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Mode Field Diameter and Coupling Loss

Channel-waveguide mode field diameter (D4σ) and butt-coupling loss, referenced to the SMF mode

Wavelength λ (μm) Index contrast Δ (%) Width W (μm) Height H (μm) SMF MFD (μm)

n_clad (silica, Sellmeier)

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n_core (from Δ)

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n_eff (vertical slab)

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WG MFD x — horizontal

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WG MFD y — vertical

—

WG MFD (equiv. circular)

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overlap η (to SMF)

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coupling loss (vs SMF)

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SMF (Gaussian, reference) WG mode — x WG mode — y

Coupling loss vs wavelength (1.2 – 1.7 μm), with Δ, W, H and SMF MFD held at the values above. ● marks the current λ.

Method

Mode field diameter (D4σ): σ² = ∫r²·I dr / ∫I dr, I = |E|², MFD = 4σ (per transverse direction).

Coupling loss to SMF: η = η_x·η_y, η_dir = (∫G·F)² / (∫G²·∫F²), Loss(dB) = −10·log₁₀ η.
G = SMF Gaussian (w = MFD_SMF/2); F = waveguide slab-mode profile (EIM, TE-TE). Cladding n from Sellmeier (Malitson 1965), core = clad / (1 − Δ/100).

Reference implementations

mfd_coupling.py MfdCoupling.java

python mfd_coupling.py 1.55 10.4 5.0 5.0 0.75
# WG MFD (equiv circular) = 7.1204 um   coupling loss (vs SMF) = 0.622 dB