Two dimensional unstable scar statistics.

Abstract

This report examines the localization of time harmonic high frequency modal fields in two dimensional 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 paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.3 4

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

“…The statistics of the scars for odd parity along the orbit are the same as the even case, but the spectra are interlaced (Warne et al, 2006). The statistics for scars that are odd with respect to the perpendicular of the orbit are different.…”

“…The normalization of the scarred eigenfunctions, introduced previously through circuit concepts, is put in the form of the electromagnetic energy theorem. This generalized formalism is needed to treat cavities with concave walls, as discussed in another paper on the stadium cavity (Warne et al, 2006). Various quantities are examined in the bowtie cavity, including projections of the field along the scarred orbit and values of the square of the field both on and off the orbit.…”

“…The asymmetrical bowtie geometry is also briefly discussed, and the odd problem statistics are constructed. More details on these scar constructions can be found in Warne et al (2006). The generalized formalism used in this article is needed to treat cavities with concave walls containing interior foci, which were briefly summarized in Warne et al (2007) (scalar axisymmetric 3D results were also presented in Warne et al [2008]); a paper is being prepared on the treatment of the stadium cavity using these methods.…”

Electromagnetic field limits set by the V-Curve.

“…The normalization is assumed to be the same throughout the cavity (homogeneity). Cavities can exhibit deviations from this simple density (the modal spacings can also deviate) due to periodic ray trajectories [21], [24], [25], [26], as well as proximity to the source (of course in low quality factor situations we would also expect field inhomogeneity).…”

Time harmonic scar statistics in two dimensional cavities

“…The elliptic formalism [7], combined with the random phase approach [11], allowed the treatment of both convex and concave boundary geometries. Details can be found in the report [12].…”