Fiber Splice Loss

Estimate single-mode splice loss from lateral offset, tilt, end-face gap and mode-field-diameter mismatch with the Gaussian mode model.

Model: Textbook approximation

Lateral Offset (µm)Angular Misalignment (°)End-face Gap (µm)Medium Index (1 air, 1.45 fusion/gel)MFD, Fibre 1 (µm)MFD, Fibre 2 (µm)Wavelength (nm)Fibre Phase Index

Lateral

0.054 dB

Angular

0.058 dB

Gap

0.000 dB

reflections 0.000 dB

MFD Mismatch

0.000 dB

Total (combined)

0.111 dB

Equal modes (w = MFD/2): offset η = exp(−d²/w²), tilt η = exp(−(π n w θ/λ)²), gap η = 1/(1 + (λz/(2π n w²))²).

MFD mismatch η = (2w₁w₂/(w₁² + w₂²))². The total is the full Gaussian overlap of all effects together, with the tilt in its unfavourable sense; with a gap it is not exactly the sum of the separate losses. n is the index of the medium the tilt and gap are in (glass for a fusion splice).

Gap and total include the reflections between the two faces when the medium index differs from the fibre's: the coherent sum of the multiply reflected Gaussian passes, r = (n_fibre − n)/(n_fibre + n). For gaps much shorter than the Rayleigh range this is the Airy etalon 1/(1 + F sin²(2πnz/λ)), up to 0.58 dB for an air gap; for long gaps the fringes persist with less contrast. The total applies this equal-mode factor to the full overlap (≈ 0.01 dB approximation with offset or MFD mismatch); parallel end faces and a source coherent over 2z are assumed (tilted faces wash out the fringes).

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Paraxial Gaussian mode overlap for offset, tilt (unfavourable sense), a gap in a medium of index n and unequal mode-field diameters, combined. Gap reflections between faces of a fibre index n_f: the coherent sum of the multiply reflected Gaussian passes (Airy etalon for gaps well inside the Rayleigh range, up to 0.58 dB for air). Not included: mode ellipticity.

Marcuse D. (1977). Loss analysis of single-mode fiber splices. Bell Syst. Tech. J. 56, 703. Gaussian offset, tilt and spot-size mismatch formulas. doi:10.1002/j.1538-7305.1977.tb00534.x
Nemoto S., Makimoto T. (1979). Analysis of splice loss in single-mode fibres using a Gaussian field approximation. Opt. Quantum Electron. 11, 447. Gap and combined misalignments. doi:10.1007/BF00619826
Joyce W. B., DeLoach B. C. (1984). Alignment of Gaussian beams. Appl. Opt. 23, 4187. Combined offset, tilt, gap and waist mismatch. doi:10.1364/AO.23.004187

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