The phenomenon of polarization interaction in certain nonlinear materials is presented, and the design of an all-optical logic device based on this concept is described. An efficient two-dimensional finite-difference time-domain code for studying third-order nonlinear optical phenomena is discussed, in which both the slowly varying and the rapidly varying components of the electromagnetic fields are considered. The algorithm solves the vector form Maxwell s equations for all field components and uses the nonlinear constitutive relation in matrix form as the equations required to describe the nonlinear system. The stability of the code is discussed and its accuracy demonstrated through the simulation of the self-phase modulation effect observed in Kerr media. Finally, the code is used to simulate polarization mixing in photonic crystal-based line defect and coupled resonator optical waveguides.