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The third-harmonic generation (THG) in GaAs∕AlGaAs cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over 10^-90. 3em{0ex}m^2∕V^2 can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.
Guanghui Wang (Thu,) studied this question.