Effective Index of Silica

Strip waveguide, EIM (TE-TE) with Sellmeier core index

Wavelength (μm) Width W (μm) Height H (μm) Δ = (n_core − n_clad)/n_core × 100 (%)

n_core (from Sellmeier)

—

n_clad

—

n_eff (vertical slab)

—

n_eff (full EIM)

—

Formulas

Sellmeier (Malitson 1965):
n²(λ) = 1 + Σᵢ Bᵢ·λ² / (λ² − Cᵢ)

Slab TE eigenvalue (fundamental):
u·tan(u) = w, u² + w² = V², V = (k₀·d/2)·√(n_core² − n_clad²)
n_eff = √(n_core² − (2u/d)² / k₀²)

EIM (TE-TE): 1) vertical slab thickness H → n_eff_v 2) horizontal slab thickness W with core = n_eff_v → n_eff