Spectra of absolute instruments from the WKB approximation

TL;DR

This paper uses the WKB approximation to accurately compute the frequency spectra of absolute optical instruments, confirming previous results and revealing that their eigenfrequencies form nearly evenly spaced groups.

Contribution

It introduces a WKB-based method for calculating spectra of absolute instruments, providing high accuracy and confirming earlier findings with a new approach.

Findings

Eigenfrequencies are very accurately approximated by WKB.

Eigenfrequencies form nearly equidistant groups.

The method is demonstrated on multiple examples.

Abstract

We calculate frequency spectra of absolute optical instruments using the WKB approximation. The resulting eigenfrequencies approximate the actual values very accurately, in some cases they even give the exact values. Our calculations confirm results obtained previously by a completely different method. In particular, the eigenfrequencies of absolute instruments form tight groups that are almost equidistantly spaced. We demonstrate our method and its results on several examples.