<span style="font-size:10.0pt;font-family: "Times New Roman";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: Mangal;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language: HI" lang="EN-US">External electric field effect on the nonlinear optical properties of a laser dressed donor impurity in a GaAs spherical quantum dot confined at the center of a Ga₁_{<span style="font-size: 10.0pt;font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-fareast-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: Mangal;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language: HI;mso-char-type:symbol;mso-symbol-font-family:Symbol" lang="EN-US">-<span style="font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Mangal;mso-ansi-language:EN-US; mso-fareast-language:EN-US;mso-bidi-language:HI" lang="EN-US">x</span></span>}<span style="font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Mangal;mso-ansi-language:EN-US; mso-fareast-language:EN-US;mso-bidi-language:HI" lang="EN-US">Al_xAs cylindrical nano-wire</span></span>

247-256Linear and third order nonlinear optical absorption coefficients and refractive index changes of an on-center donor impurity in a spherical GaAs quantum dot which is located at the center of a cylindrical Ga1-xAlxAs nano-wire, have been investigated under the simultaneous effect of electric field and laser radiation. The linear and third order nonlinear optical properties are calculated based on optical 1-2, 2-3 and 1-3 transitions by means of the compact density-matrix approach. The energy eigenvalues and corresponding wave functions are calculated using finite difference approximation and reliability of calculated wave functions is checked by computing orthogonality. It is shown that optical spectrum shifts towards lower and higher energies for 1-2 transition and shifts towards lower energies for 2-3 and 1-3 transitions as the electric field strength increases. The presence of laser field shifts absorption spectrum towards lower energies. In the absence of electric and laser field, the magnitude of absorption coefficient and refractive index changes increase in transitions between higher levels. Simultaneous presence of both electric field and laser radiation has great effect on magnitude of absorption coefficients and refractive index changes. The saturation in optical spectrum can be adjusted by electric field and laser radiation