Three-layer slab dispersion, κd = mπ + atan(ρ₁γ₁/κ) + atan(ρ₃γ₃/κ)

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Reference: three-layer slab dispersion, κd = mπ + atan(ρ₁γ₁/κ) + atan(ρ₃γ₃/κ)
Kind: analytic: a closed form, limit or conservation law: independent of any code
Calculated: the same guided n_eff
Agreement: 1e-12; observed ≤ 6.6e-14

The same slab: the guided modes against the three-layer dispersion relation κd = mπ + atan(ρ₁γ₁/κ) + atan(ρ₃γ₃/κ), ρ = 1 for TE and (n_core/n_clad)² for TM, solved by bisection (planar_codes.py slab_modes).

mode 1, PyStratify mode 2, PyStratify mode 3, PyStratify mode 4, PyStratify mode 5, PyStratify mode 6, PyStratify mode 7, PyStratify mode 8, PyStratify mode 1, dispersion relation mode 2, dispersion relation mode 3, dispersion relation mode 4, dispersion relation mode 5, dispersion relation mode 6, dispersion relation mode 7, dispersion relation mode 8, dispersion relation

Hover to read values.

largest |n_eff − n_eff(relation)|: 9.28×10⁻¹⁴
PyStratify the lines, the reference the circles

Run it yourself: test_planar_codes.py · planar_codes.py · figures.py on GitHub, PyStratify 97e52a9