On the Phenomenology of Self-organized Quasi-phase-matched Second-harmonic Generation in Optical Fibres

Abstract

A simple phenomenological theory of second-harmonic generation in centrosymmetric media is presented in this analytical paper. It is shown that in the medium without memory the energy transfer between interacting waves is negligibly small. For the medium with an optical memory (like phosphorus-germanium-doped glass fibres), the process of formation of χ ⁽²⁾ grating, owing to the third-order optical rectification and the electric-field-induced deprivation of centrosymmetric structure, is described from the phenomenological point of view. Second harmonic generation at periodical χ ⁽²⁾ grating is studied. In the case of resonant interaction, second-harmonic radiation can be systematically amplified. For the non-monochromatic and pulse-form radiations the effective length of the medium is limited largely due to the Kerr nonlinearities. The estimated effective fibre length is in good agreement with previous experiments.