Vector Modulation Interaction in a Rapidly Spun Fiber

The vector modulation interaction is a degenerate four-wave mixing process in which a strong pump drives weak signal and idler sidebands, each of which has two polarization components. In this paper, the Jones-Stokes formalism is used to study the vector modulation interaction in a rapidly spun fiber. Comprehensive formulas are derived for the signal and idler eigenvectors, and the transfer functions for the associated eigenamplitudes, which are valid for arbitrary pump polarizations. Not only do these formulas describe the sideband evolution classically, they also enable the quantum-mechanical description of the sideband evolution in both the Heisenberg and Schrödinger pictures.