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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 $z>2L$?

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  • $\begingroup$ 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. $\endgroup$ – Carl Witthoft Apr 13 at 12:10

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