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physica status solidi (b)

Induced Absorption and the Dynamical Stark Shift Associated with Biexcitons

I. Balslev

Published May 1, 1990• 2 citations
Publisher

Abstract

Abstract The nonlinear optical phenomena associated with the formation of virtual biexcitons in direct gap semiconductors are studied. Relations are set up for real‐space two‐fermion operators using methods similar to those used when deriving a well known conservation law of k‐space operators for intraband and interband transitions. Restricting the analysis to the χ(3) level, or set of density matrix equations are obtained for the exciton‐biexciton system. Analytical solutions in the limit of small detuning show that the biexcitonic induced absorption and the dynamical Stark effect are closely related, and that the Stark shift as function of the pump frequency has a pole at the frequency of the exciton‐to‐biexciton transition.

DOI
10.1002/pssb.2221590139

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Journal of Experimental and Theoretical Physics•Nov 1, 1997•0 citations
Abstract The nonlinear optical phenomena associated with the formation of virtual biexcitons in direct gap semiconductors are studied. Relations are set up for real‐space two‐fermion operators using methods similar to those used when deriving a well known conservation law of k‐space operators for intraband and interband transitions. Restricting the analysis to the χ(3) level, or set of density matrix equations are obtained for the exciton‐biexciton system. Analytical solutions in the limit of small detuning show that the biexcitonic induced absorption and the dynamical Stark effect are closely related, and that the Stark shift as function of the pump frequency has a pole at the frequency of the exciton‐to‐biexciton transition.
The biexciton optical Stark-effect under resonant pumping between the exciton and biexciton levels is studied theoretically. The probabilities of biexciton two-photon absorption of a weak probe light and of one-photon biexciton-exciton transition are calculated. The optical Stark splitting manifests itself in two-photon biexciton absorption through two absorption peaks spaced 2 (Omega) apart. Omega is the Raby frequency. In the luminescence spectrum due to biexciton-exciton one-photon transition three luminescence maxima appear which are shifted with respect to the luminescence maximum in the case without pumping.
When a direct-gap semiconductor is irradiated in the transparency region, the exciton line blue shifts. This so-called optical Stark effect of the exciton is due to a coupling between the exciton and all biexcitonic states (bound or unbound). More precisely we show that the exciton shift results only from interactions between excitons (Coulomb interaction and Pauli exclusion). At large detuning, Pauli exclusion dominates, and the excitonic shift is the same as the dressed-atom blue shift. In material having a bound biexcitonic molecule, the excitonic blue shift, observed at large detuning, becomes a red shift at small detuning close to the exciton-biexciton resonance.
Excitonic resonances in direct-gap semiconductors have proved to exhibit similar optical non-linearities as in atoms. One example is the optical Stark effect [1] which occurs when the sample is excited by a strong pump field whose frequency is detuned from the optical transition. The optical Stark effect has been described as a coupling between the electromagnetic field and the resonance with no real absorption. It can also be seen as the creation of a virtual population in the excited state. A transient gain, quadratic in pump intensity, is associated to this effect as already observed in atomic systems [2]. This hyper-Raman process involves two pump photons and occurs at frequency 2ω p – ω0, where ω p and ω0 are the pump and atomic transition frequencies, respectively (see inset of Fig. 1).
We calculate the change in the absorption strength of excitonic lines induced by a pump beam tuned in the transparency region of a direct-band-gap semiconductor. We show that, in the large-detuning limit, and unlike what happens to the energy shift, this change does not simply take the dressed-atom value, but instead this value multiplied by a factor 1-d, where d is the space dimension. We also calculate the absorption strength for low-energy unbound excitonic states, and derive the absorption-amplitude change close to the band edge. Finally, we give the first correction to the large-detuning limit of the absorption strength, in the case of the lowest excitonic level.
We study a new class of nonlinear cooperative phenomena that occur when light propagates in direct-gap semiconductors. The nonlinearity here is due to a process, first discussed by A. L. Ivanov, L. V. Keldysh, and V. V. Panashchenko, in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. For the geometry of a ring cavity, we derive a system of nonlinear differential equations describing the dynamical evolution of coherent excitons, photons, and biexcitons. For the time-independent case we arrive at the equation of state of optical bistability theory, and this equation is found to differ considerably from the equations of state in the two-level atom model and in the exciton region of the spectrum. We examine the stability of the steady states and determine the switchover times between the optical bistability branches. We also show that in the unstable sections of the equation of state, nonlinear periodic and chaotic self-pulsations may arise, with limit cycles and strange attractors being created in the phase space of the system. The scenario for the transition to the dynamical chaos mode is found. A computer experiment is used to study the dynamic optical bistability. Finally, we discuss the possibility of detecting these phenomena in experiments.