We study enhancement of self-Kerr nonlinearity in three-level cascade EIT medium by the analytical method. The results apply to the 85Rb atoms and show that, in the presence of the EIT effect, the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-5 cm2/W) around transparent region. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Influence of Doppler broadening leads to a decrease in the amplitude of the Kerr nonlinear coefficient. Analytical results are useful for experimental observation and related applications.
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