non-standard…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite…
In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework,…
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
We present several applications of mode matching methods in spectral and scattering problems. First, we consider the eigenvalue problem for the Dirichlet Laplacian in a finite cylindrical domain that is split into two subdomains by a…
The continuous advancements in ultrafast lasers, characterized by high pulse energy, great average power, and ultrashort pulse duration, have opened up new frontiers and applications in various fields such as high-energy-density science. In…
With a view to having further insight into the mathematical content of the non-Hermitian Hamiltonian associaterd with the diffusion-reaction (D-R) equation in one dimension, we investigate (a) the solitary wave solutions of certain types of…
We use the full nonlinear bifurcation theory as a powerful methodology to thoroughly classify and predict the phonon lasing dynamics in optomechanical cavities. We exemplify its scope in the very relevant and so far vaguely explored…
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,…
The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
We report temporal and spectral domain observation of regenerative oscillation in monolithic silicon heterostructured photonic crystals cavities with high quality factor to mode volume ratios (Q/V). The results are interpreted by nonlinear…