Nonlinear Optical Properties Of A D~- System In A Two-dimensional Quantum Ring

Using an appropriate coordinate transformation and the product base of harmonic oscillator method within the effective mass approximation,we have calculated the energy spectrum and corresponding wave functions of a quantum ring with two electrons and a single positive ion,i.e.a negatively charged donor center(D~-).and we obtained the binding energy spectra of the barried D~-centre in a quantum disc as a function of magnetic field strength.By adopting the compact density matrix approach,the nonlinear optical properties of an electron in the QR have been further studied.We have investigated the magnetic field effect on the linear and the third-order nonlinear susceptibilities on basis of the density matrix formalism.We have found that the transition energy exhibits optical oscillation as the external magnetic field changes,along with the linear and nonlinear susceptibilities of the D~-system in a semiconductor quantum ring.The results have shown that it is possible to control the frequency shift and the intensity in the linear and nonlinear susceptibilities of the D~-system by varying the external magnetic field and the ring width in a semiconductor quantum ring.Both the peak position and peak height occur optical oscillation at the linear and nonlinear susceptibilities,implying a possible observation of the D~-system by the optical experiment.