# Plasmon modes of cylinder metalic particle

Solving Laplace equation gives plasmon modes of spherical metalic particle radius $$R$$, plasma frequency $$\omega_p$$. Famous result is $$l = 0, 1, 2, ...$$

$$\omega_l = \sqrt{\frac{l}{2l+1}} \omega_p$$

What is same result of cylinder metalic particle, radius $$R$$ and height $$H$$?