  We study second harmonic generation in a planar dielectric waveguide having a
low-index, polymer core layer, bounded by two multilayer stacks. This geometry
allows exceptionally strong confinement of the light at the fundamental
wavelength inside the core region with virtually zero net propagation losses
for distances that exceed several centimeters, provided material and scattering
losses are neglected. A phase-matched configuration of the waveguide is
reported in which the pump signal is the lowest-order mode of the waveguide,
and the generated second harmonic signal corresponds to the third propagation
mode of the waveguide. Using a polymer waveguide core, having chi(2)=100 pm/V,
we predict a conversion efficiency of approximately 90% after a propagation
distance of 2 mm, using peak pump intensities inside the core of the waveguide
of 1.35 GW/cm^2. If the waveguide core contains polymer layers with different
glass transition temperatures, the layers can be poled independently to
maximize the overlap integral, and similar pump depletions may be achieved over
a distance of approximately 500 microns.
