Consider a simple cavity formed by placing two parallel infinite perfect conducting planes a distance d from each other as shown in the figure below. Assuming the wavelength of operation represented by $,$ find: $($a$)$ The field profile and resonance frequency of the resonance modes. How do you represent these modes $($e$.$g$.,$ TEnmq, TMnm$,$ etc.$).($b$)$ The free spectral range of the modes you found in part $($a$)($c$)$ A general formula for the electric field of the modes you found in part $($a$).($d$)$ Plot the resonance frequency and the mode volume as functions of the mode number. What can you say about the variation of mode volume with the mode number? Explain. What can you say about the variation of mode volume with the mode number? Explain.

Figure P$1$