Modal analysis method to describe weak nonlinear effects in metamaterials

Abstract

We apply a rigorous eigenmode analysis to study the electromagnetic properties of linear and weakly nonlinear metamaterials. The nonlinear response can be totally described by the linear eigenmodes when weak nonlinearities are attributed to metamaterials. We use this theory to interpret intrinsic second-harmonic spectroscopy on metallic metamaterials. Our study indicates that metamaterial eigenmodes play a critical role in optimizing a nonlinear metamaterial response to the extent that a poorly optimized modal pattern overwhelms the widely recognized benefits of plasmonic resonant field enhancements.

Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction

“…Hence, in the presence of DD interaction, one can get a bright soliton even for positive (repulsive) contact interaction (a > 0), which can be controlled by means of the Feshbach resonance with a tunable time-dependent magnetic field [33,34]. Further, in recent years, study of temporal and spatial modulated nonlinearities have attracted considerable attention in several areas, for example, nonlinear physics [41], optics [42][43][44] and conventional BECs [45,46,48,49].…”

Resonant dynamics of arbitrarily shaped meta-atoms

“…However, in many systems of interest, the required criteria for homogenizability are not satisfied, either because the metaatoms are not sufficiently sub-wavelength, the arrays are so small that boundary effects and radiation losses are very strong, or the arrangement is not periodic. As an alternative to homogenization, it is possible to consider the fields of a metamaterial's Bloch modes as the fundamental degrees of freedom 2 , however this suffers from many of the same limitations. In many cases the modes of individual resonators form a much more convenient basis to study the behavior of meta-atoms and resonant scatterers, since the number of excited modes is typically small.…”

Phase matching for surface plasmon enhanced second harmonic generation in a gold grating slab

“…A number of theoretical approaches [6][7][8][9][10][11][12] have been presented in the past for calculating nonlinear coefficients of periodic structures. Analytical 6,7,11 and semi-analytical 10,12 approaches are most suited for scenarios where a subwavelength unit cell consists of spatially slow-varying structures or the wavelengths of interest are significantly larger than the unit cell.…”

“…Analytical 6,7,11 and semi-analytical 10,12 approaches are most suited for scenarios where a subwavelength unit cell consists of spatially slow-varying structures or the wavelengths of interest are significantly larger than the unit cell. It will be shown that a numerical method is necessary to accurately model the SHG behavior of these periodic structures since a small geometrical modification of the unit cell can have a much stronger influence on it than linear optical properties.…”