Super-resolution interferometric phase measurements with directionally unbiased linear-optical devices

The everyday optical beam-splitter has four ports connecting electromagnetic field modes in a single scattering event. However, in practice, beam-splitters only route light between two modes going forward. We consider a new class of multiport linear optical scatterers which do connect all available modes to each other, a feature we call unbiased. Using a particular multiport known as the Grover four-port, we form a counterpart of the traditional Michelson interferometer with increased operational modal dimensionality. Due to the unbiased nature of the centerpiece scatterer, the interferogram produced by the device can be continuously tuned away from the standard Michelson sinusoid, becoming increasingly skewed, as the control phase of one arm is adjusted. The intensity can be made to vary much more rapidly as a function of the second arm's phase, allowing super-resolution measurements of this phase to be made. We study the tradeoff between loss and system optimal resolution, and show even in the presence of significant losses, the new system outperforms a standard Michelson interferometer.