A novel means of realizing optical logic with passive silicon-on-insulator (SOI) waveguide elements is proposed and modeled. Using what we call interference logic (IL), information is encoded and manipulated in the complex domain by properly setting the amplitude and phase of information inputs through specially designed waveguide structures, with the resulting wave interference used to compute the desired function output. We demonstrate that any arbitrary Boolean logic function can be realized in any physical system in which interference occurs. In this work, optical interference logic utilizing constructive and destructive interference of 1.55 micron light waves in multi-mode interference (MMI) couplers fabricated with SOI rib waveguides is described. Defining a vector representation of the complex information, a numerical function minimization algorithm is employed to compute the optimum input vector manipulations needed to realize a given operation's truth table. As such, with the definition of an output amplitude detection threshold separating "0" and "1" results, logic operations can be performed. A digital 2 x 1 multiplexer (MUX) is implemented in a single 4 x 1 MMI coupler where 1 of the 4 inputs serves as a reference input beam. With an input spacing of 40 micron, the 2 x 1 multiplexer has an overall dimension of 160 micron x 2.25 cm. Simple varied-dimension waveguide elements are used to adjust input wave amplitude and phase. To confirm and optimize the designs, device operation is simulated using 2D beam propagation method (BPM).© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.