When modelling the photons' behaviour in Hong-Ou-Mandel (HOM) effect, those reaching the beam-splitter from the bottom side are considered to act differently than those coming from the other one:
In addition, reflection off the bottom side of the beam splitter introduces a relative phase shift of −1 in the associated term in the superposition.
Is there an easy way to explain that if the beam splitter is symmetric?
Edit. When the two photons reach the beam splitter, in the HOM (Hong-Ou-Mandel) effect, one would think that four different things could happen:
- Both get the same direction and it is the right one
- Both get the same direction and it is the top one
- Each one gets in a different direction (*2)
The fact is that the two terms "Each one gets in a different direction" get compensated because one gets a positive constant and the other one a negative one. My question is about that fact, that is justified because of the reflection off the bottom side in one of this two situations.