Theories of singly and doubly periodic diffraction gratings

In this thesis, theories for the solution of diffraction problems involving both singly periodic and doubly periodic structures are presented. The studies have been motivated by two fields of application. The first of these is the use of singly periodic gratings in spectrographic instruments, with particular attention being devoted to diffraction anomalies and possible means for their reduction. The second pertains to the use of diffracting structures in systems having solar absorbing behaviour with the aim of optimizing their selective properties. The unity of the thesis rests not in the applications of the theories but in the rigorous electromagnetic methods used to establish the variety of formalisms presented. The first three chapters are essentially introductory in their nature and contain an extensive review of integral formalisms for singly periodic gratings. Both infinite conductivity and finite conductivity theories are discussed and are applied to the study of higher order blaze effects, groove depth determination and the characterization of anomalies of the 'plasmon' type. An original formalism for multi-layer transmission gratings is presented in chapter 4. The theory is then used in chapter 5 for the optimization of the selective properties of thin film solar absorbers. Surface roughening, modelled using a singly periodic profile modulation, is shown to improve the absorptance by up to ten percent. Chapter 6 contains a new \integral-modal\" treatment of the old problem involving the diffraction of a plane wave by a perfectly conducting grating having a triangular profile with a right-angled apex. This is included since many of the concepts discussed therein are of relevance to the following chapter. The next section chapter 7 is concerned with the diffraction properties of bi-metallic gratings (which are structures composed of two species of metals). The evolution of this study is discussed and in doing so a number of theories culminating in a new and completely general formalism are presented. Numerical results obtained reveal that anomaly suppression can be achieved by overcoating the \"off-blaze\" facet of a triangular grating with a poorly conducting metal. The remaining three chapters are devoted to the study of doubly periodic structures using modal formalisms. Chapter 8 is concerned with the diffraction properties of a crossed lamellar transmission grating which is an inductive grid whose two mutually orthogonal axes of periodicity lie in spatially separated planes. The theory and a new amplitude constraint appropriate to a general Littrow mount are given together with some numerical results indicating promising solar selective behaviour. The following chapter considers a singly periodic double grating composed of a pair of spatially separated lamellar transmission gratings. The theoretical formalism is presented together with a detailed discussion of the application of this structure as a long wavelength Fabry-Perot interferometer. Also contained in chapter 9 are the results of a comprehensive search for conservation relations (phase constraints) pertaining to singly .periodic symmetric gratings. Finally in chapter 10 a theory for inductive grids having circular apertures is discussed. It is shown that by inserting dielectric plugs in the aperture and surrounding the grid with a symmetric pair of lossless thin films the degraded transmission properties of such grids (caused by low hole to area fractions) can be substantially overcome."