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Modal expansion theories for singly periodic diffraction gratings

Andrewartha, JR 1981 , 'Modal expansion theories for singly periodic diffraction gratings', PhD thesis, University of Tasmania.

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This thesis reports on the analysis and development of rigorous
modal expansion techniques for determining the scattering properties of
singly-periodic diffraction gratings. Both reflection and transmission
gratings are considered, and although emphasis is given to a theoretical
study of the formalisms, many numerical results obtained with the latter
are also presented. Most of the formalisms pertain to gratings having
specific groove geometries and infinitely-conducting surfaces. However,
in two cases one or other of these constraints is removed.
Several of the established formalisms, based on a variety of nonmodal
techniques, are reviewed, and the essence of their method described.
The advantages that modal treatments have over these methods are explained,
and previous applications of the former are summarised.
Initial theoretical investigations concern the rectangular-groove
grating. Intensive studies reveal an alternative approach to the concept
of diffraction resonance anomalies. They also provide new insight into
the understanding of this grating 1s overall behaviour, including its
blazing and passing-off properties in the first-order Littrow mounting.
These ideas are usefully extended throughout the thesis to encompass the
behaviour of all gratings.
The theoretical treatment for the rectangular-groove grating is
adapted to account for the diffraction properties of three unusual
profiles which also possess a rectangular geometry. Two of these
structures consist of a transmission grating on a reflecting element,
and are shown to exhibit a pronounced resonance action. Tuning of the
various grating parameters governs the behaviour of the resonances and
indicates the potential use of these devices as a type of reflecting
Fabry-Perot interferometer. The third structure is a stepped reflection grating which proves capable of accurately mode l1 i ng the performance of
general profile gratings including those with sinusoidal and triangular
profi 1 es.
Single and bi-modal expansions are shown to provide useful field
approximations for not only the conventional rectangular-groove grating,
but also for two of the three related structures. These approximations
aid in the examination of resonances and other spectral phenomena.
Their regions of accuracy and validity are determined.
The assumption of perfect conductivity is relaxed in a formalism
which is described for dielectric and lossy metallic surfaces. The
method is tailored specifically to the rectangular-groove profile and is
one of the few modal expansion techniques appropriate to non-perfectly
conducting gratings.
The thesis concludes with the presentation of two formalisms
which employ an impedance-related condition to completely specify a set
of modal functions. The first formalism prescribes a solution for a
grating whose grooves are semi-circular in cross-section. Eigenfunctions
for a circular waveguide constitute the modal functions. The second
formalism accommodates reflection profiles of general groove crosssection,
and utilizes a superposition of the rectangular-waveguide eigenfunctions.
The first formalism is employed to evaluate in detail the
spectral performance of the semi-circular groove grating, while the second
is applied, not only to this grating, but also to the triangular and
sinusoidal groove gratings.

Item Type: Thesis - PhD
Authors/Creators:Andrewartha, JR
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