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The efficiency of detection of laser radiation in the magnetized transparent ferromagnetic materials was investigated. The nonlinear interaction of electromagnetic waves in the ferromagnetic for the different forms of the magnetization curve of a ferromagnetic in MatLab environment was modeled. It is shown that the detection of amplitude modulated electromagnetic radiation can be obtained as a result of such nonlinear interaction. The magnitude and sign of detected signal greatly depends on the shape of the magnetization curve and on the applied external magnetic field. The simulation results for the samples of monocrystalline yttrium iron garnet are well correlated with the experimental results.