The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides

We successfully used the tight binding theory to derive the extended discrete nonlinear Schrödinger equation to describe the soliton propagation and to obtain the soliton propagation criteria (SPC) in the nonlinear photonic-crystal waveguides (PCWs) and coupled resonant optical waveguides (CROWs) containing Kerr media. From these criteria, we obtain the soliton-propagating region of CROWs in different numbers of separated rods and strengths of self-phase modulation (SPM). The defined soliton-propagating regions coincide with the regions of modulation instability in the CROWs. In the PCWs, the positive Kerr coefficient medium needs to be added to support the pulse propagation in low frequency or low wave vector region of the dispersion curve; while negative Kerr effect is for high frequency case. Due to the linear combination of various cosine harmonic functions in the dispersion relations of both CROWs and PCWs, the pulse broadening which is mainly caused by the third-order dispersion at SPC is the lowest at the boundary of dispersion curves. However, due to the different magnitudes of coupling coefficients in CROWs and PCWs, the group velocity, dispersion and strength of SPM in CROWs are all smaller than those in PCWs.