Light rays and waves on geodesic lenses

TL;DR

This paper introduces geodesic lenses as rotationally symmetric manifolds where light rays form closed trajectories, demonstrating their unique spectral properties and potential for precise light propagation studies on curved surfaces.

Contribution

It presents the concept of geodesic lenses, analyzes their optical and quantum wave properties, and demonstrates fabrication of sub-micrometer scale lenses with high-precision curved light ray observation.

Findings

Light rays on geodesic lenses are closed trajectories.

The spectrum of geodesic lenses is degenerate and equidistant.

Curved light rays are observed with high precision in fabricated lenses.

Abstract

Starting from well-known absolute instruments for perfect imaging, we introduce a type of rotational-symmetrical compact closed manifolds, namely geodesic lenses. We demonstrate that light rays confined on geodesic lenses are closed trajectories. While for optical waves, the spectrum of geodesic lens is (at least approximately) degenerate and equidistant with numerical methods. Based on this property, we show a periodical evolution of optical waves and quantum waves on geodesic lenses. Moreover, we fabricate two geodesic lenses in sub-micrometer scale, where curved light rays are observed with high accurate precision. Our results may offer a new platform to investigate light propagation on curved surfaces.