Transmission of light through a thin metal film with periodically and randomly corrugated surfaces

We calculate the transmission of p- and s-polarized light, incident normally from vacuum, through a thin metal film deposited on a semi-infinite dielectric substrate. The vacuum-metal and metal-dielectric interfaces are one-dimensional randomly rough interfaces defined by x₃ ≤ -ζ(x₁) and x₃ ≤ -H+ζ(x₁), respectively, where the function ζ(x₁) has the form , with 0≤dn} are independent, identically distributed, random deviates drawn from a uniform distribution. By means of a rigorous numerical approach the transmissivity of a single realization of the film is calculated as a function of the wavelength λ of the incident light, the amplitude d, and the width of the distribution from which the {d_n} are drawn. The results for silver and gold films for 0.2 μm1) the transmissivity at the wavelengths of the surface plasmon polaritons for light of p polarization is decreased, for a given value of d, from its value in the absence of the randomness, but a significant enhancement remains even when d_n is allowed to take values in the interval (-0.2,0.2). At all other wavelengths the transmissivity for light of p polarization is unaffected by this degree of randomness, and the transmissivity for light of s polarization is unaffected by this degree of randomness at all wavelengths considered. Thus, periodicity is sufficient to produce a significantly enhanced transmissivity in p polarization, but it is not necessary.