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An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga1−xAlxAs cylindrical nano-wire has been performed in the presence of an external electric held. The band nonparabolicity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that (i) Presence of electric field causes both blue and red shifts in absorption spectrum; (ii) The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; (iii) For large values of electric field the effect of conduction band nonparabolicity is less dominant and parabolic band is estimated correctly; (iv) In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.

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