Doppler effect induced by rotating lenses

The orbital angular momentum inherent to light beams with a helical wavefront can be transferred to non-isotropic lenses. A system of three cylindrical lenses suffices to transform an arbitrary paraxial input beam by inverting one transverse direction of the mode function. This also inverts the orbital angular momentum of a Laguerre-Gaussian beam with mode index m. The corresponding transfer of angular momentum shows up directly as a frequency shift 2mΩ when the lens system is set in rotation at frequency Ω around the axis.

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