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We have found the cross-phase modulation (XPM) for cross-polarized beams to be equal to the self-phase modulation (SPM) in bulk AlGaAs semiconductor waveguide at photon energies lower than half the band gap. For multiple quantum well (MQW) waveguide the ratio of the cross-phase modulation coefficient to the self-phase modulation coefficient is approximately one for the pump polarized perpendicular to the well plane (TM) and one-half for pump beams in the plane of the wells (TE).
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Villeneuve et al. (1995) studied this question.