Stimulated four-photon mixing is investigated in birefringent optical fibers. By pumping the birefringent fiber with the Q-switched Nd:YAG laser beam, the Stokes/anti-Stokes pair are generated via the phase-matching process where the Stokes field is along the slow mode, the anti-Stokes along the fast mode, and the pump fields divided into two polarization modes.
Pump intensity dependency in output spectra of the stimulated four-photon mixing is experimentally characterized. Specifically, the output spectra are time-resolved and the observed frequency shifts in Stokes and anti-Stokes fields are explicitly correlated to the instantaneous pump intensity within the pump pulse envelope. It is found that the phase-matching condition undergoes a systematic change in time, depending on the instantaneous pump intensity. The phase-matched frequency shift at the maximum gain is observed to decrease linearly with increase of input pump power. The rate of change in frequency shift is measured to be $-0.045cm^{-1}/W$.
This intensity-dependent frequency shift is theoretically analyzed for the present phase-matching scheme. The coupled wave formulation based on the third order nonlinear optics treatment is used. The associated gain coefficient is specified in terms of basic material and wave parameters, viz. input pump power, phase-mismatch factor, complex nonlinear index of the medium, and structural parameters of the fiber. The calculated rate of change in frequency shift is shown to agree with the experimental result within 5%.
Also, the pump polarization dependency in Stokes and anti-Stokes output power is examined. The maximum outputs of the Stokes and anti-Stokes fields are found to occur at the input pump polarization angle θ = 38˚. This asymmetry in pump polarization dependency is found due to the effect of Raman gain, and it is quantified satisfactorily from the gain coefficient calculated as a function of the input pump polarization angle.
Various output spectra are obtained by changing the polarization state of input pump field. They are mainly due to stimulated four-photon mixing, stimulated Raman scattering, and their mixed effects. A different type of four-photon process is observed. It is interpreted as the mixing of the pump, stimulated Raman Stokes, and the four-photon anti-Stokes fields. Also, changes in Raman Stokes spectra are observed, which are explained qualitatively by internal self-pumping within Raman gain band.
Wavelength-selective optical time domain reflectometry is employed for the measurement of nonlinear gain along the fiber. The experimental results show the feasibility of this method.
