Spin and Orbital Angular Momenta of Light Reflected from a Cone

TL;DR

This paper investigates how reflective optical elements, especially cones and wedges, influence the spin and orbital angular momenta of light, revealing conditions under which angular momentum is transferred or conserved.

Contribution

It provides a detailed analysis of angular momentum transfer in retro-reflecting cones and wedges, highlighting the role of symmetry and absorption in angular momentum exchange.

Findings

A hollow metallic cone with 90° apex angle reverses the light's spin angular momentum without transferring it to the cone.

A transparent 90° cone can alter the mixture of spin and orbital angular momenta but cannot transfer angular momentum without absorption or symmetry breaking.

A wedge-shaped reflector with 90° apex angle can transfer angular momentum to the reflector when reflecting circularly polarized light.

Abstract

We examine several retro-reflecting optical elements, each involving two reflections. In the case of a hollow metallic cone having an apex angle of 90\degree, a circularly-polarized incident beam acquires, upon reflection, the opposite spin angular momentum. However, no angular momentum is transferred to the cone, because the reflected beam picks up an orbital angular momentum that is twice as large but opposite in direction to that of its spin. A 90\degree cone made of a transparent material in which the incident light suffers two total internal reflections before returning, may be designed to endow the retro-reflected beam with different mixtures of orbital and spin angular momenta. Under no circumstances, however, is it possible to transfer angular momentum from the light beam to the cone without either allowing absorption or breaking the axial symmetry of the cone. A simple example of broken symmetry is provided by a wedge-shaped metallic reflector having an apex angle of 90\degree, which picks up angular momentum upon reflecting a circularly-polarized incident beam.