Abstract

Very high frequency corrugated surfaces have become the object of increased study over recent years. With these structures, the period of the surface corrugation is of the order of, or much smaller than, the optical wavelengths with which they are used. Devices employing such corrugated surfaces have unusual and interesting polarization and diffraction characteristics. However, properties of these devices have only been understood by solving large systems of equations. Parameters which affect these solutions include corrugation period, depth, and duty cycle. In addition, the ratio of corrugation dimensions to optical wavelength is very significant. These parametric values also have a significant impact on the numerical stability of common techniques used for solving these grating problems. Usual methods of solution include iterative methods and the so-called mode matching methods. For parameter values of interest to us, we have found that these methods converge slowly, are subject to numerical instabilities, and sometimes require massive computation. We have adapted a method called the dual-series method which, through contour integration, avoids these difficult numerical problems. In addition, the dual-series method yields analytical expressions where other methods produce only numerical values.

© 1986 Optical Society of America