Theoretical Study for Wavelength Conversion of Cascaded Second-Order Nonlinearity in Silica Fiber

Abstract

In this paper, A novel wavelength divison multiplexing (WDM) nets is proposed by use of cascaded second-order nonlinearities (χ⁽²⁾:χ⁽²⁾) in the D-fiber grating after periodically thermal/electric-field poling, and is theoretically analyzed for the first time. The coupled mode equations of the χ⁽²⁾:χ⁽²⁾ nonlinearities are derived, and the analytic expressions for the electric-field amplitude of converted light wave and the conversion efficiency η are obtained under the small signal approximation, which are well consistent with numerical calculations. Both analytic expressions and numerical results show that, under the phase matching, η 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 η and Δλ of this fiber grating can be reached over -17dB and 120nm, respectively. With the increase of L, η increases rapidly while Δλ decreases quickly. The results of simulated calculations and theoretical analysis show that the cascaded χ⁽²⁾:χ⁽²⁾ process is different from quasi-phases-matched difference-frequency generation.