Three-dimensional dark spatial solitary waves in saturable nonlinear defocussing media

Three-dimensional dark spatial solitory waves of the TM type are found to exist in a uniform saturable self defocusing nonlinear medium only within a certain range of the beam effective index n_eff which may be wider or narrower compared with the corresponding one in the Kerr law medium, depending on nonlinear saturation index. This contrasts with the TE type, the existence of which in a saturable nonlinear medium is limited in the range of n_eff equal to or narrower than that in the Kerr law nonlinear medium. The physical mechanism behind the distinct contrast is also discussed.