Complex optical and nanophotonic systems require that we think about light and optical devices in new ways. The powerful approach of singular value decomposition lets us describe optical components and communication channels through pairs of input and output functions – communications modes for the best channels, and mode-converter basis sets for optimal device descriptions. Using interferometer meshes, we can also synthesize arbitrary linear optical components this way, including self-configuring, self-correcting, and self-stabilizing systems in a combination of novel architectures and algorithms. The approach also allows new radiation laws and a novel quantization of the electromagnetic field.
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