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Physical Review A

Stationary properties of dispersive optical bistability in CuCI

Chi C. Sung, C. M. Bowden, Joseph W. Haus, W. K. Chiu

Published Oct 1, 1984• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.30.1873

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Stationary properties of dispersive optical bistability in a dense exciton-biexciton system: copper chloride

C. M. Bowden, Joseph W. Haus, Chi C. Sung +1 more

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.

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Dec 18, 1984•0 citations

Optical Bistability in CuCl

B. Hönerlage, J.‐Y. Bigot, R. Lévy

As it is well known from nonlinear optics, the dielectric function ε( Q ˜ ,ω) and the resulting polariton dispersion are functions of the excitation intensity. Since in CuCI biexcitons with energy EBi may be created by the absorption of two photons provided by different light sources, ε( Q ˜ , Ω ) depends on the density of photons with frequency ωℓ, defined such that.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

The Nonlinear Absorption Coefficient for Direct Two-Photon Creation of Biexciton

W. Ungier, Maciej Suffczynski

The absorption coefficient for the two-photon creation of biexciton is calculated for CuCl and wurtzite crystals. Because of the resonance effect only the intermediate lowest optically active excitonic states are taken into account. The absorption coefficient is expressed by a functional of the biexciton envelope. The numerical results are computed with the envelope function of Hylleraas-Ore type (modified and minimized by Brinkman et al). The obtained results for CuCI are in good agreement with absorption measurements published by Gale and Mysyrowicz.

Acta Physica Polonica A•Feb 1, 2002•0 citations

Optical Nonlinearity and Bistability due to the Biexciton Two-Photon Resonance in CuCI

Nasser N. Peyghambarian, Dror Sarid, H. M. Gibbs

It is well established that biexcitons can be generated directly by two-photon absorption in CuCI. The intensity dependent nonlinearity arising from this resonance can be used to obtain optical bistability. Recently, Koch and Haug(1) and also Hanamura(2) have predicted the possibility of a bistable operation in a CuCI Fabry-Perot etalon. Hanamura uses a density matrix formalism and predicts that the switching can respond in a picosecond time scale due to the virtual formation of biexcitons. Koch and Haug obtain the complex dielectric function from a Green's function formalism and suggest a bistable behavior for a thin CuCI slab. They use a constant value for the biexciton linewidth, γxx, and a zero value for the exciton linewidth, γx. Their results indicate that a 1-μm-thick CuCI etalon, with natural reflecting surfaces, can give rise to bistability with a switch-on intensity of about 0.1 MW/cm2. The biexciton resonance, however, is located on the tail of the exciton resonance, which acts as a background absorption.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

Optical bistability of a dense exciton-biexciton system: CuCl

Chi C. Sung, C. M. Bowden

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.

Physical Review A•Apr 1, 1984•24 citations

Optical Bistability in Semiconductors

Chi C. Sung, C. M. Bowden

There are two different models to explain the observed optical bistability (OB) in GaAs. Haken and Goll1 use the saturation of the two-level (electron and hole) atoms as the mechanism of OB, whereas the Stark shift of excitons is the dominant factor in the work by Koch and Haug.2 We analyze both models, including the local field effect.3 It is shown that the validity of each model depends very much upon the parameters involved. We also give a similar analysis for CuCℓ where the biexcitons are important. In contrast to the earlier work by Abram and Maruani,4 we find by careful analysis, including the origin of the background dielectric constant, that the local field correction is not important in this case. The contribution of the exciton and biexciton interaction, however, can be important and should be included in the calculation of OB given by Haug.5 The changes in the numerical results of Ref. 5, by including the exciton-biexciton interaction and the local field correction are to be represented.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•1 citation
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.
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.
The absorption coefficient for the two-photon creation of biexciton is calculated for CuCl and wurtzite crystals. Because of the resonance effect only the intermediate lowest optically active excitonic states are taken into account. The absorption coefficient is expressed by a functional of the biexciton envelope. The numerical results are computed with the envelope function of Hylleraas-Ore type (modified and minimized by Brinkman et al). The obtained results for CuCI are in good agreement with absorption measurements published by Gale and Mysyrowicz.
It is well established that biexcitons can be generated directly by two-photon absorption in CuCI. The intensity dependent nonlinearity arising from this resonance can be used to obtain optical bistability. Recently, Koch and Haug(1) and also Hanamura(2) have predicted the possibility of a bistable operation in a CuCI Fabry-Perot etalon. Hanamura uses a density matrix formalism and predicts that the switching can respond in a picosecond time scale due to the virtual formation of biexcitons. Koch and Haug obtain the complex dielectric function from a Green's function formalism and suggest a bistable behavior for a thin CuCI slab. They use a constant value for the biexciton linewidth, γxx, and a zero value for the exciton linewidth, γx. Their results indicate that a 1-μm-thick CuCI etalon, with natural reflecting surfaces, can give rise to bistability with a switch-on intensity of about 0.1 MW/cm2. The biexciton resonance, however, is located on the tail of the exciton resonance, which acts as a background absorption.
There are two different models to explain the observed optical bistability (OB) in GaAs. Haken and Goll1 use the saturation of the two-level (electron and hole) atoms as the mechanism of OB, whereas the Stark shift of excitons is the dominant factor in the work by Koch and Haug.2 We analyze both models, including the local field effect.3 It is shown that the validity of each model depends very much upon the parameters involved. We also give a similar analysis for CuCℓ where the biexcitons are important. In contrast to the earlier work by Abram and Maruani,4 we find by careful analysis, including the origin of the background dielectric constant, that the local field correction is not important in this case. The contribution of the exciton and biexciton interaction, however, can be important and should be included in the calculation of OB given by Haug.5 The changes in the numerical results of Ref. 5, by including the exciton-biexciton interaction and the local field correction are to be represented.