Investigation of the sum of orbital angular momentum generated by conical diffraction

The conical diffraction (CD) of a wave propagating along the optical axis of a biaxial crystal is an intriguing phenomenon with current applications including imaging and optical communications. The emerging light can have a fractional or integer orbital angular momentum (OAM) along the propagation direction per unit thickness of a transverse section. The measurement of the OAM of a beam is not an easy task, particularly for non-integer values. We operated the CD of 1053 and 1047 nm beams with a KGd(WO₂)₄ crystal, in various input and output polarization states. Then, the sum-frequency was obtained with a KTiOPO₄ crystal located near the second Raman spike. The integer or fractional OAM of both the fundamental and sum-frequency waves were visualized with the cylindrical lens method. All the experimental patterns, far field, near field and field in the focal plane of the cylindrical lens, are quite well described by a self-consistent model based on plane wave propagation and their interferences. The sum of the OAM due to quadratic nonlinear conversion is evidenced from experimental and calculated patterns. (paper)