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Refractive Index of Si₃N₄

Sellmeier equation (Luke 2015, LPCVD stoichiometric Si₃N₄) — phase index n and group index n_g, λ = 0.4 – 2.5 μm

Refractive index n
—
Group index n_g
—
n — phase index n_g — group index

Equations

Sellmeier (Luke et al. 2015):
n²(λ) = 1 + Σᵢ Bᵢ·λ² / (λ² − Cᵢ)
B₁ = 3.0249, C₁ = 0.1353406²  ·  B₂ = 40314, C₂ = 1239.842²
Valid range: 0.31 – 5.504 μm.
Group index:  n_g(λ) = n − λ·dn/dλ = n + (λ²/n) · Σᵢ Bᵢ·Cᵢ / (λ² − Cᵢ)²

Reference implementations

n_si3n4.py NSi3N4.java n_si3n4_gui.py (Tkinter GUI) 

# Python: print n and n_g at a wavelength
python n_si3n4.py 1.55       # lambda=1.5500 um   n=1.996280   n_g=2.039573

# Java
javac NSi3N4.java && java NSi3N4 1.55

# Tkinter GUI: enter wavelength, markers move on both curves
python n_si3n4_gui.py