Time Harmonic Two-Dimensional Cavity Scar Statistics: Concave Mirrors and Stadium

Warne, Larry K.; Jorgenson, Roy E.; Kotulski, Joseph D.; Lee, Kelvin

doi:10.1080/02726343.2014.922394

Cited by 3 publications

(1 citation statement)

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“…The approach used by Antonsen [1], on convex mirror geometries in two dimensions, is generalized [2], [3], [4] by introducing the curved ray path formalism, used previously by Vaynshteyn [5] on stable orbits. This combined approach was used recently to investigate scars in two-dimensional geometry [6], [7]. This report explores both the scalar (acoustic) [8], [9] and vector (electromagnetic) problems in three-dimensional axisymmetric geometry, first with convex walls, and second with concave walls supporting interior foci.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

Warne¹,

Jorgenson²

2014

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This report examines the localization of high frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated first but the approximations required to treat the vector field components are also examined. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric case forms the opposite extreme (where the two mirror radii at each end of the ray orbit are equal) from the two-dimensional solution examined previously (where one mirror radius is vastly different from the other). The enhancement of the field on the orbit axis can be larger here than in the two-dimensional case.

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