Sequence-frequency three-wave mixing emissions in a birefringent optical fiber

Efficient parametric stimulated and parametric mixing processes involving waves with many optical frequencies can occur in a highly birefringent single-mode optical fiber due to the third-order nonlinear susceptibilityχ⁽³⁾. Three types of multiple-order sequence-frequency emissions, two associated with the LP01mode, with fundamental frequency-shiftsΔ ν̄of approximately 1500 cm-1and 150 cm-1, and one associated with theLP<₁₁mode, withΔ ν̄ 1000cm-1, have been observed. Emissions are seen to be due to both degenerate stimulated four-photon mixing, which provides simultaneous amplification proportional to the square of the pump intensity for Stokes and anti-Stokes generation from noise, and parametric three-wave mixing in which already generated Stokes and anti-Stokes fields are mixed with a strong pump field to produce the newly generated field. Both the 1500 cm-1and the 150 cm-1fundamental anti-Stokes shifts associated with the LP01mode sequence-frequency emissions originate from the off-diagonal component ofχ⁽³⁾. The value of the shifts are such as to have compensation of the bulk material phase mismatch Kmof fused silica with the high birefringence of the mutually orthogonalLPˣ₀₁andLPʸ₀₁modes. On the other hand. the 1000 cm-1shift of the mixed-mode excitation of the LP01and LP11modes originates from the diagonal component ofχ⁽³⁾, and has a value such that the phase mismatch due to the mode dispersion Kwcancels the material dispersion term Km. The observed polarization directions of the generated waves are in good agreement with theoretical predictions, supporting the identification of the relevant waves. This is the first report of three-wave mixing due to the off-diagonal component ofχ⁽³⁾. Three-wave mixing due to the diagonal component has been seen previously, as has stimulated four-photon mixing due to both the diagonal and off-diagonal components.