Coupling Loss

Butt-coupling between SMF and a rectangular channel waveguide (modal overlap, EIM-based).

Wavelength (μm) SMF MFD (μm) WG width W (μm) WG height H (μm) Δ (%)

n_core (Sellmeier)

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n_clad

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n_eff (vertical slab)

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η_x (horizontal overlap)

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η_y (vertical overlap)

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η_total

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Coupling loss

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Quality

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Mode field profiles — solid: SMF Gaussian, dashed: WG mode. Closer overlap means lower loss.

Horizontal cross-section (x)

Vertical cross-section (y)

Equations

SMF mode (Gaussian): E_SMF(r) = exp(−r²/w_smf²), w_smf = MFD/2

WG mode (separable EIM): E_WG(x,y) = X(x)·Y(y), each is the symmetric-slab fundamental TE.

Overlap factorizes: η = η_x · η_y, η_dir = (∫ G·F dr)² / (∫G² dr · ∫F² dr) Loss(dB) = −10·log₁₀(η)