Scattering matrix (Redheffer star product)

← Verification · Thin films · Plane wave

Reference: scattering matrix (Redheffer star product)
Kind: method: an independent formulation inside this repo (a scattering matrix, a plane-wave superposition, a quadrature): proves the formulation
Calculated: R, T on lossy, oblique and opaque stacks
Agreement: 1e-10 abs

Air / 100 nm silica / 40 nm metal (n = 0.05 + 3i) / glass at 600 nm: against the scattering-matrix star product An absorbing stack, s and p. The reference chains the interfaces' and layers' two-port scattering matrices by Redheffer's star product (planar_checks.py), a different algebra from PyStratify's transfer matrices that never multiplies by exp(+Im(k_z) d); the test also takes 120 µm of n = 2 + 0.5i, where T is below 1e-30 in both.

R_s, PyStratify T_s, PyStratify R_p, PyStratify T_p, PyStratify R_s, S-matrix T_s, S-matrix R_p, S-matrix T_p, S-matrix

Hover to read values.

largest |R − R_S|, |T − T_S|: 1.28×10⁻¹⁴
PyStratify the lines, the reference the circles

Glass / 400 nm air / 130 nm of n = 2 / glass at 550 nm: through the critical angle against the scattering-matrix star product Beyond 41.8° the air gap is evanescent and light tunnels through it to the n = 2 layer and the glass. The reference chains the interfaces' and layers' two-port scattering matrices by Redheffer's star product (planar_checks.py), a different algebra from PyStratify's transfer matrices that never multiplies by exp(+Im(k_z) d); the test also takes 120 µm of n = 2 + 0.5i, where T is below 1e-30 in both.

R_s, PyStratify T_s, PyStratify R_p, PyStratify T_p, PyStratify R_s, S-matrix T_s, S-matrix R_p, S-matrix T_p, S-matrix

Hover to read values.

largest |R − R_S|, |T − T_S|: 1.67×10⁻¹⁵
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