Four-photon mixing and dispersion in single-mode fibers

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Abstract
We show that phase matching for the four-photon mixing process in a single-mode fiber depends only on the propagation constant total dispersion βII(ω). Frequencies ωs and ωa for the Stokes and anti-Stokes waves must satisfy ωs < ωzd < ωa, where ωzd is the frequency for which dispersion is zero; βII(ωzd) = 0. Variations in the frequency shift Ω(ωp) are described for pump frequency ωp around ωzd, 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., Ω(ωzd) = 0. Since the creation of Stokes and anti-Stokes waves is intimately related to the βII(ω) versus ω curve, some interesting results are predicted for advanced design fibers.