Dispersed stable states spectrum of the wave equation with space-time periodic potential
1 Los Alamos National Laboratory - Los Alamos, NM 87544, USA
2 Ohio State University - Columbus, OH 43210, USA
Received: 16 August 2013
Accepted: 28 August 2013
We study the stable states of the wave equation with d-spatial and 1-time dimensions and with space-time periodic potential. The dispersed stable states spectrum of such -periodic wave equation is due to the incommensurability of the speed of light and the ratio of space and time periods. A Bloch-Floquet analysis leads to a -cube as a reduced Brillouin zone, but because of the speed incommensurability the stable states in this cube may form a spectrum of sets with a reduced dimensionality. For electromagnetic waves in photonic crystals the medium may amplify some waves with lengths fitting the crystal lattice. The energy from the external field can be pumped to the waves via the dipole moment oscillations.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 42.70.Qs – Photonic bandgap materials / 78.67.Pt – Multilayers; superlattices; photonic structures; metamaterials
© EPLA, 2013