Second-harmonic generation in fibers

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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.