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Journal of Modern Optics

Optical nutation in GaAs/GaxA11−xAs quantum well structures

Sharmila Banerjee, Pranay K. Sen

Published Aug 1, 1996• 3 citations
Publisher

Abstract

The possibility of occurrence of the coherent optical transient effect known as optical nutation has been analytically established in the semiconductor quantum well (QW) structure, namely GaAs/GaxA11−xAs most extensively used in optical electronics. Ultra-short-pulse low-intensity band-to-band excitation of electrons to the 1s Wannier-Mott exciton state of the crystal has been considered to play an important role in the coherent radiation—QW interaction. Numerical estimations of the complex optical susceptibility and the transmitted intensity under the transient regime reveal ringing behaviour confirming the occurrence of optical nutation in III-V semiconducting QW structures.

DOI
10.1080/09500349608232838

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Journal of Physics Conference Series•Sep 24, 2014•0 citations
The possibility of occurrence of the coherent optical transient effect known as optical nutation has been analytically established in the semiconductor quantum well (QW) structure, namely GaAs/GaxA11−xAs most extensively used in optical electronics. Ultra-short-pulse low-intensity band-to-band excitation of electrons to the 1s Wannier-Mott exciton state of the crystal has been considered to play an important role in the coherent radiation—QW interaction. Numerical estimations of the complex optical susceptibility and the transmitted intensity under the transient regime reveal ringing behaviour confirming the occurrence of optical nutation in III-V semiconducting QW structures.
Using a coherent radiation-semiconductor interaction model based upon the time dependent perturbation technique, the occurrence of optical nutation has been analytically investigated in direct-gap semiconductors such as GaAs, GaSb, InAs, and Hg1-xCdxTe, duly irradiated by near resonant laser beams. The present approach is much more simplified and straightforward than the conventional Maxwell-Bloch approach used so far for the study of coherent optical transient effects in molecular and atomic systems. The dispersion and absorption expressed in terms of the real and imaginary parts of the crystal optical susceptibility\chi_{r}and\chi_{i}exhibit temporally damped ringing behavior of Neumann and Bessel types, respectively. These processes have been identified as dispersive and absorptive optical nutation. The theory is developed for arbitrary laser intensity in presence of damping due to nonoptical processes. To understand the mechanisms of dispersive and absorptive optical nutation, we have restricted only to low-power resonant band-to-band transitions neglecting excitonic and damping effects. While studying analytically the transient behavior of\chi_{r}and\chi_{i}for a given pump field strength, it is noticed that the absorptive component exhibit remarkable qualitative agreement with the experimental observations of optical nutation in13CH3F.
We have proposed a simplified theoretical model to examine the optical nutation in one-dimensional semiconductor quantum wires. We explored the role of excitons, biexcitons, and the effect of confinement in enhancing transient optical processes in such semiconductor nanostructures. We apply the time dependent perturbation technique to the coherent radiation-semiconductor interaction for a three-level system in the near band gap resonant excitation regime. We have incorporated the relaxation and dephasing mechanisms phenomenologically. The induced polarization is calculated theoretically and the role of biexciton density on the polarization is analyzed. Numerical estimations of refractive and absorptive optical nutation have been made for a GaAs∕AlxGa1−xAs quantum wire duly shined by femtosecond pulse Ti: sapphire laser. Our results agree qualitatively with available experimental observations.
The effect of an external magnetic field on optical coherent transient phenomena has been analyzed for semiconductor quantum well structures (QWS). The Lüttinger Hamiltonian is used to incorporate the complex valence band structure which is modified due to the application of the magnetic field. We have considered a GaAs/AlGaAs QWS with magnetic field applied in the direction perpendicular to the plane of the well. We get two quantum levels due to confinement, and doubly degenerate heavy-hole and light-hole bands corresponding to each quantum level, thus leading to eight hole subbands. This results in an 8×8 Hamiltonian in an appropriately chosen basis. Energy eigenvalues and eigenvectors have been calculated by numerically diagonalizing the above Hamiltonian. The absorption characteristics and the optical coherent transient phenomena have been studied by solving the effective semiconductor Bloch equations in the weak excitation regime. The polarization induced in conjunction with the results obtained by solving the modified Lüttinger Hamiltonian has been used to analyze the transient characteristics. We observe a blueshift in transition energy with an increase in magnetic field. The features are changed dramatically when one includes band mixing. The crossing of subbands in the absence of band-mixing effects changes over to anticrossing behavior when band mixing is included. Multiple oscillations are observed in the optical nutation signal that can be attributed to band-mixing effects. Absorption spectra also show a significant blueshift with an increase in magnetic field and additional peaks appear when band mixing is included.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.
Optical nutation in GaAs/Al0.3Gao.7As core-shell quantum dot (CSQD) shined by femtosecond laser has been analyzed theoretically. The nutation signal intensity, arising due to photo-induced electronic transitions between ground state and first excitonic state, has been calculated using time dependent perturbation theory and rotational wave approximation. The dependency of the properties of optical nutation signal viz. its maximum amplitude and the oscillation frequency of the nutation signal has been studied at various CSQD's core radius and shell thickness.