Helical mode conversion using conical reflector

In a recent paper, Mansuripur et al. [Phys. Rev. A 84, 033813 (2011)] indicated and numerically verified the generation of the helical wavefront of optical beams using a conical-shape reflector. Because the optical reflection is largely free from chromatic aberrations, the conical reflector has an advantage of being able to manipulate the helical wavefront with broadband light such as white light or short light pulses. In this study, we introduce geometrical understanding of the function of the conical reflector using the spatially-dependent geometric phase, or more specifically, the spin redirection phase. We also present a theoretical analysis based on three-dimensional matrix calculus and elucidate relationships of the spin, orbital, and total angular momenta between input and output beams. These analyses are very useful when designing other optical devices that utilize spatially-dependent spin redirection phases. Moreover, we experimentally demonstrate the generation of helical beams from an ordinary Gaussian beam using a metallic conical-shape reflector.