An ensemble of interacting metal nanostructures supporting localized surface plasmon resonances can be described as a plasmonic circuit. We show that such circuits can perform all-optical linear mathematical operations on multiple input signals, a mechanism we describe as nanoscale optical signal processing. An example plasmonic circuit that mixes together two optical signals at the subwavelength scale and outputs a measure of their phase difference is demonstrated experimentally. It is also shown that the difference circuits function as meta-atoms in a metamaterial that has potential for position-dependent signal processing of an incident light wave.
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