Closed-form approximation of symmetric thin-film multi-layer plasmonic dispersion equation solutions

An original asymptotic method is developed and used to find closed-form approximations to the symmetric thin-film three- and multi-layer plasmonic dispersion equations. Closed-form analysis of three-layer metal-insulator-metal (MIM: "M" is metal and "I" is insulator) and IMI devices shows a complementary physics underpinning their properties. Analysis of multi-layer symmetric devices, considered for a seven-layer MIMIMIM example, uncovers a remarkable departure from the physics governing MIM and IMI features. Multi-layer propagation length and attenuation are determined by proximity, in the space of cladding thickness and wavelength, to singularities that exist in the limit of vanishing imaginary part of the cladding dielectric constant. Exploitation of this phenomenon will expand the development of a broader range of thin-film applications in optoelectronics.