Computational criterion for application of the characteristic effective medium approximation to ultrathin Co-Au multi-bilayer structures

The basic optical properties, reflectivity and transmissivity, of three sets of Co-Au bilayer structures are calculated for normal incidence in the wavelength range 300-700 nm. Each set consists of a total number of bilayer identity periods m=1, 2, 3, 4, 5, 6. The thickness of the bilayer in each set is 5, 7, and 9 nm. The composition of the bilayer is kept fixed: 40% Co and 60% Au. The calculations are done for ideal layered Co-Au stacks using the characteristic matrix technique. Calculations for each stack based on the thicknesses of the two composite layers and their optical constants are contrasted against calculations using the characteristic effective medium approximation, CEMA. A third calculation of the optical properties for each stack is performed, again using the CEMA, but when the whole stack, called the effective stack, ES, is treated as one uniform medium of effective optical constants. The comparison of the three sets of calculations for all sets is intended to shed more light onto the validity of the CEMA approximation that has been established for thin bilayer structures whose constituents have thicknesses much less than the wavelength of the incident radiation. The study establishes a limit based on the product of the number of layers m and the identity period of the stack h, beyond which the CEMA approximation cannot be applied. This limit is consistent with a previous study carried out on Ag-SiO ultrathin stacks.