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The theory and recent applications of waves in periodic structures are reviewed. Both the Floquet and coupled waves approach are analyzed in some detail. The theoretical part of the paper includes wave propagation in unbounded and bounded active or passive periodic media, wave scatterring from periodic boundaries, source radiation (dipole, Cerenkov, transition, and Smith-Purcell) in-periodic media, and pulse transmission through a periodic slab. The applications part covers the recent development in a variety of fields: distributed feedback oscillators, filters, mode convertors, couplers, second-harmonic generators, deflectors, modulators and transducers in the fields of integrated optics and integrated surface acoustics. We also review the work on insect compound eyes, mehanical structures ocean waves, pulse compressions, temperature waves, and cholestric liquid crystals. Particles interaction with crystals is briefly reviewed, especially in the case of zeolite crystals and supelattices. Recent advances in fabrication techniques for very fine gratings me also covered. Finally, speculations about future problems and development in the field of waves in periodic structures are given.
C. Elachi (Thu,) studied this question.
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