Further observations on the variation with dielectric constant and thickness of the reflectance and phase change on reflection of films

Studies of the behaviour with ₁, ₂ and film thickness of the optical functions reflectance (R) and phase change on reflection (Φ_r) have previously been made for both very thin and very thick films. Abelès J. Opt. Soc. Amer. 47 (1957) 473] has formulated equations for very thin films where functions of ₁ and ₂ are the coefficients of a power series of the optical thickness, x(2πd/λ) up to x², whilst in the case of very thick films (solids) the relationships between ₁ and ₂ can be represented in polar coordinates L and α by ₁=L cos α, ₂=L sin α where L_R=2y²₀W²(1+cos α−1/W²) W=(1+R)/(1−R)] and L_Φr=2(y₀/ tan Φ_r)²(1−cos α+tan ² Φ_r) Ward, Opt. and Laser Tech. 27 (1995) 125]. The present study is concerned with films of intermediate optical thicknesses (1.0<2πd/λ<solid) and has revealed that the polar-type relationships previously noted for solid materials are augmented by secondary structures of maxima and minima whose position and amplitude can be predicted by adapting the exact equations for R and Φ_r.