Spin-to-orbital angular momentum exchange via reflection from a cone

In a recent paper we explored the novel reflection properties of several conical optical elements using numerical simulations based on Maxwell's equations. For example, in the case of a hollow metallic cone having an apex angle of 90 degrees, a circularly-polarized incident beam acquires, upon reflection, the opposite spin angular momentum in addition to an orbital angular momentum twice as large as the spin, whereas a 90 degrees 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. In the present paper we introduce an approximate analysis based on the Jones calculus to elucidate the physics underlying the reflection properties, and we point to the strengths and weaknesses of the approach.