Dispersion and absorption properties of the Y-type-four-level system with electromagnetically induced transparency

The linear and nonlinear dispersion and absorption properties of a Y-type four-level system, which driven by a weak probing field and two coupling fields, are investigated. Using the perturbation method, third-order perturbation iterative solutions of the steady density matrix equations are obtained. Numerical results and the analysis with the dressed state show that when the two coupling fields are in two-photon resonance, the dispersion and absorption spectra are symmetrical, there is only one transparency window in the system. When the two coupling fields are off two-photon resonance, the dispersion and absorption spectra are no longer symmetrical, and there are two transparency windows in the system. The third-order nonlinear properties of the system are mainly determined by the population difference between the levels which associate with the probing field, and the contributions of the transitions associated with the coupling fields are negligible.