The Influence of Second Order Optical Nonlinearity on Effects of the Nonlinear Index of Refraction

In recent years, efforts to exploit the third-order optical nonlinearity in devices for optical signal transmission (soliton propagation) and signal processing (nonlinear switching) have multiplied [1, 2, 3]. In contrast to the theoretical description of soliton propagation in optical fibers, the simulation of χ(3)-effects in integrated optic signal-processing components employing materials without inversion symmetry necessitates the consideration of the non-vanishing second-order nonlinear susceptibility χ(2). Here, the input optical field drives an, in general, phase-mismatched second harmonic (ω + ω → 2ω) which, in a further second-order mixing process with the input field (2ω – ω→ ω), generates a nonlinear polarization at the input field frequency. This nonlinear polarization, caused by two simultaneously occuring second-order mixing processes, combines with and modifies the effect of the directly generated third-order polarization.