Interaction of two different frequency photonic crystal waveguide modes through the resonant excitation of modes on off-channel Kerr nonlinear media

The properties of two photonic crystal waveguide modes at different frequencies that propagate down a straight photonic crystal waveguide are studied for cases in which the two modes interact with off-channel structures composed of Kerr nonlinear dielectric media. The optical nonlinearity of the off-channel structures mediates an interaction between the two modes that allows the modes to modulate the transmission of each other down the waveguide channel. This interaction and mutual modulation is shown to be pronounced in the case when either of the two waveguide modes resonantly excites a localized mode on the off-channel features formed of Kerr nonlinear media. Cases that are considered are a straight linear dielectric media waveguide with off-channel structures formed as: (a) a single off-channel Kerr site that supports a bound localized electromagnetic mode, (b) multiple off-channel Kerr sites that support a bound intrinsic localized electromagnetic mode, and (c) multiple off-channel Kerr sites that support an intrinsic localized mode that in turn interacts with a semi-infinite waveguide of linear dielectric media. In cases (a) and (b) the effects of resonant excitation of single site and intrinsic localized modes in the Kerr medium on the transmission characteristics are determined. In case (c) the effects of resonant excitation of intrinsic localized modes in the Kerr medium on the transmission characteristics of the two waveguide modes into the infinite and semi-infinite waveguides are studied.