The Mathematical Institute, University of Oxford, Eprints Archive

On the theory of complex rays

Chapman, S. J. and Lawry, J. M. H. and Ockendon, J. R. and Tew, R. H. (1999) On the theory of complex rays. SIAM Review, 41 (3). pp. 417-509. ISSN 0036-1445


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The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions.

The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Sp{} in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel--Kramers--Brilbuin expansion of these wavefields.

Item Type:Article
Uncontrolled Keywords:geometrical optics; geometrical theory of diffraction; exponential asymptotics; Stokes' phenomenon; Helmholtz equation
Subjects:O - Z > Partial differential equations
O - Z > Optics, electromagnetic theory
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:611
Deposited By: Jon Chapman
Deposited On:24 May 2007
Last Modified:29 May 2015 18:25

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