Free carrier effect on the refractive index change in quantum-well structures

Dielectric response of spatially inhomogeneous free carriers in quantum wells is studied by random phase approximation (RPA) for a high frequency (near infrared) light field. A general form for susceptibilities is derived for a guided optical mode. The analysis shows that a conventional treatment (Drude model) for the TE mode provides a good approximation. The susceptibility for the TM mode is almost the same as that for the TE mode, in spite of quantization of carrier motion, as long as the photon energy is much larger than the intersubband transition energy. The free carrier component of the refractive index change in quantum-well waveguides is thus isotropic near the band gap. Carrier confinement will not reduce the free carrier component in the linewidth enhancement factor around the lasing wavelength