Silicon Photonics for Forney Style Factor Graph Computation

Factor graphs can be used to diagram calculations which include inputs and outputs characterized by probability distributions (eg, multiple noisy measurement inputs, resulting in an uncertain output). Instantiating such a factor graph as a photonic integrated circuit requires identifying optical elements which can operate as "scaling nodes" (with an output that is a scalar multiple of the input), "summing nodes" with an output which is the sum or difference of two inputs), and "equality nodes" (with two or more outputs that are equal to the input.) In this proposal, the signal level is defined as the ratio of the power in one waveguide (labeled ōsigö) to power to the power in an adjacent waveguide (labeled ōrefö). The purpose of this referencing is to make it possible to implement the equality node of a factor graph -- when the power in both the signal and reference waveguides is reduced by half at a splitter, the ratio is left unchanged, and is equal on both output paths.ĀAn additional advantage is that this kind of relative measurement makes optical amplification unnecessary in the implementation of the scaling node: one can make the ratio bigger by making attenuating the light in the reference channel, rather than amplifying the signal channel. This scalability also makes summation more straightforward: the reference waveguide can be used to ensure that optical fields which are being added (eg, at a directional coupler, with a phase shifter to ensure constructive interference, or destructive in the case of subtraction) are on the same scale, even if they have been subject to different optical losses prior to the addition operation. Vector operations can be inmplemented if each vector component is represented by a differentĀinput wavelength.Ā Optical networks of this type can be ōprogramableö if they make use of interferometers or resonators along with on-chip phase shifters, to route light from one port to another. A phase shifter inside one arm of an interferometer can also be used to write intensity noise if necessary, which can become a direct analog of noise on the measurement being represented. The primary objective of Phase 1 would be to design and model the performance of such a network for Forney-style factor graph problems, understanding the requirements in terms of optical power and on number of chip phase shifters, the density of nodes and programmability of message paths.