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Chapter 19:
Analytical Theory for Efficient Surface-Relief Gratings in the Resonance Domain
Surface-relief gratings are widely used in a variety of applications such as planar optics, optical communications, grating waveguide structures, ultrashort laser pulse shaping and spectroscopy. Typically, they are capable of wide angular and spectral selectivities and are easy to replicate for mass production. When the periods of such gratings approach that of the illumination wavelength, they are considered to operate in the resonance domain where only three diffraction orders +1st, 0, −1st are nonevanescent. The analysis of surface-relief gratings in the resonance domain is usually done by numerical methods that are based on rigorous diffraction theory and deals with gratings of given parameters. Common methods involve staircase “z calculations” for obtaining numerical solutions with a large number of diffraction orders. However, these cannot deal with the specific features of resonance-domain diffraction gratings. Thus, other numerical methods have been developed for resonance-domain surface-relief gratings with given parameters in order to determine their diffraction efficiency. Unfortunately, it is difficult to exploit these for optimizing the parameters and trade-offs that may be available for the gratings. In this chapter, a new approach for analyzing resonance-domain surface-relief gratings is presented. The approach is based on obtaining “equivalent” sinusoidal graded-index gratings that can be analyzed with well-established volume gratings theory and experimental evidence, thereby leading to analytic solutions. With these solutions, it is possible to determine the optimal period, depth and groove shape of the surface-relief gratings that will provide high diffraction efficiency in the 1st order while suppressing the −1st order, according to the Bragg condition.
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