  Starting from the Maxwell's equations and without resort to the paraxial
approximation, we derive equations describing stationary (1+1)-dimensional
beams propagating at an arbitrary direction in an optical crystal with cubic
symmetry and purely quadratic nonlinearity. The equations are derived
separately for beams with the TE and TM polarizations. In both cases, they
contain and cubic nonlinear terms, the latter ones generated via the cascading
mechanism. The final TE equations and soliton solutions to them are quite
similar to those in previously known models with mixed quadratic-cubic
nonlinearities. On the contrary to this, the TM model is very different from
previously known ones. It consists of four first-order equations for transverse
and longitudinal components of the electric field at the fundamental and second
harmonics. Fundamental-soliton solutions of the TM model are also drastically
different from the usual "quadratic" solitons, in terms of the parity of their
components. In particular, the transverse and longitudinal components of the
electric field at the fundamental harmonic in the fundamental TM solitons are
described, respectively, by odd and single-humped even functions of the
transverse coordinate. Amplitudes of the longitudinal and transverse fields
become comparable for very narrow solitons, whose width is commensurate to the
carrier wavelength.
