Abstract

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≤d<H/2. In this expression the {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 {dn} are drawn. The results for silver and gold films for 0.2 µm<λ< 1.0 µm show that in comparison with the transmissivity of a film with planar surfaces (d = 0), the transmission is strongly enhanced in the case of a film with a periodically modulated thickness for light of both p and s polarization even for moderate values of d (= 0.2H). In the case of p polarization the transmissivity is further enhanced at the wavelengths of the surface plasmon polaritons supported by the scattering system. In the presence of nonzero randomness in the function ζ(x1) 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 dn 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.