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Refractive Index of Si

Sellmeier equation (Salzberg & Villa, crystalline silicon) — phase index n and group index n_g, λ = 1.4 – 6.0 μm

Wavelength λ (μm)

Refractive index n

—

Group index n_g

—

n — phase index n_g — group index

Equations

Sellmeier (Salzberg & Villa 1957):
n²(λ) = 1 + Σᵢ Bᵢ·λ² / (λ² − Cᵢ)
B₁ = 10.6684293, C₁ = 0.301516485² · B₂ = 0.0030434748, C₂ = 1.13475115² · B₃ = 1.54133408, C₃ = 1104²
Valid range: 1.36 – 11 μm.

Group index: n_g(λ) = n − λ·dn/dλ = n + (λ²/n) · Σᵢ Bᵢ·Cᵢ / (λ² − Cᵢ)²

Reference implementations

n_si.py NSi.java n_si_gui.py (Tkinter GUI)

# Python: print n and n_g at a wavelength
python n_si.py 1.55         # lambda=1.5500 um   n=3.477724   n_g=3.605295

# Java
javac NSi.java && java NSi 1.55

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