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Theories of singly and doubly periodic diffraction gratings


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Botten, LC 1978 , 'Theories of singly and doubly periodic diffraction gratings', PhD thesis, University of Tasmania.

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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

Item Type: Thesis - PhD
Authors/Creators:Botten, LC
Keywords: Diffraction gratings
Copyright Holders: The Author
Copyright Information:

Copyright 1978 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (Ph.D.)--University of Tasmania, 1978. Includes bibliographical references

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