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Physical Review A

Optical bistability of a dense exciton-biexciton system: CuCl

Chi C. Sung, C. M. Bowden

Published Apr 1, 1984• 24 citations
Publisher

Abstract

The steady-state solution of the Langevin equation for a dense exciton-biexciton system is investigated. The corrections to the previous work, the contribution of the field---exciton-biexciton interaction, and the local-field correction are shown to modify the threshold of optical bistability significantly.
DOI
10.1103/physreva.29.1957

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Abstract A semiclassical exciton-biexciton model for CuCl is used to obtain the stationary solutions for optical bistability (o.b.) by numerical integration of the second-order Maxwell equation in the limit of large Fresnel numbers. The results obtained from the calculation, which we call exact (ex.), are compared with corresponding numerical results by using the slowly varying envelope approximation (s.v.e.a.) as well as corresponding analytical results obtained by using the mean-field approximation (m.f.a.). The results obtained with the s.v.e.a. are shown to be in close quantitative (within 5%) agreement with the ex. results for each point in the parameter space considered, whereas the m.f.a. gives reasonably good qualitative results only (more than 20% quantitative discrepancy with ex.). Furthermore, o.b. is predicted from these calculations for incident laser field detunings on either side of the two-photon biexciton resonance as well as in the neighbourhood of the resonance. The nonlinearity in the dielectric function that causes o.b. is seen to be very nearly of the Kerr medium type, and consequently, the two-photon biexciton resonance contributes only weakly to the o.b. characteristics.
Experimental evidence for the occurrence of optical bistability using the biexciton two-photon resonance in CuCl is presented. These observations agree with recent theoretical predictions that require an intensity of 10 MW/cm2{\mathrm{cm}}^{2}cm2 and 10-\ensuremath{\mu}m-thick etalons with 90% reflective coatings. Earlier much less demanding predictions neglected two important physical effects: unsaturable background absorption at the biexciton from the tail of the exciton resonance and broadening of the biexciton resonance with intensity.
The stationary solution for optical bistability (OB) using a semiclassical exciton-biexciton model of CuCl is calculated exactly in the limit of large Fresnel number. The numerical solution of the second-order Maxwell equation is compared with corresponding results obtained with use of the slowly-varying envelope approximation (SVEA) as well as the mean-field approximation (MFA). It is found that results obtained using the SVEA are in close quantitative agreement with the numerical solution of the second-order Maxwell equation for each point in the parameter space considered, whereas the MFA correspondingly gives good qualitative results only. Furthermore, it is shown that the nonlinearity in the dielectric function for exciton-biexciton CuCl which causes OB is very nearly of the Kerr-medium type, and consequently, the two-photon biexciton resonance contributes only weakly to the OB characteristics.
An investigation is reported of static and dynamic optical bistability and optical switching in a system of coherent excitons and biexcitons in semiconductors subject to the exciton-photon interaction and optical conversion of excitons into biexcitons. The Heisenberg equations of motion for excitons and biexcitons and the wave equation for the field are used to derive a system of nonlinear differential equations describing the dynamic evolution of such a system. The equation of state for a theory of optical bistability is derived for the static case. A study is made of the stability of stationary optical bistability states. A computer experiment is used in an investigation of the switching times between the branches
The dynamical evolution of the electromagnetic field amplitudes is numerically calculated using an exciton-biexciton model of CuCl. For a bistable system we determine the switch-down and switch-up times and find them to be well explained by the polariton escape time using the group velocity for the polaritons. Our switching times, about 80 psec at photon energies of 3177 meV, are at least an order of magnitude larger than a previous theoretical estimate and we predict the switching times will become longer as the exciton resonance is approached.