Efficient frequency conversion in optical fibers with tailored birefringence

Four wave mixing in optical fibers has long been recognised as important method of generating new optical frequencies. The process holds promise as a means of wavelength switching for optical communications, but the presence of a nonlinear term in the phase-matching condition normally prevents strong energy exchange between the waves. We present here a scheme for optimising the conversion efficiency. The four wave mixing process considered here is called polarisation modulation instability (PMI) where a strong pump wave on one axis of a birefringent fiber results in the growth of two equally detuned sidebands on the other axis. In the absence of any external seed the sidebands start to grow with a frequency shift f₀ where the wavevector mismatch is zero. This mismatch is a function of the power of the pump and the fibre´s birefringence, dispersion, and nonlinearity. Our analysis of the evolution of the power in the sidebands utilises three coupled mode equations which describe the interaction of a monochromatic pump, with a pair of sidebands polarised along the orthogonal fibre axis. In the absence of Raman gain, it is possible to solve these equations so that by varying the birefringence along the fibre, the sidebands with a frequency shift of f ₀ are phase matched for the entire length of the fibre