Dynamic optical interconnects: volume holograms as optical two-port operators

We view a real-time volume holographic medium as a programmable two-port device that operates on an optical electric field. A photorefractive two-port operator can be used to establish the interconnects required by neural network models. The index grating that forms in the medium serves to fully interconnect two layers of processing units and at the same time sums the input signals to the output layer. The dynamics of grating formation in photorefractive media are used to indicate the time evolution of the two-port operator when the diffraction efficiency of the medium is small. We experimentally demonstrate a projection operator whereby we store and recall, in iron-doped lithium niobate, seven 1-D images. The image storage is done without the usual angle or spatial encoding of reference beams. A projection operator is used to recognize what features of an input belong to a space defined by a set of stored vectors. The two-port operator can also be used to perform the complementary function: to recognize what features of an input do not belong to this space.