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Superlattices and Microstructures

Magnetostatic modulation of nonlinear refractive index and absorption in quantum wires

Alexander A. Balandin, S. Bandyopadhyay

Published Jun 1, 1998• 0 citations
Publisher

Abstract

The magnetic-field dependence of the nonlinear differential refractive index Δnand absorption Δα in quantum wires—measured by non-degenerate pump and probe spectroscopy—is investigated theoretically. The nonlinearities arise from population saturation of the excitonic state under optical pumping and the formation of biexcitons (excitonic molecules). Both Δnand Δ α exhibit positive and negative peaks at certain pump and probe detuning frequencies associated with the formation of biexcitons and bleaching of excitons, respectively. The amplitude, lineshape and the frequency at which these peaks occur can be modulated by a magnetic field which opens up the possibility of realizing novel magneto-optical devices. Additionally, the magnetic field may allow us to realize a relatively large variation in the differential refractive index over a range of frequencies without significant accompanying absorption, thereby allowing the observation of optical bistability.

DOI
10.1006/spmi.1996.0258

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The magnetic-field dependence of the nonlinear differential refractive index Δnand absorption Δα in quantum wires—measured by non-degenerate pump and probe spectroscopy—is investigated theoretically. The nonlinearities arise from population saturation of the excitonic state under optical pumping and the formation of biexcitons (excitonic molecules). Both Δnand Δ α exhibit positive and negative peaks at certain pump and probe detuning frequencies associated with the formation of biexcitons and bleaching of excitons, respectively. The amplitude, lineshape and the frequency at which these peaks occur can be modulated by a magnetic field which opens up the possibility of realizing novel magneto-optical devices. Additionally, the magnetic field may allow us to realize a relatively large variation in the differential refractive index over a range of frequencies without significant accompanying absorption, thereby allowing the observation of optical bistability.
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In this work, the influence of an external magnetic field on the refractive index changes and optical absorption coefficients of a typical GaAs/AlxGa1−xAs coaxial cylindrical quantum well wire is studied. Energy eigenvalues and eigenvectors in the presence of a magnetic field are calculated using the fourth-order Runge-Kutta method and optical properties are obtained using the compact density matrix approach. It is found that the resonant peak values of the linear and the third-order nonlinear refractive index changes as well as the optical absorption coefficients of a cylindrical quantum wire decrease with increasing the magnetic field. However, these optical properties of a coaxial cylindrical quantum well wire are nonmonotonic functions of the magnetic field, due to the anticrossing of the subbands. The anticrossing effect leads to a large increase of the resonant peak values of these optical properties. Results also indicate that the resonant peak values of these optical properties decrease with increasing the barrier width.
Transient optical nonlinearities of semiconductor quantum dots in the strongly confined regime are studied, in which the exciton, biexciton and magnetic field effects are taken into account. The photo induced band-to-band electronic transitions are considered from both the heavy-hole (hh) and light-hole (lh) valence bands to the lowest (1s) exciton state below the fundamental absorption edge. The time dependent perturbation technique for a three-level system, under the near band gap resonant excitation regime, has been employed; with the incorporation of the relaxation and dephasing mechanisms phenomenologically. The induced polarization is calculated from where the real and imaginary parts of the third-order nonlinear optical susceptibility, responsible for the occurrence of nonlinear refraction and nonlinear absorption respectively, have been derived. The temporal and detuning spectra of nonlinear refraction and absorption; and their dependence on density of biexcitons and a moderately strong magnetic field, have been analyzed. It is observed that the nonlinear refraction and nonlinear absorption enhance with increasing magnetic field in small CdS quantum dots.
We report the observation of an intensity-dependent refractive-index nonlinearity in CdS due to a resonance state where an excitonic molecule is created by induced absorption of light. The refractive indexnas a function of the incident laser photon energyEis measured directly by light refraction in thin crystal prisms. A renormalized dielectric function describes the measuredn(E)spectra well. This strong refractive-index nonlinearity is well suited to produce an optical bistability and to further strengthen the evidence of CdS to be an important material for laser-induced dynamic gratings.
The saturation behavior of the nonlinear index δnNL in the band tail of GaAs/AlGaAs multiple quantum wells is experimentally studied in quasi-steady state and in a low absorption region (below 300 cm−1), where dispersive optical bistability is observed. Measurements at different detunings from the exciton resonance allow us to study the absorption dependence of the saturation parameters. The saturation intensity IS is found inversely proportional to the linear absorption coefficient, while the saturating nonlinear index δnS is approximately constant. This evidences that the nonlinear index saturation is due to a saturation of the carrier density versus light intensity, due to the saturation of the band tail absorption itself.