Propagation of self-trapped circular beams in strongly nonlocal nonlinear media

A very general family of self-trapped circular beams (CiBs) in circular cylindrical coordinates is presented in strongly nonlocal nonlinear media. The complex amplitude of the CiBs is depicted by the product of the Whittaker functions and the Gaussian function, and is characterized by two parameters. Special cases of the CiBs and the even and odd mode CiBs are the standard, elegant, and generalized Laguerre–Gaussian beams and the even and odd mode standard, elegant, and generalized Laguerre–Gaussian beams.