Sherwood 2015

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approvedazhao_fvolpe_huygensprinciple_wavefronttracing_poster.pdf2015-04-06 12:06:09Anji Zaho

Huygens' principle-based wavefront tracing in non-uniform media

Author: Anji Zaho
Requested Type: Poster Only
Submitted: 2015-01-27 18:34:03

Co-authors: P.-D. Letourneau, F.A. Volpe

Contact Info:
Columbia University
500 W 120th St.
New York, NY   10027

Abstract Text:
We present preliminary results on a novel numerical method describing wave propagation in non-uniform media. The method could be applied to electromagnetic and electrostatic waves in non-magnetized plasmas. We also outline how to extend it to anisotropic media such as magnetized plasmas. The method is inspired by Huygens' principle, in the sense that it models the wavefront as an array of point sources. The spatial density of points and the power distribution among them are established according to Gauss-Hermite quadrature for Gaussian beams, or adapted quadrature in more general settings. These point sources emit wavelets, which interfere. In principle the electric field could be evaluated in a region in front of the original wavefront, and a new iso-phase surface could be identified. However, more simply and more quickly, a bisection method is used here to localize the nearest zeroes of electric field. This corresponds to a specific phase-increment from one wavefront to the other, but it is easily generalized by anticipating or delaying all the initial phases by the same amount. A simple reiteration of this method allows to trace wavefronts and their intensity profiles. The method is more time-consuming than ray tracings, but it accounts for diffraction. Two examples provided are diffraction around an obstacle and the finite waist of a focused Gaussian beam. The calculations were performed in two dimensions, but can be easily extended to three dimensions. We will also discuss the extension to anisotropic media by means of anisotropically expanding (i.e., ellipsoidal) wavelets.


March 16-18, 2015
The Courant Institute, New York University