Band structure and spatial electromagnetic field distribution in the 2D photonic crystals with nontrivial elementary cell

Periodic systems with the silver-based waveguides are discussed. The elementary cell in such systems consists of several waveguides. We employ the multiple scattering formalism based on solving the Maxwell equations solution for a single cylinder. The method involving the lattice-sum transformation into a fast convergent series is implemented. This enables us not only to increase the computational accuracy but also to reduce the necessary time for performing the numerical simulation. It is shown that under condition of nonzero propagation constant, the guided modes located closely in the frequency region appear. The number of these modes equals the number of waveguides in the elementary cell of the system. As a quasi-wave vector approaches the edge of the Brillouin zone, the frequency of these modes decreases. Increasing the propagation constant affects the modes shifting them towards the high frequency region. It is also shown that it is possible to match simultaneously wave vector and frequency of guided modes in the zigzag shaped systems.

Theory for anomalous refraction of visible light by the plane array of metallic waveguides

The effect of anomalous or negative angle refraction in the periodic systems of silver waveguides is investigated. This effect arises solely due to the waveguide interaction and requires the system of specific geometrical configuration. It is also shown that the propagation constant provides a flexible mechanism to manipulate the anomalous refraction. We employ the multiple scattering formalism based on the exact solution of the Maxwell equations for a single waveguide problem. Also the method based on the lattice sum transformation into a fast convergent series is involved. This technique dramatically decreases the time necessary for performing the numerical simulations and increases the accuracy of the computational process. It is shown that all the directions, which the periodic system is possible to radiate, can be obtained beforehand, i.e. analytically, without numerical simulations. The latter ones are needed to determine energy the flux going into each of those directions.

Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies

This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called ‘Wood anomaly frequencies’. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.

Long-ranged contributions to solvation free energies from theory and short-ranged models

Long-standing problems associated with long-ranged electrostatic interactions have plagued theory and simulation alike. Traditional lattice sum (Ewald-like) treatments of Coulomb interactions add significant overhead to computer simulations and can produce artifacts from spurious interactions between simulation cell images. These subtle issues become particularly apparent when estimating thermodynamic quantities, such as free energies of solvation in charged and polar systems, to which long-ranged Coulomb interactions typically make a large contribution. In this paper, we develop a framework for determining very accurate solvation free energies of systems with long-ranged interactions from models that interact with purely short-ranged potentials. Our approach is generally applicable and can be combined with existing computational and theoretical techniques for estimating solvation thermodynamics. We demonstrate the utility of our approach by examining the hydration thermodynamics of hydrophobic and ionic solutes and the solvation of a large, highly charged colloid that exhibits overcharging, a complex nonlinear electrostatic phenomenon whereby counterions from the solvent effectively overscreen and locally invert the integrated charge of the solvated object.