Things I Think About

Here is a list, in no particular order, of things that have come to my mind while working/talking about optics.

Higher Order Whispering Gallery Modes:

Inside a whispering gallery, if a beam doesn't align with itself after one lap, does anything prevent it from aligning with itself after n laps? If this is true, then in principle there should be many resonating angles.

Limit of Huygen's Principle:

Mathematically, when we consider Huygen's Principle in an aperature, we say that every point in the aperature acts as a point source. We do this by integrating, so each point is infinitely small. My question: is there a resolution to this principle? In other words, if we consider a numerical approximation of the integral, and let dx get smaller and smaller, is there a limit where this approximation becomes "too good?" If such a limit exists, would it be the wavelength of the wave?

I have no idea why/how this idea came to me, just a hunch. For some reason the idea of an infinite number of sources bothers me. In the odd chance I'm on to something, the effects of this approximation being "too good" are probably negligible.