Bloch modes at the surface of a photonic crystal interacting with a waveguide.

We theoretically studied the influence of an infinite set of waveguides on the evanescent field of Bloch waves at the surface of a one-dimensional photonic crystal (PC) excited by a TE Gaussian beam undergoing total internal reflection. The set of waveguides is regarded as a periodic inhomogeneous medium with period a. Numerical results are presented for the case in which a is greater than λ, which is the wavelength used to excite the surface mode. When the waveguide tip is very close to the surface of the PC, a fraction of the surface wave is reflected by the tip, producing an interference pattern that can be observed in the near field. In this case, the system simulates scanning tunneling optical microscopy in 2D geometry, and an image of the field distribution of the surface mode is obtained by quantifying the flux energy throughout the waveguide.

Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor.

Scattering of s-polarized electromagnetic planes waves from a film, with a shallow random rough one-dimensional surface, bounded by vacuum and a perfect conductor is calculated. An integral equation that relates the amplitude of the scattered field to the incident wave is found by use of the Rayleigh hypothesis. The integral equation is solved numerically and by use of the perturbation theory, up to the fourth order in the surface profile function. In the angular dependence of the incoherent part of the differential reflection coefficient, the backscattering peak and two additional satellite peaks are observed, owing to two guided waves supported by the film. Analysis of the perturbation solution reveals that the background scattering exhibits minima and maxima as functions of the thickness. By studying the behavior of the scattering as a function of the absorption index of the film, it is shown that the amplitudes of the peaks are low when k approximately 10(-2) and high when k approximately 10(-4).

Method for calculating optical coating stabilities.

The reflectivity R of a multilayer stack and its first and second derivatives with respect to the phase change are derived here by a recursive method. These equations improve the determination of stability conditions for coatings and widen the applications to treatments other than antireflection coatings, as reported by Mouchart [Appl. Opt. 16, 2486 (1977)]. Some calculations are performed on grazing incidence antireflection coatings, all-dielectric mirrors, and bandpass filters with non-quarter-wave layers.