# what does it mean to unfold a resonator

A way to find the modes propagating in a resonator of length $$L$$ is to write the field as $$E(x,y,z)e^{i \omega t}$$ and calculate $$E(x,y,z)$$ inside an equivalent periodic lens structure. Then imposing self consistency on the round trip $$E(x,y,z+2L)=\sigma E(x,y,z)$$ we find modes. Can you explain the concept behind this technique, for example, what is the meaning of E(x,y,z) when $$z>2L$$?

• If I understand what you're asking, when $z > 2L$ , you have gone past the next periodic lens, and you can start over with $z= 0$ for propagation to the following periodic lens. – Carl Witthoft Apr 13 at 12:10