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Physical Review Letters

Optical Nonlinearity Induced by Giant Dipole Moment of Wannier Excitons

Akira Shimizu

Published Aug 1, 1988• 39 citations
Publisher

Abstract

A new mechanism for enhancing optical nonlinearities in quantum well structures, subject to an electric field normal to the layers, is investigated. It is found that large nonlinearities are induced by virtual transitions of Wannier excitons with "giant dipole moments." In contrast to other mechanisms, this enhancement mechanism is independent of correlations between excitons, for any order of nonlinearities. This fact results in a resonant enhancement at half the excitonic energy, and an ultrafast response, even faster than other virtual-process-induced mechanisms.

DOI
10.1103/physrevlett.61.613

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A new mechanism for enhancing optical nonlinearities in quantum well structures, subject to an electric field normal to the layers, is investigated. It is found that large nonlinearities are induced by virtual transitions of Wannier excitons with "giant dipole moments." In contrast to other mechanisms, this enhancement mechanism is independent of correlations between excitons, for any order of nonlinearities. This fact results in a resonant enhancement at half the excitonic energy, and an ultrafast response, even faster than other virtual-process-induced mechanisms.
A new concept on optical nonlinearity due to virtual transitions in quantum well structure with electric field, named virtual charge-induced optical nonlinearity, is proposed, with a showing of some examples of theoretical result on the nonlinearity. The switching time of the nonlinearity is expected to be extremely short, 100 fs. The nonlinearity seems to be observable and quite useful for the design of an ultrafast optical gate. A possibility of optical bistability without external optical feedback, based on the proposed nonlinearity, is pointed out.
The Coulomb interaction among photoexcited virtual carriers or virtual excitons in two-dimensional heterostructures is theoretically considered by using bare-states and the dressed-states approaches. It is shown that, if the wave functions of the ground and the excited states are spatially separated, then the Coulomb interaction causes coherent pulsations of the transition energy. As a result, significant (an order of magnitude) enhancement of the dynamic Stark shift and of other ultrafast nonlinearities can be achieved. The enhancement of ultrafast nonlinearities is evaluated as a function of the geometry, the doping level, broadening, and other parameters. The effects of the Coulomb interaction on coherent transient phenomena is considered. The problem of practical realization of the predicted effects is addressed.
Recent works in the area of ultrafast nonlinearities due to virtual carriers in semiconductor heterostructures have generated significant interest among researchers. It has been shown that excitons in QW's behave very much like conventional two-level atoms, to the extent that exciton-exciton interaction can be neglected. Therefore, fast coherent phenomena usually associated with two-level system may occur in excitonic QW transitions. Indeed, dynamic (AC) Stark effect in QW's have been demonstrated. When semiconductor QW's were pumped below the absorption edge there were a strong "blue" shift of the exciton resonance, accompanied by a strong bleaching.
We study the nonlinear optical response of molecular assemblies consisting of coupled two-level molecules with arbitrary geometry including inhomogeneous broadening and exciton dephasing. An analytical expression for the third-order optical susceptibility is derived based on a certain closure of the equation-of-motion hierarchy. An exact expression for the third-order response of small crystalline aggregates with exciton population relaxation is derived, and used to show that for low relaxation rate \ensuremath{\Gamma} the cooperative part of the nonlinear response scales as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1/2}$ in d=1, and up to logarithmic corrections, as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$ in d=2 and 3. We show that cooperative enhancement is caused by exciton scattering. This is to be contrasted to other cooperative effects such as superradiance, which are related to the size of molecular coherence domains and therefore scale as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}\mathit{d}/2}$. In a numerical study for dipole-dipole interactions in d=1, 2, and 3 dimensions we find that the local-field approximation is valid only in selected cases, and in general fails to reproduce the magnitude and the resonance structure of ${\mathrm{\ensuremath{\chi}}}^{(3)}$.
We observe ultrafast and large nonlinear optical responses of a semiconductor thin film where excitons are weakly confined and their center-of-mass motion is quantized. The observed degenerate four-wave mixing (DFWM) signal of a GaAs double-hetero-structure layer exhibits an anomalous thickness-dependence, and is much enhanced at the thickness of 110nm. The decay time of the response is the order of ps, which depends on the thickness of the layer and on the number of the layer. These phenomena are elucidated by the theory of the nonlocal interaction between excitonic states and the light beyond the long wavelength approximation regime. The enhancement at the thickness is due to the size-resonant enhancement of the internal field with a nano-scale spatial structure, where the second quantized level of the exciton center-of-mass motion mainly contributes to the large response at the thickness. We, furthermore, demonstrate ultrafast response in a reflective type nonlinear polarization rotation switch with the 110nm thick three double-hetero. The signal intensity of 20% for the reflective pulse was obtained at a pump intensity of 10nJ/cm2, and the decay time is 1.5ps at low temperatures. These results provide a novel design of a semiconductor structure in order to obtain both large and ultrafast nonlinear response that is suitable for device application.
Excitonic resonances in semiconductors are very sensitive to applied optical fields. We present here a comparison between the effects of resonant and non resonant optical excitation, creating respectively real or virtual excitons. A blue shift of the exciton line and a reduction of the oscillator strength are simultaneously observed in multiple-quantum-well-structures for the two following cases : presence of a population of real excitons in very thin wells (two-dimensional systems), or presence of an intense offresonance non absorbed optical field (virtual excitons) independently of the well thickness. The latter configuration (optical Stark effect) has been studied as a function of pump intensity, determining in particular how the saturation of the blue shift is related to the exciton bleaching.