Polarization Rotation in Silicon Waveguides: Analytical Modeling and Applications

The efficient use of optical nonlinearities in silicon is crucial for the implementation of silicon-based photonic devises. In this paper, we present an approximate analytical study of nonlinear polarization rotation in silicon-on-insulator (SOI) waveguides; the rotation is predominantly caused by the effects of self-phase modulation and cross-phase modulation, stemming from the anisotropic Kerr nonlinearity. In the first part of the paper, we analyze the transmittance of the Kerr shutter in the continuous-wave regime and address the problem of its optimization. It is essential for the generality of our conclusions that both free-carrier effects and two-photon absorption are properly accounted for in this study. We specifically show that the signal transmittance may be optimized by adjusting the waveguide length, the pump power, and the incident linear polarizations of pump and signal beams. In the second part of the paper, we examine the problem of power equalization with SOI waveguides. We validate the derived analytical solutions by comparing their predictions with the data from numerical simulations and illustrate the solutions by the examples of practical interest. The results of our work may prove useful for the design and optimization of SOI-based Kerr shutters, all-optical switches, and power equalizers.