  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.
