Fresnel, single interface, incl. opaque

← Verification · Thin films · Plane wave
Reference
Fresnel, single interface, incl. opaque
Kind
analytic: a closed form, limit or conservation law: independent of any code
Calculated
r, t, R, T
Agreement
1e-14
A metal film (n = 0.2 + 3i) in air at 600 nm, normal incidence: thickening it toward the bulk Fresnel reflectance A thin metal film transmits; as it thickens T falls exponentially and R settles on the reflectance of the bulk metal. The test takes the film to 20 µm, where T must be exactly 0 and R, the Poynting vector at 0, 10 and 20 µm finite (no overflow of exp(Im(k_z) d)), and checks Fresnel's 0.04 and 0.96 for glass at normal incidence.
2040608010012014000.20.40.60.81thickness [nm]R, T
R, PyStratify T, PyStratify |(1 − n)/(1 + n)|², the bulk Fresnel reflectance
Hover to read values.
  • |R − R_bulk| at 20 µm (the test's opaque film): 2.22×10⁻¹⁶
  • PyStratify the lines, the reference the circles

Run it yourself: unified_checks.py · test_unified.py · figures.py · UNIFIED_CHECKS.md on GitHub, PyStratify 97e52a9