An analysis of two and three-dimensional steady-state transformation o
f the Gaussian electromagnetic beams at the interface between linear a
nd nonlinear media into nonlinear surface waves (NSWs) is made. In the
two-dimensional problem, for a media with cubic nonlinearity (a stead
y-state model) the feasibility of NSW excitation into two ways is cons
idered (direct excitation of stable NSW and excitation of unstable NSW
followed by its transformation into a stable one). Excitation efficie
ncy is determined numerically; it is close to 100% for beams of optima
l shape. The possibility of self-localization of radiation (three-dime
nsional NSWs) at the interface of a media with saturation nonlinearity
is shown by the momentum method. NSWs can be excited by incident Gaus
sian beams of optimal shape and propagate along both plane and curved
interface. The analytical results are confirmed by computer simulation
.