Thickness dependence of the surface-polariton relaxation rates in a crystal slab

A few useful formulas are derived concerning the damping properties of long-wavelength surface polaritons (SP) in a crystal slab. For example, it is shown that the SP propagation length in a metal slab with thickness 2a satisfying $\text{ω}{}_{\mathrm{p}}\text{a}\text{c}\text{< 1}$ (c is the velocity of light and ω_p the electronic plasma frequency) is increased by the factor $\text{3}\text{2}\text{(}\text{c}\text{ω}{}_{\mathrm{p}}\text{a}\text{)}{}^4$ in comparison with the corresponding value for SP in a semi-infinite metal.