Optical Vortices in a Fiber: Mode Division Multiplexing and Multimode Self-Imaging

The optical vortices (Dennis et al., 2009; Desyatnikov et al., 2005; Soskin & Vasnetsov, 2001) or angular harmonics exp(imφ) describe a wavefront peculiarity, or helical dislocation, when in passing around the origin of coordinates the light field phase acquires a phase shift of 2πm, where m is the optical vortex's order. The generation and propagation of the laser vortices in free space has been studied fairly well, meanwhile, the excitation of individual vortex modes and obtaining desired superpositions thereof in optical fibers present a greater challenge (Berdague & Facq, 1982; Bolshtyansky et al., 1999; Dubois et al., 1994; Karpeev & Khonina, 2007; Mikaelian, 1990; Soifer & Golub, 1994; Thornburg et al., 1994; Volyar & Fadeeva, 2002). Note that the most interesting is the excitation and propagation of pure optical vortices that are not stepor graded-index fiber modes. However decomposition of the light fields in terms of angular harmonics has a number of advantages over other bases, including modal ones, when dealing with problems of laser beam generation and analysis and mode division multiplexing. As distinct from the classical LP-modes, the angular harmonics are scaleinvariant when coupled into the fiber and selected at the fiber's output using diffractive optical elements (DOEs) (Dubois et al., 1994; Karpeev & Khonina, 2007; Soifer & Golub, 1994; Thornburg et al., 1994). This gives much freedom in choosing parameters of an optical scheme, allowing one to effectively counteract noises, as it will be demonstrated below. A term "mode division multiplexing" (MDM) is used for multimodal optical fibers when describing methods for data transmission channel multiplexing, with each spatial fiber mode being treated as a separate channel that carries its own signal (Berdague & Facq, 1982; Soifer & Golub, 1994). The essence of mode division multiplexing is as follows: laser beams as a linear superposition of fiber modes can be used to generate signals that will effectively transmit data in a physical carrier a multimodal fiber. The data transmitted can be contained both in the modal composition and in the energy portion associated with each laser mode. The MDM concept has not yet been turned to practical use because a definite mode superposition with desired between-mode energy distribution is difficult to excite. Another reason is that there is energy redistribution between modes when transmitting data in real