  We show that a specific superposition principle is valid for \emph{nonlinear}
Josephson plasma waves in layered superconductors. We study theoretically the
reflection and transmission of terahertz waves through a finite-size
superconducting slab placed inside a rectangular waveguide with ideal-metal
walls. We assume that the superconducting layers are parallel to the waveguide
axis. We show that there exist two specific mutually-orthogonal polarizations
for waves which, in spite of the nonlinearity, reflect and transmit through the
superconductor \emph{independently}. The wave of the first polarization causes
a strong shielding current along the crystallographic \textbf{ab}-plane of the
superconductor. Therefore, this wave reflects nearly completely from the
superconductor and excites only an evanescent mode inside it. The wave of the
other polarization does not contain the electric field component parallel to
both the sample surface and the crystallographic \textbf{ab}-plane, and excites
much weaker shielding currents. Therefore, it partially reflects and partially
transmits through the sample. Moreover, this wave excites the nonlinear mode in
the layered superconductor, and the transmission coefficient of the
superconductor depends on the amplitude of the incident wave of this
polarization.On the basis of the discussed superposition principle, we suggest
a new method for solving nonlinear problems of waves interaction in layered
superconductors. Namely, it is reasonably to represent incident, reflected, and
transmitted waves of any polarizations as superpositions of the modes with the
two specific polarizations considered here, and then solve the problem
separately for these modes. We apply this method to the case of nonlinear
interaction and mutual transformation of the transverse electric and transverse
magnetic modes in layered superconductors.
