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May 31, 2020 at 16:51 comment added S. McGrew If the polarizations are not in phase, the two cannot be combined into a single mode. With one polarization axis in phase and the other out of phase, the result will be a partially polarized, partially coherent mode.
May 31, 2020 at 16:32 comment added triclope Do you know what the mathematical relation between inputs and output is? I'm trying to understand your description, but got stuck with an edge case of the input being a in a superposition of polarization (H, V) and input spatial modes (1, 2) with one polarization in phase and the other not: $ |H\rangle_1 + |H\rangle_2 + i|V\rangle_1 - i|V\rangle_2 $.
May 28, 2020 at 15:57 history answered S. McGrew CC BY-SA 4.0