Abstract: In this paper, the electromagnetic response of multi scatterers excited by a Gaussian plane wave is calculated using simultaneous extrapolation in time and frequency domains based on Laguerre function expansion. The key of the algorithm is expressed as follow. At first, the early time and low frequency response is obtained using method in time and frequency respectively. Then, the whole response is obtained to extrapolate simultaneously in both time and frequency domains using early time and low frequency information. The approach is attractive because the results are exact and the computation involved is minimal. Thus, the overall analysis is computationally very efficient.