Propagation of Photons through Optical Fiber: Spin-Orbit Interaction and Nonlinear Phase Modulation
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We investigate two medium-facilitated interactions between properties of light upon propagation through optical fiber. The first is interaction between the spin and intrinsic orbital angular momentum in a linear optical medium. This interaction gives rise to fine structure in the longitudinal momenta of fiber modes and manifests in rotational beating effects. We probe those beating effects experimentally in cutback experiments, where small segments are cut from the output of a fiber to probe the evolution of both output polarization and spatial orientation, and find agreement between theoretical predictions and measured behavior. The second is nonlinear optical interaction due to cross- and self-phase modulation between the complex-valued temporal amplitude profile of pump pulses and the amplitude profiles of generated signal and idler pulses in optical fiber photon-pair sources utilizing the four-wave mixing process named modulation instability. We develop a model including the effects of these nonlinear phase modulations (NPM) describing the time-domain wave function of the output biphoton in the low-gain regime. Assuming Gaussian temporal amplitude profiles for the pump pulse, we numerically simulate the structure of the biphoton wave function, in symmetric and asymmetric group velocity matching configurations. Comparing the overlap of the joint temporal amplitudes with and without NPM indicates how good of an approximation neglecting NPM is, and we investigate the effects of NPM on the Schmidt modes. We find that effects of NPM are small on temporally separable sources utilizing symmetric group velocity matching, but appreciably change the state of temporally entangled sources with the same group velocity matching scheme. For sources designed to produce entangled biphotons, our simulations suggest that NPM increases the Schmidt number, which may increase entanglement resource availability with utilization of a phase-sensitive detection scheme. We find that NPM effects on temporally separable sources designed with asymmetric group velocity matching produce non-negligible changes in the state structure. The purity is unaffected at perfect asymmetric group velocity matching, but if the pump is detuned from the correct wavelength, the purity degrades. The largest changes to the state due to NPM occur in long fibers with long pulse durations and low repetition rates.