# Fabry-Perot cavities and phase difference

I'm reading a paper which says

The beam that reflects from a Fabry–Perot cavity is actually the coherent sum of two different beams: the 'promptly reflected beam', which bounces off the first mirror and never enters the cavity; and a 'leakage beam', which is the small part of the standing wave inside the cavity that leaks back through the first mirror.

I understand this. However, the author then writes

If the cavity is resonating perfectly, then the promptly reflected beam and the leakage beam are exactly 180° out of phase. In this case the two beams interfere destructively, and the total reflected beam vanishes.

I don't understand why these two beams would be 180° out of phase.

This is my (flawed?) understanding:

The light beam comes in as beam 1. Beam 2, the part that is reflected, get a 180° phase shift w.r.t. beam 1. Beam 3 continues without any phase shift w.r.t. beam 1. Part of beam 3 is reflected as beam 5. So, beam 5 has a 180° phase shift w.r.t. beam 3. The part of beam 5 that goes back through the first mirror is called beam 6, and this has the same phase as beam 5. So, both 2 and 6 are both shifted by 180°, each. So, they are in phase, and would constructively interfere... right?

• Note the requirement on the cavity resonating perfectly. This means that any attempt at explaining this with a finite number of in-cavity reflections (let alone just one) are doomed to failure. Commented Sep 12, 2013 at 15:04
• @EmilioPisanty So... how would you explain it then? Commented Sep 12, 2013 at 15:07
• The way I've always seen it done is using transfer matrices. From what I understand, it handles all the reflections in each material by just looking at the resultant E and B fields and matching boundary conditions, very similar to the quantum tunneling problem through a finite barrier. Commented Sep 12, 2013 at 15:37