Theoretical study for wavelength conversion of cascaded second-order nonlinearity in silica fiber

In this paper, A novel wavelength conversion method for wavelength division multiplexing (WDM) nets is proposed by use of cascaded second-order nonlin earities (chi ((2)):chi ((2))) in the D-fiber grating after periodically th ermal/electric-field poling, and is theoretically analyzed for the first ti me. The coupled mode equations of the chi ((2)):chi ((2)) nonlinearities ar e derived, and the analytic expressions for the electric-field amplitude of converted light wave and the conversion efficiency eta are obtained under the small signal approximation, which are well consistent with numerical ca lculations. Both analytic expressions and numerical results show that, unde r the phase matching, eta is proportional to the logarithm of the square of pump light power, and the 4th power of the grating length L and the second -order nonlinearity d. The calculated results also show that eta and Delta lambda of this fiber grating can be reached over -17dB and 120run, respecti vely. With the increase of L, eta increases rapidly while AA decreases quic kly. The results of simulated calculations and theoretical analysis show th at the cascaded chi ((2)):chi ((2)) process is different from the quasi-pha ses-matched difference-frequency generation.