Application of modal techniques to multiply configured gratings

The main theme of this thesis is the development of new rigorous formalisms to describe the diffraction properties of multiply configured, perfectly conducting, gratings with simple groove geometries. This class of gratings is composed of singly or doubly periodic elements. The formalisms are derived using modal techniques which are particularly suited to solving the diffraction properties of these gratings. Considerable attention is paid to the far infrared properties of the gratings with the aim of describing their performance as interference filters used in this wavelength range. The thesis contains a general review of the previous contributions to the theoretical study of diffraction gratings, including a review of investigations which have been undertaken into the properties of far infrared interferometers. This is followed by a discussion of a formalism describing the diffraction properties of lossless dielectric and finitely conducting gratings. This study represents one of the first generalisations of a modal formalism to structures which are other than perfectly conducting, and is a step towards the solution of the diffraction properties of capacitive or finitely conducting inductive grids. The remainder of the thesis is concerned with perfectly conducting gratings having basically rectangular geometries. The structures considered are either singly periodic or doubly periodic. The double periodicity results either directly from the geometry of the element (as for example in the case of inductive grids) or is contrived by suitable arrangement of singly periodic elements. The performance of singly periodic interference filters, composed of two or more lamellar gratings, is then described. The first such structure to be considered is the double grating and the diffraction properties of this arrangement are described in detail. The associated analysis is performed by explicitly specifying the fields in each groove region by a modal expansion. The geometry of the double grating is then generalised to consider a grating composed of a stack of an arbitrary number of singly periodic elements, and the properties of this structure are analysed using a new rigorous multiple scattering technique. These singly periodic gratings have application as Fabry-Perot interferometers only for radiation having a particular linear polarization. If the incident radiation is unpolarized it is necessary to use doubly periodic devices such as inductive grids. For this reason the performance of the double grid interferometer is considered, and a rigorous formalism for it is derived using an approach similar to that used for the double grating. The properties of multi-element grids are then analysed using a multiple scattering approach. Interesting conservation properties for lossless singly and doubly periodic structures are presented and are related to the geometrical symmetry of the structure. These relations provide constraints on the scattering matrices of the diffraction system. Finally, two formalisms are presented describing the diffraction properties of a structure which is doubly periodic by virtue of the positioning of its two singly periodic elements. This arrangement is termed the crossed lamellar transmission grating. The first formalism uses a modal expansion to describe the field within the grooves of each element, while the second employs a rigorous multiple scattering approach. In particular, it is demonstrated that this structure has application as a solar heat mirror.