Abstract
Three‐dimensional dark spatial solitary waves of TM type are found to exist in the self defocusing nonlinear medium of the Kerr‐law type over the range of the wave effective index neff from 0.82n0 to n0 of the linear refractive index of the medium. This contrasts with TE type which exists over all possible values of neff ranging from 0 to n0. The field profile shape of TM waves is also shown to vary with the wave effective index, whereas that of TE waves is independent of neff.