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Chinese Physics Letters

Nondegenerate Four Wave Mixing in Rare-Earth Doped Fiber Under the Influence of Coherent Population Trapping

Guo Yang, Ming Hai, Liu Fang-Xin, Xu Li-Xin

Published Apr 1, 2000• 0 citations
Publisher

Abstract

By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order nonlinear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω 23 = ±√Γ 2 Γ 3 . On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δ f < 30 GHz at the wavelength λ c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.

DOI
10.1088/0256-307x/17/4/015

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An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.
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