Poincaré crystal on the one-dimensional lattice

Computing One-Dimensional Global Manifolds of Poincaré Maps by Continuation

We present an algorithm to compute one-dimensional stable and unstable manifolds of saddle periodic orbits in a Poincaré section. The computation is set up as a boundary value problem by restricting the beginning and end points of orbit segments to the section. Starting from the periodic orbit itself, we use collocation routines from AUTO to continue the solutions of the boundary value problem ...

One-dimensional photonic crystal design

In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piecewise constant refractive indices we develop an algorithm to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and ...

One-dimensional controllable photonic crystal

The nonlinear one-dimensional model of controllable photonic crystals is considered. A photonic crystal is formed in a dielectric film on which the electromagnetic pump and signal waves fall. It is shown that the shape of the superlattice is controlled by the variation of the external electrostatic field imposed on the film. Thus it leads to changing boundaries of the allowed and forbidden zone...

On the Riemann property of angular lattice sums and the one-dimensional limit of two-dimensional lattice sums

On the Riemann property of angular lattice sums and the one-dimensional limit of two-dimensional lattice sums BY ROSS C. MCPHEDRAN*, I. J. ZUCKER, LINDSAY C. BOTTEN AND NICOLAE-ALEXANDRU P. NICOROVICI CUDOS, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia Department of Physics, King’s College London, The Strand, London WC2R 2LS, UK School of Mathematical Science...

Incommensurate Structure with No Average Lattice : an Example of One Dimensional Quasi-crystal