Abstract

Recent observations of a large and ultrafast (<100 fs) nonlinear refraction in semiconductor lasers near their transparency edge has generated much interest owing to their potential use for all optical switching.[1,2] The mechanisms responsible for such nonlinearities have been partially attributed to virtual interband transitions (AC Stark effect). We have extended an earlier model [3] which successfully described the dispersion and band-gap scaling of the electronic n₂ in passive semiconductors in their transparency range (hω<E_g) to explain such nonlinearities in semiconductor amplifiers at photon energies near the transparency point (hω>E_g). This simple model uses a nonlinear Kramers-Kronig transformation to obtain n₂ from a nondegenerate absorption spectrum as calculated using a "dressed state" formalism accounting for the effects of two-photon absorption, electronic Raman, and the optical Stark shift of the bands. In extending this model to active semiconductors, it is essential to include the Fermi-Dirac (FD) distribution with quasi-Fermi levels and T₂ broadening of these levels. In addition, assuming that upon Stark shifting the bands, the FD distribution re-establishes in a time τ_e-e ≅ 10^-14 sec shorter than the pulsewith, an enhancement of n₂ at the transparency point is predicted. Fig.1 depicts the calculated values of n₂ for AlGaAs (E_g ≅ 1.5 eV) as a function of the photon energy for various quasi-Fermi levels. It is seen that n₂ reaches a maximum negative value near the transparency point of each curve. Semiconductors with smaller band-gaps will exhibit a larger nonlinearity since n₂ scales as E_g^-4 as in the case of a passive medium.[3] The sign and magnitude of n₂, as predicted by this theory, is in good agreement with the experimentally reported values in AlGaAs [1] and InGaAsP [2] diode lasers.

© 1991 Optical Society of America