Parametric amplification and frequency conversion in optical fibers

TLDR

Stimulated parametric emission is prominent only in short fibers, whereas long fibers are dominated by stimulated Raman scattering. The characteristic length is expressed in terms of the initial pump linewidth and low‑power parametric bandwidth—estimated from pump wavelength and frequency shift—and coupled‑wave equations provide gain and amplification formulas that mirror plane‑wave results but include overlap‑integral coupling coefficients. We find that the parametric four‑photon gain for light pulses decreases for fibers longer than a characteristic length.

Abstract

We find that the parametric four-photon gain for light pulses decreases for fibers longer than a characteristic length. This length is related to the common experimental observation that stimulated parametric emission is usually prominent only in short fibers while in long fibers stimulated Raman scattering dominates. Despite the fact that the actual process involves an intensity dependent bandwidth and broadening of the pump linewidth from self-phase modulation, it is possible to develop a simple expression for the characteristic length which requires only the initial pump linewidth and the low-power parametric bandwidth. This bandwidth can often be estimated from the pump wavelength and the measured frequency shift between the pump and the generated waves. Expressions for gain and amplification are derived from coupled wave equations and in the Appendixes it is shown that these are of the same form as the planewave equations, but modified by coupling coefficients called overlap integrals.