Optical fibers with a frequency-dependent Kerr nonlinearity: Theory and applications

This review provides a detailed discussion of both the mathematical treatment and the impact of a frequency-dependent Kerr nonlinearity on the propagation of short pulses in optical fibers. We revisit the theoretical framework required to deal with the frequency dependence of the nonlinear response without incurring any physical inconsistencies, such as the non-conservation of the photon number. Then, we point out the role of the zero-nonlinearity wavelength, its interplay with the zero-dispersion wavelength, and their influence on evolution of optical pulses in optical fibers, specifically by looking at soliton propagation and the ensuing generation of Cherenkov radiation. Finally, by means of a space–time analogy involving the collision of a weak control pulse and an intense soliton, we describe an all-optical switching scheme in the presence of a zero-nonlinearity wavelength within a photon-conserving framework.