Effective optical constants and effective optical properties of ultrathin trilayer structures

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This work presents an extension of the characteristic effective medium approximation (CEMA) to ultrathin trilayer systems. The extension has been carried out analytically and is supported by corresponding calculations of the effective optical constants of Cu–Au–Cu and Ag–SiO–Ag trilayer systems using the CEMA approximation. This work is in essence a generalization of the characteristic effective medium approximation introduced earlier for ultrathin bilayer structures. This method is used to derive the effective optical constants of a trilayer system, consisting of three thin layers with each constituent layer of thickness much less than the wavelength of the incident radiation. Within this regime a trilayer system is viewed as one effective layer referred to as an effective stack (ES) with well defined effective optical constants, which can be used to calculate the optical properties of the trilayer stack within a specified wavelength range. The CEMA based calculations of the effective optical constants are applied to two trilayer systems with a total of five stacks. Three are Cu–Au–Cu and two are Ag–SiO–Ag stacks. The thicknesses of the parent layers in the Cu–Au–Cu stack range from 3 to 30 nm for Cu and 4 to 40 nm for Au; in the Ag–SiO–Ag stack the constituent layers are 6 nm for Ag, but range from 5 to 10 nm for SiO. This study is for normal or near normal incidence spectroscopy in a wavelength range that extends from visible to near infrared. The agreement between CEMA based ES stack results and those of the standard CMT technique is very satisfactory.