  Radiative heat transfer between uniform plates is bounded by the narrow range
and limited contribution of surface waves. Using a combination of analytical
calculations and numerical gradient-based optimization, we show that such a
limitation can be overcome in complicated multilayer geometries, allowing the
scattering and coupling rates of slab resonances to be altered over a broad
range of evanescent wavevectors. We conclude that while the radiative flux
between two inhomogeneous slabs can only be weakly enhanced, the flux between a
dipolar particle and an inhomogeneous slab---proportional to the local density
of states---can be orders of magnitude larger, albeit at the expense of
increased frequency selectivity. A brief discussion of hyperbolic metamaterials
shows that they provide far less enhancement than optimized inhomogeneous
slabs.
