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A continuation method is developed for solving the inverse medium scattering problem of time harmonic Maxwell equations in R 3 . By using multifrequency scattering data, our reconstruction algorithm first employs the Born approximation for an initial guess and proceeds via recursive linearization on the wavenumber k. At each linearization step, one forward and one adjoint state of the Maxwell equations are solved. Numerical examples are also presented and discussed.doi:10.1088/0266-5611/20/2/l01 fatcat:zlp2qqynoncvpmenzayck33wwi