Spectrophotometry
Model spectrophotometric R, T, A spectra for a single absorbing thin film using transfer matrix method with complex refractive index.
Optical Thickness (nd): 146.0 nm
QWOT at 550 nm: 94.2 nm
Optical thickness 2nd/λ at 550 nm: 0.53
α at 550 nm (n, k constant in λ): 228 cm⁻¹
Key Formulas
N = n + ik (complex refractive index)
r01 = (n₁cosθ₁ − N₂cosθ₂)/(n₁cosθ₁ + N₂cosθ₂) (s-pol Fresnel)
rtotal = (r₀₁ + r₁₂·e2iδ)/(1 + r₀₁·r₁₂·e2iδ) (thin film)
δ = 2πN₂d·cosθ₂/λ (phase thickness)
A = 1 − R − T (energy conservation)
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
A coherent single film with a constant complex index on a semi-infinite substrate, s and p by transfer matrix. T is the light entering the substrate; a real slab's back surface is not included.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (absorbing films). CRC Press. doi:10.1201/9781420073034
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §1.6. Cambridge University Press.