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Used to work in photonics. The star coupler portion is a Rotman lens, the whole thing is different (an AWG). It's used to spectrally separate an input (or in this case, inputs) across different outputs.

So the inputs are all the same spectrum and come out shifted by various amounts or something like that?

See link "Working with Luceda AWG Designer" on top of the page you linked. It's got a nice explainer.

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