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 susceptibility
\chi^{(3)}
. Three types of multiple-order sequence-frequency emissions, two associated with the LP
01
mode, with fundamental frequency-shifts
\Delta \bar{\nu}
of approximately 1500 cm
^-1
and 150 cm
^-1
, and one associated with the
LP<_{11}
mode, with
\Delta \bar{\nu} \simeq 1000
cm
^-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
^-1
and the 150 cm
^-1
fundamental anti-Stokes shifts associated with the LP
01
mode sequence-frequency emissions originate from the off-diagonal component of
\chi^{(3)}
. The value of the shifts are such as to have compensation of the bulk material phase mismatch K
m
of fused silica with the high birefringence of the mutually orthogonal
LP^{x}_{01}
and
LP^{y}_{01}
modes. On the other hand. the 1000 cm
^-1
shift of the mixed-mode excitation of the LP
01
and LP
11
modes originates from the diagonal component of
\chi^{(3)}
, and has a value such that the phase mismatch due to the mode dispersion K
w
cancels the material dispersion term K
m
. 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 of
\chi^{(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.