The dependence of absorption coefficient α and refractive index n on the intensity of incident light are studied near the exciton resonance. The non-boson behaviour of excitons may serve as a mechanism of optical nonlinearity leading to bistable shapes of α and n above the resonance.
We report the observation of an intensity-dependent refractive-index nonlinearity in CdS due to a resonance state where an excitonic molecule is created by induced absorption of light. The refractive indexnas a function of the incident laser photon energyEis measured directly by light refraction in thin crystal prisms. A renormalized dielectric function describes the measuredn(E)spectra well. This strong refractive-index nonlinearity is well suited to produce an optical bistability and to further strengthen the evidence of CdS to be an important material for laser-induced dynamic gratings.
An exciton-phonon mechanism for producing cavityless optical bistability is suggested. We consider the influence of the oscillating subsystem of a crystal on the absorption process of a laser wave in the region of exciton frequencies. It is shown that exciton-phonon interaction leads to nonlinear dependence of the absorption coefficient on the density of the exciton gas. The increase of absorption with increasing exciton density, however, is possible only in the frequency region on the long-wavelength tail of the exiton band. As a result, the exciton density of the crystal becomes a hysteresis function of external parameters (intensity of the incident wave, temperature, etc.). We calculate the absorption coefficient of excitons and define the frequency and temperature regions where optical bistability may exist. We analyze different relaxation mechanisms of excitons and explain the experimental results of observing optical bistability in different semiconductor crystals.
Starting from a Hamiltonian which describes the interaction of the many-electron system of a crystal with the quantized light field, we derive nonlinear coupled equations of motion for the light-field amplitude, the electron-hole-pair amplitude, and the inversion. These equations yield the basis for the investigation of space-dependent nonlinear interaction effects between light and electrons in direct band-to-band transitions. With the aid of these equations we investigate the saturation behavior of direct band-to-band transitions for an incident monochromatic electromagnetic plane wave. We determine the nonlinear absorption coefficient and nonlinear refractive index. We compute the nonlinear transmissivity taking into account the boundary conditions at the end faces of the crystal and discuss the effect of optical bistability.
We report on an experimental study of the origin of the nonlinearities and the size of the nonlinear index at various wavelengths close to the exciton resonance and the material band gap. It is concluded that for intensities required for optical bistability, the nonlinearity is mainly excitonic for MQWs with well sizes W of 50 and 152 Å which are either smaller or slightly larger than the exciton radius a. For 299-Å MQW, (W ≃ 2a), where the MQW behaves more like bulk but still has distinct excitonic features, the nonlinearity is due to the combination of exciton screening, band filling, and screening of the continuum states. For bulk GaAs, the effect of exciton is comparatively small and the latter two effects are responsible almost equally for the change in the refractive index. The measured nonlinear indices are rather similar for all these samples with the bulk GaAs and 299-Å MWQ exhibiting slightly larger Δn (change in index) for similar carrier densities (or for similar light intensities). The 50-Å MQW has a slightly smaller value of nonlinear index because the nonlinearity which in this sample is due to the saturation of the exciton resonance occurs at higher excitation intensities due to larger exciton binding energy.