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We have derived the dispersion relation for double GaAs semiconductor grating, using nonlinear boundary condition approach. The grating medium is assumed to non-magnetic and it has sinusoidal undulation of angular frequency ω on both side of the film. In the limit when plasma wavevector k p is greater than k‖ wavevector of the wave, we obtained two branches in the dispersion curve which corresponds to electrostatic charge disposition on the two sides of grating. In the limiting case k p < k‖, the grating radiate the electromagnetic field in the vicinity area.

A new nonlinear-boundary-condition approach for deriving the dispersion relation on the surface of GaAs grating structures is presented. We have used the linear set of wave equations and introduced the grating nonlinearities through the boundary conditions only. We have observed that the presence of a grating splits the surface-plasmon modes into two parts and generates a band gap. This approach is simple and, in the limiting case, reduces to well known theoretical calculations. The dispersion relation is solved for thin-film and thick-film gratings, in the limit in which the dielectric constant is less than zero. The results thus obtained may be used for millimetre waves and are also applicable to the optical region.

Electromagnetic excitation, inside small volumes, results in perturbations which play an important role in the validation of theoretical formulations. Efforts to catch a glimpse of the action inside of the small space, can aid better thin film designs. In the non-linear anisotropic regime the results of such interactions provide important insights into the bulk level behavior of matter. Using this approach, a zinc oxide (ZnO) based photonic crystal is designed with spherical air voids. A Gaussian continuous wave excitation of the refractive index contrast (ZnO=1.9 and Air =1) photon waveguide generated thus, is characterized for the redistribution of electromagnetic field. When, centered at a specific wavelength (1.9 µm), the graph of the frequencies that can exist inside the crystal, is plotted against the limited k-space vector. The dispersion diagram that emerges shows a band of frequency states that cannot exist inside such a design. Physically this constitutes a k-space which is devoid of any detectable disturbances. Crystallographically, the reduced Brilluoin zone can be used to make a thin layer of ZnO that can act as a frequency stop layer, in a real multilayered photoelectric device.

In this work, we developed a unique mathematical model to solve dispersion relation for surface polaritons (SPs) in artificial composite materials grating. Here, we have taken two types of materials for analysis. In the first case, the grating composed of epsilon-negative (ENG) material and air interface. In second case, grating composed of left-handed materials (LHMs) and ENG medium interface is considered. The dispersion curves of both p and s polarized SPs modes are obtained analytically. In the case of ENG grating and air interface, polaritons dispersion curves exist for p-polarization only, whereas for LHM grating and ENG medium interface, the polaritons dispersion curves for both p and s polarization are observed.