Diffraction analysis of perfectly conducting surface-relief gratings

Yon-Lin Kok, Purdue University

Abstract

Two types of surface-relief gratings are considered in this thesis. They are the rectangular-groove corrugated grating (one dimensional surface variation) and the doubly periodic grating corrugated with cubical cavities (two dimensional surface variation). I investigate the problem of a linearly polarized electromagnetic wave scattered by such gratings with the assumption that the metallic material of the grating be perfectly conducting. In the diffraction analysis for both of the grating structures, electromagnetic field functions are directly obtained from the Helmholtz wave equation without approximations. According to Floquet's theorem, the fields above the grating can be expanded in terms of Rayleigh expansions while the fields inside the grooves or the rectangular cavities are represented as Fourier series consisting of sinusoidal eigen functions. I applied the conventional mode-matching method and the spectral iteration method to compute the phase values and the efficiencies of the diffracted waves. These methods could only produce solutions of low accuracy in the sense that only flux conservation criterion is satisfied. When one attacks the solution of high accuracy where the boundary conditions of the field function are strictly enforced almost everywhere, it is found that the singularities of the field function at the groove edges make the computations numerically unstable. I successfully resolved this problem by exploiting the solution techniques of Riemann-Hilbert problems in complex variable theory. This analytical technique faithfully reproduces the function singularities present in the fields. Results were readily derived for the singly periodic case, which described the detail mechanism of the polarization rotation phenomenon in the diffracted electromagnetic waves. For the doubly periodic grating diffraction problem, the mode-matching method generates fairly flux-conserved results when the incident wavelength is greater than at least one of the grating periods. I examined the variations of the optical spectrum with respect to the relevant scattering parameters that include the wave incident angles, wavelength, polarization directions and the grating dimensions. The specular order diffraction efficiency is found to depend mainly on the cavity's dimension rather than the grating periods, which introduces a new type of grating anomalies.

Degree

Ph.D.

Advisors

Gallagher, Purdue University.

Subject Area

Optics

COinS