Transmission through a Kerr barrier in photonic crystal waveguides: dispersioneffects

Abstract

The transmission of guided modes through a barrier of Kerr nonlinear optical mediacontained within a photonic crystal waveguide of linear dielectric media is studied in orderto determine the effects of the dispersion of the incident waveguide modes ontheir barrier transmission coefficients. In McGurn (2008 Phys. Rev. B 77 115105)the conditions under which resonances exist in the guided mode transmissionthrough the barrier were investigated for an incident waveguide mode having asingle fixed frequency and a wavevector near the edge of the Brillouin zone. Thetransmission coefficient maxima were determined as functions of two parameterscharacterizing the Kerr nonlinearity of the barrier media and shown to exhibit acomplex pattern in the two parameter space of the Kerr parameters, associated withvarious kinds of modes excited within the barrier. In the present paper the focusis on how the pattern of transmission resonance maxima in the two parameterKerr parameter space is affected by varying the wavevector and frequency ofthe guided modes incident on the barrier. In addition, the effects of the barriersize on the pattern are determined. The focus of the paper is on affirming theclassification scheme proposed in our previous papers upon the introduction ofdispersive effects. The dynamical equations of our model are quite general, so it isexpected that this scheme will be useful in studying the nonlinear dynamics of othernonlinear physical models which may or may not be based on photonic crystalwaveguides.