Rectangular electromagnetic cavity ($\nu =\frac{c}{2}\sqrt{(l/L_x{)}^2+(m/L_y{)}^2+(n/L_z{)}^2}$)

A closed rectangular perfect conductor cavity has discrete normal modes selected by zero tangential electric field at the walls. Each frequency has the displayed form. With all three indices positive there are two independent polarizations of an electromagnetic wave; modes with exactly one zero index have one, and those with two zero indices are absent. For example the $n=0$ family can have $E_z\propto \sin (\pi lx/L_x)\sin (\pi my/L_y)$, independent of $z$. It satisfies the wall conditions because $E_z$ is normal to the $z$ faces and tangential to the side walls. Omitting such zero-index families is harmless for leading bulk density of states, but changes the low-temperature physics of a thin cavity.