Optimization of Nonlinear Performance of Silicon-Nanocrystal Cylindrical Nanowires

The efficiency of light-matter interaction inside a nonlinear waveguide is determined by the local intensity of light, which varies with the lateral dimensions of the waveguide. In this paper, we develop a semianalytical method for optimization of the nonlinear performance of silica nanowires doped with highly nonlinear silicon nanocrystals (SiNCs). Our method reduces the problem of intensity maximization inside the nanowire to the solution of two coupled transcendental equations, one of which is the dispersion relation for the guided optical mode and the other is the necessary condition for the effective mode area (EMA) to attain its global minimum. By applying the developed method to the nanowires with different densities of SiNCs, we demonstrate that one may achieve a sufficiently strong confinement of the optical mode inside them, without resorting to the use of high-index semiconductor or metallic claddings. Specifically, we show that the effective area of the lowest-order TE mode may be reduced below 0.2 μm² at 750-nm wavelength, provided that SiNCs occupy more than half of the nanowire's volume. We also present empirical formulas for the optimal nanowire radius, effective mode index, and minimum EMA, based on the numerical results obtained with our method. These formulas are useful for the rapid design optimization of cylindrical nanowires in all-optical photonics nanocircuitry.