Enhanced third-order nonlinear optical response of photonic bandgap materials

We calculate the nonlinear phase shift acquired bq a laser beam in propagat ing through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the d irection of propagation. We find that the: nonlinear phase shift shows reso nances for laser frequencies close to the edge of tilt stop hand of the pho tonic bandgap structure. Enhancements of the nonlinear phase: shift compare d with that of a homogeneous nonlinear optical material by a factor of appr oximately five are predicted under realistic laboratory conditions. m-e fin d that similar enhancements of the two-photon absorption rare can occur for a material with an imaginary nonlinear susceptibility. We also treat the c ase of a photonic bandgap material containing a 'defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approxi mately thirty.