Biexciton induced refractive index changes in a semiconductor quantum dot

• Calculations of biexciton and exciton states for different quantum dot sizes.
• Investigation of the refractive index changes in details, based on transitions between theses states in a three level model.
• Size-dependent three-photon size-dependent three-photon nonlinear refractive index change versus incident photon energy.

We present a detailed theoretical study of linear and third order nonlinear refractive index changes in a optically driven disk-like GaN quantum dot. In our numerical calculations, we consider the three level system containing biexciton, exciton, and ground states and use the compact density matrix formalism and iterative method to obtain refractive index changes. Variational method through effective mass approximation are employed to calculate the ground state energy of biexciton and exciton states. The evolution of refractive index changes around one, two and three photon resonance is investigated and discussed for different quantum dot sizes and light intensities. Size-dependent three-photon nonlinear refractive index change versus incident photon energy compared to that of two-photon is obtained and analyzed. As main result, we found that around resonance frequency at exciton–biexciton transition the quantum confinement has great influence on the linear change in refractive index so that for very large quantum dots, it decreases. Moreover, it was found that third order refractive index changes for three photon process is strongly dependent on QD size and light intensity. Our study reveals that considering our simple model leads to results which are in good agreement with other rare numerical results. Comparison with experimental results has been done.

Frequency dispersion of nonlinear change in refractive index around the three photon resonance at ω=ωeg/3ω=ωeg/3 and two photon resonance at ω=ωbg/2ω=ωbg/2 for different QD radii.Figure optionsDownload as PowerPoint slide