Sources of localized waves
The synthesis of two types of Localized Wave (L W) pulses is considered; these are the 'Focus Wave Model (FWM) pulse and the X Wave pulse. First, we introduce the modified bidirectional representation where one can select new basis functions resulting in different representations for a solut...
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| Format: | Others |
| Language: | en |
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Virginia Tech
2014
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| Online Access: | http://hdl.handle.net/10919/38460 http://scholar.lib.vt.edu/theses/available/etd-06062008-171252/ |
| Summary: | The synthesis of two types of Localized Wave (L W) pulses is considered; these
are the 'Focus Wave Model (FWM) pulse and the X Wave pulse. First, we introduce the
modified bidirectional representation where one can select new basis functions resulting
in different representations for a solution to the scalar wave equation. Through this new
representation, we find a new class of focused X Waves which can be extremely
localized. The modified bidirectional decomposition is applied to the nonhomogeneous
scalar wave equation, resulting in moving sources generating L W pulses. In this work,
we also address the possibility of exciting L W pulses from dynamic apertures, or
apertures the effective radius of which is varied with time. Ideal L W pulses cannot be
realized because they require infinite time excitation. However, in the case of finite L W
pulses, the aperture of excitation is finite and is varied from a time - T to T. We show
that the resulting L W pulses are more resistant to decay than classical monochromatic
Gaussian pulses occupying the same beam waist. Both types of finite L W pulses, such
as the FWM and X Wave pulse, can propagate without significant decay to much greater
distances than classical monochromatic pulses. This desirable behavior is attributed to
the superior aperture efficiency of the L W pulses, which in turn is attributed to their
unique spectral structure. === Ph. D. |
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