Take the below image for example: Let's imagine the cladding is really just perfect mirrors, where all light energy is reflected back towards the core. I understand that modes arise by imposing the condition that round-trip (two bounces) light must accumulate 2π radians of shift.
However, clearly with perfect mirrors, the light will continue to reflect forever. In this case, what does the light look like? Do we tend to represent it as linear combinations of the modes?
Also, if the answer is "the light interferes with itself destructively", then where does the power go?