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15 October 2012 Visualization of optical fields with ellipsoidal geometry
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Abstract
The ellipsoidal coordinate system has the interesting property that every other orthogonal coordinate system in which the three-dimensional Helmholtz equation is separable, is a special case of it. In this work, we explore the solutions to the wave equation in ellipsoidal coordinates in order to visualize the behavior of optical fields with ellipsoidal geometry. We show several parity properties which allow us to create fundamental modes of vibration with different symmetries around the (x; y), (x; z) and (y; z) planes. We discuss the resonant modes of an ellipsoidal cavity and the traveling waves with ellipsoidal geometry. We propose a method to calculate the second linearly independent solution to the ellipsoidal wave equation
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Antonio Ortiz-Ambriz, Miguel A. Bandres, and Julio C. Gutiérrez-Vega "Visualization of optical fields with ellipsoidal geometry", Proc. SPIE 8490, Laser Beam Shaping XIII, 84900P (15 October 2012); https://doi.org/10.1117/12.931509
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