Four-photon mixing and dispersion in single-mode fibers

We show that phase matching for the four-photon mixing process in a single-mode fiber depends only on the propagation constant total dispersion beta(II)(omega). Frequencies omega(s) and omega(a), for the Stokes and anti-Stokes waves must satisfy omega(s) < omega(zd) < omega(a), where omega(zd) is the frequency for which dispersion is zero; beta(II)(omega(zd)) = 0. Variations in the frequency shift Omega(omega(p)) are described for pump frequency omega(p) around omega(zd), i.e., in the region where delicate balances of material and waveguide dispersion effects are used in fiber design. We show that no new waves are created when the pump and zero-dispersion frequencies coincide, i.e., Omega(omega(zd)) = 0. Since the creation of Stokes and anti-Stokes waves is intimately related to the beta(II)(omega) versus omega curve, some interesting results are predicted for advanced design fibers.