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Photonics and Nanostructures - Fundamentals and Applications

Third-order non-linear susceptibility in a three-level QD system

Amin Habbeb AL-Khursan, M.K. Al-Khakani, K.H. Al-Mossawi

Published Jul 23, 2009• 41 citations
Publisher
DOI
10.1016/j.photonics.2009.06.004

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Abstract This paper presents the dynamics of Kerr nonlinearity and the phenomenon of slow group velocity in a Quantum Dot (QD) system, using the mechanism of electromagnetically induced transparency (EIT). Employing a three-level QD setup and leveraging a ladder-type excitation approach, we analyse the interaction between a weak probe pulse and a strong control beam. By employing density matrix formalism, we derive the expressions for both linear and nonlinear optical susceptibilities, along with first-order linear dispersion terms. Our findings reveal that susceptibilities in the QD system, both linear and nonlinear, can be finely adjusted to desired probe frequencies through control parameter manipulation. Moreover, under the EIT regime, we observe the Kerr susceptibility on the order of 10−12 m2 V2 at a probe wavelength 1.359 μm. Additionally, the group velocity of the probe field experiences a remarkable slowdown by a factor of 103 compared to the speed of light in vacuum. Results obtained may have potential applications in fabricating nonlinear optical devices.
Abstract The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.
The third-order susceptibility is investigated in a five-level atomic system in which the laser beams couple the ground state to a four-level closed-loop system. It is found that under the condition of the multiphoton resonance, one can enhance the Kerr nonlinearity of such a medium by properly adjusting the amplitudes and phases of the applied fields. In this case, the linear and nonlinear absorption reduce considerably in a region with a positive group velocity. It is demonstrated that the third-order susceptibility is very sensitive to the relative phase of the applied fields. An analytical model is presented to elucidate such phase control of the Kerr nonlinearity. A comparison is also made between the Kerr-nonlinear indices for the five-, four-, and three-level systems. It is realized that the magnitude of the Kerr nonlinearity for the five-level system is larger than that of the three- and four-level counterparts. Finally, it is shown that effect of Doppler broadening can lead to an enhanced Kerr nonlinearity while maintaining linear and nonlinear absorption.