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Physical Review B

Intrinsic optical intersubband bistability in quantum well structures: Role of multiple reflections

Victor Bondarenko, Miroslaw Zaluzny

Published Jan 8, 2015• 6 citations
Publisher

Abstract

We theoretically investigate the nonlinear intersubband response, in particular the intrinsic optical bistability (IOB), of quantum well (QW) structures embedded into layered systems. A semiclassical approach is employed based on the plane-wave approximation, the transfer-matrix formalism, the sheet model, and the density-matrix formalism developed to calculate the two-dimensional nonlinear intersubband electron conductivity and the IOB. A variety of presented numerical results demonstrate the importance of inhomogeneity of spatial distribution of radiation intensity induced by multiple radiation reflection for the IOB in layered structures. It is shown that knowing the radiation intensity distribution in the area occupied by QWs, in part standing-wave patterns, are crucial for understanding of IOB pictures. The IOB in systems of one, two, three, five, and ten QWs is investigated. The multistability phenomenon is addressed.

DOI
10.1103/physrevb.91.035303

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We theoretically investigate the nonlinear intersubband response, in particular the intrinsic optical bistability (IOB), of quantum well (QW) structures embedded into layered systems. A semiclassical approach is employed based on the plane-wave approximation, the transfer-matrix formalism, the sheet model, and the density-matrix formalism developed to calculate the two-dimensional nonlinear intersubband electron conductivity and the IOB. A variety of presented numerical results demonstrate the importance of inhomogeneity of spatial distribution of radiation intensity induced by multiple radiation reflection for the IOB in layered structures. It is shown that knowing the radiation intensity distribution in the area occupied by QWs, in part standing-wave patterns, are crucial for understanding of IOB pictures. The IOB in systems of one, two, three, five, and ten QWs is investigated. The multistability phenomenon is addressed.
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.
We discuss, theoretically, employing formalism based on the transfer matrix method and the so-called sheet model, the linear and nonlinear (saturated) optical phase shifts associated with intersubband transitions in multiple quantum well (MQW) structures. A commonly used total internal reflection geometry is considered. Numerical simulations are performed for two-level GaAs∕AlxGa1−xAs MQWs. They show that the above-mentioned phase shift can be greatly modified by optical interference effects and radiative coupling between QWs particularly at the grazing angle of incidence. For the restricted range of parameters even the bistable behavior of the nonlinear phase shift and reflectivity are possible.
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.