Today, the behavior of wave in multilayer media in applied electromagnetics has been an important issue. Finding Green’s function of multilayer media in wave number spectrum domain is analytical which can be calculated for different combination of source and field. This thesis is based on cascaded transmission lines which readily can be evaluated by the aid of circuit and transmission line theory. By this method, the complete set of Green’s functions of scalar and vectorial potentials in multilayer media for horizontal and vertical electric dipole would be obtained. So, for the calculation of local Green’s function, we need to use Sommerfeld integral instead of Cantur integral to avoid of high complexity. And also for description of multilayer media problems, we can utilize mixed potential integral equations (MPIE) by means of time-space domain Green’s function. One of the key problems of integral equations of time domain in multilayer media is nonexistence of time domain Green’s function in the closed form. Therefore, in this situation, complex time Green’s function has been introduced which is a kind of approximation for time domain Green’s function in closed form. In this method, Green’s function of wave number spectrum domain is defined based on exponential series of frequency and wave number spectrum variables. So, because of nonlinearity of objective function, linear method for calculation of coefficient and two-dimensional expansion is not applicable. Then, appropriate optimization methods can be employed for the calculation of unknown coefficients of expansion. One effective and novel method for solving of two-dimensional expansion is the use of hybrid method consist of quasi Newton method (BFGS) and optimization methods like PSO and Taguchi. In this thesis, after precise calculation of a Green’s function for vertical electric dipole in two-layer media (air and ground) and for horizontal electric dipole in microstrip by cascaded transmission lines, and with the combination of PSO optimization method and Taguchi method as well as BFGS nonlinear method; two-dimensional exponential coefficient with higher accuracy and rate of convergence for Green’s function of wave number spectrum domain in two-layer media and one microstrip are considered. Keywords: Multilayer media, complex time Green’s function, microstrip, Sommerfeld integral, BFGS method, PSO method, Taguchi method