Vector potential in cavity of arbitrary shape

[Tianwu Zang]

we know that vector potential in a resonator satisfies the equation $$\int$$$$A$$($$\lambda$$)$$A$$$$^{*}$$($$\lambda$$$$^{'}$$)$$d$$$$V$$=$$4$$$$\pi$$c$$^{2}$$$$\delta_{\lambda\lambda$$$$^{'}$$
So how about in cavity of arbitrary shape? Does this equation still valid?
Thanks!

 

[Meir Achuz]

The equation represents the orthogonality of modes of different frequencies.
It would hold in a cavity of any shape, but the functions A would be harder to find.