I am trying to understand how a Mach-Zehnder interferometer works. It seems that it will work whether we use two beam splitters that consist of either
- glass prisms glued together
- a sheet of glass with dielectric coating
- a sheet of glass with a thin metallic coating
Let us ignore the slight optical path difference induced by light travelling inside glass (for a perfectly symmetric interferometer setup these delays will cancel each other anyway).
I can make sense of scenario 2 as explained here - if light hits the dielectric beam splitter one of the outgoing beams must have a phase shift of $\pi$ so that energy is conserved (see derivation here). More precisely, if light hits the beam splitter coming from the less dense medium (red), part of the light is reflected with a phase shift of $\pi$, whereas the transmitted part has no phase shift. But what exactly happens at the interface glass - dielectric so that no phase shift occurs (blue)?
To summarize I want to understand the amount of phase shift that each of these types of beam splitters induce as well as the mechanisms involved.
