V-b Curve

Symmetric step-index slab waveguide. Single-mode condition: V < π/2.

Wavelength (μm) Core thickness d (μm) Δ (%)

n_core (Sellmeier)

—

n_clad

—

V (operating)

—

V cutoff (TE_1)

π/2 ≈ 1.5708

b (fundamental TE_0)

—

Single mode?

—

Equations

V = (k₀·a)·√(n_core² − n_clad²), a = d/2, k₀ = 2π/λ

b = (n_eff² − n_clad²) / (n_core² − n_clad²) ∈ [0, 1]

Cutoff for TE_m: V_c = m·π/2. Single-mode region: V < π/2.