Transmission through a Kerr barrier in photonic crystal waveguides: dispersion effects

The transmission of guided modes through a barrier of Kerr nonlinear optical media contained within a photonic crystal waveguide of linear dielectric media is studied in order to determine the effects of the dispersion of the incident waveguide modes on their barrier transmission coefficients. In McGurn (2008 Phys. Rev. B 77 115105) the conditions under which resonances exist in the guided mode transmission through the barrier were investigated for an incident waveguide mode having a single fixed frequency and a wavevector near the edge of the Brillouin zone. The transmission coefficient maxima were determined as functions of two parameters characterizing the Kerr nonlinearity of the barrier media and shown to exhibit a complex pattern in the two parameter space of the Kerr parameters, associated with various kinds of modes excited within the barrier. In the present paper the focus is on how the pattern of transmission resonance maxima in the two parameter Kerr parameter space is affected by varying the wavevector and frequency of the guided modes incident on the barrier. In addition, the effects of the barrier size on the pattern are determined. The focus of the paper is on affirming the classification scheme proposed in our previous papers upon the introduction of dispersive effects. The dynamical equations of our model are quite general, so it is expected that this scheme will be useful in studying the nonlinear dynamics of other nonlinear physical models which may or may not be based on photonic crystal waveguides.