We study second harmonic generation (SHG) from non-centrosymmetric nanocrystals under linearly polarized (LP) and circularly polarized (CP) excitations. Theoretical models are developed for SHG from nanocrystals under both plane-wave and focused excitations. We find that the focused excitation reduces the polarization dependency of the SHG signal. We show that the SHG response under CP excitati...

In this investigation, by an analytical approach, the influence of several key parameters, especially temperature on sound isolation capacity symmetrically finite orthotropic laminated composite plate is studied. The modeled with classic thin-plate theory and assumed to be simply supported all four sides. incident acoustic pressure as a harmonic plane wave impinging at arbitrary angle. transmis...

We study a scattering-assisted second harmonic generation process of a structured fundamental wave, whose phase front is periodically modulated, in a homogenous nonlinear medium. Scattering-assisted multiple-conical second harmonic in a one-dimensional structured fundamental wave and second harmonic belts in two-dimensional cases were observed. The experimental results are consistent with our a...

We calculate the Green’s functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green’s functions which describe scattering or bound states (depending on the specific potential in each case) are obtained exactly using an algebraic method related to the SO(2,1) Lie group. From these Green’s functions we obt...

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes b...

Parametric simultaneous solitary wave (simulton) excitations are shown possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example we consider the nonlinear coupling between the upper cutoff mode of acoustic branch (as a fundamental wave) and the upper cutoff mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness appr...

The commonly used periodic patterning for quasi phase-matching plane-waves is theoretically adequate for completely depleting and transferring a fundamental wave to its second harmonic. However, when working with Gaussian beams the conversion efficiency of such a design lacks due to the inherent Gouy phase shift and the spatially varying beam profile, yielding roughly 88 % conversion efficiency...

However, in reality most interfaces are not planar on both micro and macro scales. The purpose of this study is to investigate the interaction between elastic waves and a slightIy non-planar interface. The method of asymptotic analysis is used to derive elose form solutions for the problem of reflection and scattering of a time-harmonic SH-wave at a slightly, but otherwise arbitrarily, non-plan...

ABSTRACT. An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic and rigid surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML pro...

We consider the scattering of time harmonic electromagnetic plane waves by a bounded inhomogeneous medium and show that under certain assumptions a lower bound on the index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. It is then shown by numerical examples that this eigenvalue can be determined from a knowledge of the far fi...