Graded-azimuthal-index fiber as a control element for radial-index and orbital-angular-momentum modes of Laguerre-Gaussian beams

We propose an azimuthally varying graded-index fiber that can efficiently create and control a definite set of radial-index and orbital-angular-momentum (OAM) modes of Laguerre-Gaussian beams and their superpositions. A rigorous coupled-wave analysis formalism is developed, which provides a ready analysis for the azimuthal-refractive-index variation in the Laguerre-Gaussian basis. In particular, we present effective control in the generation and coupling of the various OAM modes, including radial-index modes of the Laguerre-Gaussian beam within the fiber, wherein the propagation length of the fiber and the wavelength act as the control parameters. We further present the possibility of switching every alternate channel in a wavelength division multiplexing protocol to a higher-order spatial mode within the optical fiber to substantially reduce interchannel crosstalk. The graded azimuthal index fiber can be utilized in high-speed fiber-optic communications as a versatile control element for OAM modes and the radial-index mode of the Laguerre-Gaussian beam transformation.