  A rigorous formulation of the canonical boundary-value problem is presented
to find the surface plasmon-polariton waves guided by the interface of a
one-dimensional photonic crystal and metal along the direction of the
periodicity. The problem is formulated using the rigorous coupled-wave approach
and a dispersion equation has been obtained. The Muller's method and
Newton--Raphson method were used to obtain illustrative numerical results of
the dispersion equation. The solutions were found to converge as the number of
Floquet harmonics increased. This formulation does not require the computation
of the photonic bandgaps and directly computes the surface-wave modes. This
formulation could engender new applications of plasmonics exploiting the
neglected interface along the direction of periodicity of the one dimensional
photonic crystals.
