Bare-substrate Fresnel ratio

← Verification · Thin films · Plane wave

Reference: bare-substrate Fresnel ratio
Kind: analytic: a closed form, limit or conservation law: independent of any code
Calculated: Ψ, Δ
Agreement: 1e-12

Bare substrates in air at 633 nm: the ellipsometric angle Ψ against the Fresnel ratio Ellipsometry's ratio ρ = tan Ψ e^{iΔ} of a bare substrate is the ratio of its Fresnel coefficients, −r_p / r_s in PyStratify's sign convention; the test asserts four (substrate, angle) pairs to 1e-12, the plot sweeps the angle, at 633 nm. For the lossless n = 1.5 Δ jumps by 180° at Brewster's angle, 56.3°.

n = 1.5, PyStratify n = 1.5 + 0.3i, PyStratify n = 0.2 + 3i, PyStratify n = 1.5, −r_p / r_s from Fresnel n = 1.5 + 0.3i, −r_p / r_s from Fresnel n = 0.2 + 3i, −r_p / r_s from Fresnel

Hover to read values.

largest |ρ − (−r_p / r_s)|: 2.86×10⁻¹⁵
PyStratify the lines, the reference the circles

Bare substrates in air at 633 nm: the ellipsometric angle Δ against the Fresnel ratio Ellipsometry's ratio ρ = tan Ψ e^{iΔ} of a bare substrate is the ratio of its Fresnel coefficients, −r_p / r_s in PyStratify's sign convention; the test asserts four (substrate, angle) pairs to 1e-12, the plot sweeps the angle, at 633 nm. For the lossless n = 1.5 Δ jumps by 180° at Brewster's angle, 56.3°.

n = 1.5, PyStratify n = 1.5 + 0.3i, PyStratify n = 0.2 + 3i, PyStratify n = 1.5, −r_p / r_s from Fresnel n = 1.5 + 0.3i, −r_p / r_s from Fresnel n = 0.2 + 3i, −r_p / r_s from Fresnel

Hover to read values.

largest |ρ − (−r_p / r_s)|: 2.86×10⁻¹⁵
PyStratify the lines, the reference the circles

Run it yourself: planar_checks.py · test_planar_checks.py · figures.py · PLANAR_CHECKS.md on GitHub, PyStratify 97e52a9