  The high-T_c cuprate superconductors are now believed to be intrinsically
inhomogeneous. We develop a theory to describe how this inhomogeneity affects
the intermodulation coefficient of such a material. We show that the continuum
equations describing intermodulation in a superconducting layer with spatially
varying properties are formally equivalent to those describing an inhomogeneous
dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we
calculate the effect of inhomogeneity on the intermodulation coefficient in a
high-T_c material, using several assumptions about the topology of the layer,
and some simple analytical approximations to treat the nonlinearity. For some
topologies, we find that the intermodulation critical supercurrent density
J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly
leading to more desirable material properties. We discuss this result in light
of recent spatial mappings of the superconducting energy gap in BSCCO-2212.
