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Journal of Optics B Quantum and Semiclassical Optics

Intrinsic optical intersubband bistability and saturation in a quantum well microcavity structure

X. Chen

Published Aug 13, 1999• 12 citations
Publisher

Abstract

On the basis of a local-field theory, the field distribution including third-order nonlinearity in a quantum well microcavity structure is derived, and an expression of intersubband optical absorption is thus obtained. It is found that local-field corrections at certain condition can act as a positive feedback so that a bistability can be established. In a quantum well microcavity structure, by changing the length of the cavity, the angle of incidence, the field confinement and the line widths, one can effectively detune the local-field feedback so that the threshold intensity and the `S'-type loop of the optical bistability can be modified.

DOI
10.1088/1464-4266/1/5/305

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Physica Scripta•Jul 1, 1995•27 citations
On the basis of a local-field theory, the field distribution including third-order nonlinearity in a quantum well microcavity structure is derived, and an expression of intersubband optical absorption is thus obtained. It is found that local-field corrections at certain condition can act as a positive feedback so that a bistability can be established. In a quantum well microcavity structure, by changing the length of the cavity, the angle of incidence, the field confinement and the line widths, one can effectively detune the local-field feedback so that the threshold intensity and the `S'-type loop of the optical bistability can be modified.
We present a theoretical formalism, based on the transfer-matrix method and the so-called sheet model, describing light propagation in multiple-quantum-well (MQW) structures in the range of the saturated intersubband absorption. A commonly used total internal reflection geometry is considered. Intensity of the reflected light as a function of the input intensity is calculated for two-level $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ MQW. Numerical simulations show that the optical nonlinearity of the structures can be greatly modified by optical interference effects. In the case of sufficiently thick structures and grazing angle of incidence the multiple reflections inside the MQW can lead even to bistability.
An intrinsic optical bistability in a double quantum well is described theoretically. The effect is based on the resonant tunneling of electrons against the electric-field force (the counterfield electron transfer) and is driven and controlled by far-ir radiation exciting an intersubband transition. The theory relies on the density-matrix technique and takes into account optical intersubband excitation, interwell tunneling, the relaxation of populations and polarizations, and the mean-field effects of the transferred electron charge (shifts of the levels and changes of matrix elements). Hysteresis-type curves are obtained for both the charge-transfer probability and the optical absorption as functions of the light intensity. The theory shows the effect to be readily observable under realistic conditions, with the exciting-light intensity as low as 50 W/cm2{\mathrm{cm}}^{2}cm2.
In the past few years advance in nanofabrication techniques have made it possible to make well-like compound semiconductor structures of low nanometer size.In these structures,the state of the electron in the direction perpendicular to the length of the well is quantized with sufficiently large separation in energy levels and the motion of the electron parallel to the length is that of a quasi-free electron.One of the most remarkable properties of these one-dimensional electron system is that the optical transitions between the size-quantized subbands are feasible.The result shows there is a large optical nonlinearities in asymmetric quantum wells.The problem of optical saturation of intersubband absorption has recently attracted considerable attention.The problem is very important to the development of superlattice devices such as fast infrared detectors and(modulators) because one needs to know the range of input optical intensities for which linear operation is(possible.) The analytical expression of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained in Pschl-Teller wells using the density matrix formalism taking into account the(intrasubband) relaxation.Since there are two adjustable parameters κ and λ in Pschl-Teller wells,the shapes of the wells will change with the change of the parameters κ and λ,accordingly the linear and the third-order nonlinear optical absorption coefficients will change with the parameters κ and λ.It is shown that the optical absorption coefficient depends on the parameter,and the optical intensity strongly. The absorption saturation will occur with I increase.Numerical results are presented for a typical AlGaAs/GaAs Pschl-Teller well.
Abstract Abstractauthoren A generalized cubic equation is presented to describe the intrinsic optical bistability (IOB) process in a two‐level system within the rotating wave approximation when repopulation of the two levels is governed not only by the incident radiation with changing intensity but also by an additional external factor (X‐factor). Numerical simulations are performed for two‐ and three‐quantum‐well (QW) systems without and within a microcavity. The obtained results demonstrate that a relatively small change of the X‐factor‐caused repopulation of the subbands (as in all QWs simultaneously as in only one selected QW) can produce a dramatic effect on the reflectance dependence upon the incident radiation intensity, in particular on the IOB pictures. It is shown that the IOB process (dubbed as the IOBX) can be driven by the cyclic change of the X‐factor‐caused repopulation of the subbands at a carefully chosen fixed value of the incident radiation intensity.
Taking as a starting point the Liouville equation for the one-body density matrix operator, a general expression for the third-order nonlinear current density responsible for the optical Kerr effect associated with intersubband transitions in a quantum well is derived by use of the perturbative expansion method. The nonlinear current density is related to the local field inside the quantum well via a nonlocal relation. By combining the field-induced nonlinear part of the current density with the Maxwell equation, a nonlinear integral equation for the local field is established. For a two-level quantum well, the integral equation is solved exactly. The nonlinear optical reflectivity, transmittance, and absorbance of the quantum well in turn are obtained. Numerical calculations of the light-induced change of the optical spectra are presented for a Al 0.5 Ga 0.5 As/GaAs/Al 0.5 Ga 0.5 As quantum well. The numerical results show that the optical reflectivity and absorbance decrease, and the transmittance increases as the optical intensity of the incident light is increased. In the case where the quantum-well structure is heavily doped, a notable light-induced red-shift of the location of the resonance peak in the optical spectra stemming from the combined local-field effect and field-induced population redistribution is predicted.