We prove that spatial Kerr solitons, usually obtained in the frame of a nonlinear Schrödinger equation valid in the paraxial approximation, can be found in a generalized form as exact solutions of Maxwell’s equations. In particular, they are shown to exist, both in the bright and dark version, as TM, linearly polarized, exactly integrable one-dimensional solitons and to reduce to the standard paraxial form in the limit of small intensities. In the two-dimensional case, they are shown to exist as azimuthally polarized, circularly symmetric dark solitons. Both one- and two-dimensional dark solitons exhibit a characteristic signature in that their asymptotic intensity cannot exceed a threshold value in correspondence of which their width reaches a minimum subwavelength value.
© 2005 Optical Society of America
Alessandro Ciattoni, Bruno Crosignani, Paolo Di Porto, and Amnon Yariv, "Perfect optical solitons: spatial Kerr solitons as exact solutions of Maxwell's equations," J. Opt. Soc. Am. B 22, 1384-1394 (2005)