Derivatives of elegant Laguerre-Gaussian beams: vortex structure and orbital angular momentum

作者：Lopez Mago Dorilian^*; Davila Rodriguez Josue; Gutierrez Vega Julio C

来源：Journal of Optics, 2013, 15(12): 125709.

DOI：10.1088/2040-8978/15/12/125709

• optical vortices
• Laguerre-Gaussian beams
• vortex arrays

The commutation between the paraxial wave equation and the derivative operator allows us to generate novel beam solutions. In this work, we analyze the solutions generated by the derivatives with respect to Cartesian coordinates of elegant Laguerre-Gaussian beams. We present compact expressions for the derivatives of arbitrary integer order and study the resulting orbital angular momentum (OAM) and phase structure. We found that the derivative operator preserves OAM but the topological structure is modified. The resulting topological charge depends on the initial seed beam and the order of the derivative. We also introduce a two-parameter differential operator resulting from the linear combination of Cartesian derivatives delta(x) and delta(y). In analogy with the Poincare sphere for polarized beams, this operator can be mapped on the surface of a unit sphere. The results can find applications in the generation and control of optical vortex structures.

• 出版日期2013-12