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In this article the equations for two waves propagating in two fibers of nonlinear Kerr coupler for optical Mach-Zehnder interferometer are derived. Based on the resolution of those equations, the expressions describing relation between coherent length, input intensity of the wave, nonlinear coefficient of refractive index for 3dB Kerr coupler are introduced and discussed.

In this work, we study the influence of Doppler broadening on cross-Kerr nonlinearity in a four-level inverted-Y atomic system under electromagnetically induced transparency (EIT) condition. The first- and third-susceptibilities in the presence of Doppler effect are derived as a function of probe, signal and coupling beams and temperature of medium. Under EIT condition, cross-Kerr nonlinearity is enhanced several orders of magnitude compared to that without EIT. The Doppler effect leads to a reduction in the transparent efficiency and thus reduces the amplitude of cross-Kerr nonlinear coefficient. For hot atomic gaseous medium, such consideration of the Doppler effect may be useful for experimental observations and apply to photonic devices operating at different temperature conditions.

Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity is basically modified and greatly enhanced in the spectral region corresponding to EIT transparent window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature. Such controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity.

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.