Fiber Coupling Efficiency

Estimate Gaussian-beam-to-single-mode-fiber coupling efficiency from beam NA, mode field diameter, lateral offset and tilt.

Model: Textbook approximation

Beam divergence NA (1/e² half-angle)0.22

0.02–0.5

Fibre mode field diameter10.4 µm

2–30 µm

Lateral offset0 µm

0–20 µm

Angular misalignment0 deg

0–5 deg

Wavelength1550 nm

400–2000 nm

Medium index n1

1–1.5

Total coupling

52.89%

Insertion loss

2.77 dB

Mode mismatch

52.9%

Beam waist w₀ / fibre mode w

2.24 / 5.20 µm

Fibre mode NA λ/(πw)

0.095

Offset factor

100.0%

Tilt factor

100.0%

Beam waist w₀ = λ/(π·NA), fibre mode radius w = MFD/2, both on the fibre face.

η_mismatch = (2w₀w/(w₀² + w²))²; η_offset = exp(−2d²/(w₀² + w²)); η_tilt = exp(−2(π n θ/λ)² w₀²w²/(w₀² + w²)).

Best coupling is when the beam NA equals the fibre mode NA. Paraxial: reliable for NA ≲ 0.3 (w₀ ≳ λ). Single-mode Gaussian model: for a multimode fibre or an extended source, use the étendue (NA and core area) instead.

Coupling efficiency vs lateral offset

Coupling efficiency
Current point

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

Single-mode Gaussian overlap of a beam waist w₀ = λ/(π·NA) on the fibre face with the fibre mode (MFD/2), with offset and tilt. Paraxial (NA ≲ 0.3); not for multimode fibre or extended sources.

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
Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550. Waist from far-field divergence, w₀ = λ/(π·NA). doi:10.1364/AO.5.001550

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Related calculators

Mode Field Diameter

Fiber mode size and coupling sensitivity.

Fiber V-Number

Single-mode / multimode guidance.

Gaussian Beam Propagation

Beam waist and divergence feeding coupling performance.

Fiber Splice Loss

Another alignment-sensitive fiber insertion problem.

Fiber Coupling Efficiency

Estimate Gaussian-beam-to-single-mode-fiber coupling efficiency from beam NA, mode field diameter, lateral offset and tilt.

Beam divergence NA (1/e² half-angle)0.22

0.02–0.5

Fibre mode field diameter10.4 µm

2–30 µm

Lateral offset0 µm

0–20 µm

Angular misalignment0 deg

0–5 deg

Wavelength1550 nm

400–2000 nm

Medium index n1

1–1.5

Total coupling

52.89%

Insertion loss

2.77 dB

Mode mismatch

52.9%

Beam waist w₀ / fibre mode w

2.24 / 5.20 µm

Fibre mode NA λ/(πw)

0.095

Offset factor

100.0%

Tilt factor

100.0%

Beam waist w₀ = λ/(π·NA), fibre mode radius w = MFD/2, both on the fibre face.

η_mismatch = (2w₀w/(w₀² + w²))²; η_offset = exp(−2d²/(w₀² + w²)); η_tilt = exp(−2(π n θ/λ)² w₀²w²/(w₀² + w²)).

Coupling efficiency vs lateral offset

Coupling efficiency
Current point

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

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
Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550. Waist from far-field divergence, w₀ = λ/(π·NA). doi:10.1364/AO.5.001550

Report a problem