where V 2 is the two-dimensional Laplace operator and k is the wavenumber of the radiation field. The function Vstands for a typical component of the electric or magnetic field. In cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hn (kr ) exp (int~), where Hn is the Hankel function of integer order n while r and ot are a radial and an angular coordinate, re...

In this paper all optical ultra compact 4:2 encoder is proposed and designed using two dimensional photonic crystals (PC). The structure has silicon rods of refractive index 3.4 embedded in air host by creating line defects hexagonal lattice platform. analysis the design done for various experimental values radius, constant pitch finite difference time domain (FDTD) plane wave expansion (PWE) m...

The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material.  The freque...

(paraxial wave equation) in bipolar coordinate system. A new type of exact solution of the reduced 3 dimensional spatial PWE (paraxial wave equation) for the case of bipolar coordinates is presented here. First, we consider a self-similar representation of the solution in a bipolar coordinate system, the second we additionally reduce PWE under a proper paraxial assumption. Analyzing the structu...

The solution of Helmholtz and Maxwell equations by integral formulations (kernel in exp(i kr)/r) leads to large dense linear systems. Using direct solvers requires large computational costs in O(N(3)). Using iterative solvers, the computational cost is reduced to large matrix-vector products. The fast multipole method provides a fast numerical way to compute convolution integrals. Its applicati...

• A model of locally resonant piezoelectric/elastic phononic crystal double-layer nanobeam is proposed. Band structures with nonlocal effects are calculated by plane wave expansion method. Symmetric and antisymmetric bands divided. Influences various parameters on band discussed. The paper proposed a (LR) (PC) periodically attached “spring-mass” resonator additional spring between upper lower n...

A new finite plane wave series expansion for spherical wave functions of the first kind is presented in this paper. The formulation converts the spherical wave function described in the spherical coordinate system into a series of plane wave functions represented in the Cartesian coordinate system. The series expansion will be very useful in modal analysis of three dimensional guided wave struc...

Digital encoders are one of the key devices required in optical communication and digital signal processing systems. In this paper, a new photonic crystal structure is used to design all-optical 4 × 2 encoder constructed from GaAs rods with square lattice pentane background based on plasmonic effect. Gold have also been at interface dielectric lines defect, which create properties into structur...

In this paper, a Photonic Crystal Ring Resonator (PCRR) based demultiplexer is proposed and designed to drop four different channels. The proposed structure is consists of bus waveguide, dropping waveguide and butterfly shaped ring resonator. The demultiplexer performance parameters such as transmission efficiency, dropping efficiency, crosstalk, quality factor and resonant wavelength are inves...