  We present a new approach to the Helmholtz spectrum for arbitrarily shaped
boundaries and general boundary conditions. We derive the boundary induced
change of the density of states in terms of the free Green's function from
which we obtain non-perturbative results for the Casimir interaction between
rigid surfaces. As an example, we compute the lateral electrodynamic force
between two corrugated surfaces over a wide parameter range. Universal
behavior, fixed only by the largest wavelength component of the surface shape,
is identified at large surface separations, complementing known short distance
expansions which we also reproduce with high precision.
