Cross Phase Modulation in Photonic Crystals

In the present paper we consider a simultaneous propagation of two weak pulses (the 'probe' and 'trigger') in the tripod configuration atomic medium, irradiated by a strong quasi-standing control field. The latter leads to a periodic modulation of the refractive index of the medium which now becomes a photonic crystal. While propagating in such a medium both probe and trigger are split into transmitted and reflected components the nonlinear phase shifts of which are of particular interest. We calculate the nonlinear periodic susceptibilities and make numerous simulations of the propagation of the stationary pulses in different conditions. We calculate the phases of the outgoing fields and find the optimal values of parameters characterizing the system, i.e. when the nonlinear phase shifts of both transmitted and reflected probe and trigger components are large. We show a convenient way of controlling the process by shifting the frequency of the incoming probe. We plot the transmission and reflection spectra for different values of parameters of the system, which could be used as a flexible beam splitter, for which the phases and intensities of outgoing beams can be independently changed.