Second-harmonic generation in fibers

Abstract

In this analytical paper, a formalismfor second-harmonic and sum-frequency generation in glass fibers is developed. It considers only the lowest-order nonlinearities in regular, step-index fibers. Plots showing the dependence of index-matching frequencies on the core radius and index difference across the core-cladding interface are given. Estimates are given for the conversion efficiencies due to the nonlinear polarization at the core-cladding interface and the bulk nonlinear polarization proportional to E ∇E, which includes quadrupolar terms. It is concluded that the interface effects would be dominant. Calculations for the longitudinal-electric-field-induced nonlinear polarization proportional to E² that involve the same mode coupling are also included. The calculated conversion efficiencies are small and cannot explain the recently observed high conversion efficiencies that were obtained under nonindex-matched conditions. A maximum conversion efficiency of around 10⁻⁵ is predicted under index-matching conditions.