In quantum optics, are fiber beam splitters described by the same operators as free space beam splitters?

For example, a free-space non-polarizing beam splitter introduces a phase shift for the reflected component. Is it still true for a 2x2 fiber optic coupler? If it is, how do we know which output fiber corresponds to the transmitted component and which to the reflected component?

And is the same operator used for a free-space polarizing beam splitter and for a fiber-based polarization beam splitter?

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    $\begingroup$ I can't give you a precise answer, but from my understanding the beam splitter formalism as often found in quantum optics is very general, and applies to both fiber and free space beam splitters. The phase shift on one of the output ports relative to the other is also present. But you can imagine: it kind of doesn't matter which output has the phase shift and which one doesn't, as your output1 and output2 fields pick up phases anyways just by propagating through the fiber to the connectors. So on which output you dump the phase shift is kind of your choice for all practical purposes. $\endgroup$ – Georg E. Aug 26 at 0:31

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