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Focusing of vortex beams: Lommel treatment

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Abstract

Focusing of vortex beams by a lens with circular aperture in the paraxial scalar Debye regime is analyzed. The amplitude in the focal region can be expressed naturally in terms of higher order Lommel functions of two variables. Using recurrence relationships, these can then be expressed in terms of low-order Lommel functions. The phase variation in the focal region is investigated, showing some interesting behavior of the Gouy phase anomaly.

© 2014 Optical Society of America

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