Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance

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Abstract
We present a new model (including both temperature and electron-hole effects) of two-beam coupling in photorefractive semiconductors under an external dc field E0. This model predicts that the exponential gain Γ can exhibit an intensity-dependent resonant behavior, yielding a π/2 phase shift of the space-charge field with respect to the incident fringe pattern. This optimum intensity strongly depends on crystal temperature but it is practically independent of the grating period. As an illustration this model is applied to InP:Fe. In this case the resonance occurs when the hole photoionization rate and the electron thermal emission rate are equal. Values of Γ as high as 20 cm−1 at 1.06 μm, for a fringe spacing of 15 μm and E0 =10 kV/cm, are predicted. The comparison between theory and experimental data requires taking into account the variation of the pump intensity throughout the sample (due to optical absorption), which reduces the volume where the resonance condition is fulfilled; in this way a satisfactory fit of the experimental gain versus intensity curve has been obtained. The characteristics of this new resonance mechanism suggest several gain enhancement techniques which are briefly discussed. In particular, an increase of Γ by using an additional incoherent backward propagating beam is predicted and experimentally demonstrated.