Derivation of dimensional and material requirements for propagation and processing of temporal optical solitons in planar geometry channel waveguides

We investigate the dispersion of the group velocity of light in slab and rectangular waveguides and obtain analytic expressions for the first derivative of the propagation vector with respect to the angular frequency and numerical values for the second derivative for both geometries. The last quantity is an important parameter in the temporal soliton propagation equation, which motivates this research. Provided the dispersion within the channel can be adjusted properly, planar geometry waveguides can represent good candidates for the optical processing of temporal solitons carried by optical fibers. We discuss the manner in which the dispersion coefficient depends on waveguide dimensions and material constants, and we determine the parameters that optimize soliton processing.