Coupling Efficiency Fiber Calculator

Inputs

Example data table

Formula used

This calculator uses common Gaussian-mode approximations for coupling into a single-mode fiber.

• Mode size mismatch: η_size = ( 2 w_b w_f / (w_b² + w_f²) )²
• Lateral offset: η_offset = exp( -2 r₀² / (w_b² + w_f²) ), where r₀ = √(dx² + dy²)
• Angular tilt: η_angle = exp( - ( π w_eq θ / λ )² ), with w_eq = √((w_b² + w_f²)/2) and θ = √(tx² + ty²)
• NA acceptance (approx.): if NA_beam > NA_fiber, then η_NA ≈ (NA_fiber/NA_beam)², else 1
• Total: η_total = η_size · η_offset · η_angle · η_NA · 10^(-Loss_dB/10)

Here, w_f is the fiber mode radius (MFD/2). If Δz ≠ 0, the beam radius at the facet is estimated as w_b = w0 √(1 + (Δz/zR)²).

1) Coupling efficiency in single-mode fiber systems

Coupling efficiency is the fraction of optical power that enters the guided fundamental mode. It sets link budget and detector signal level. Moving from 80% to 60% adds about 1.25 dB insertion loss, often larger than a good fusion splice. For coherent or interferometric work, stable coupling reduces amplitude noise caused by bench vibration.

2) Gaussian overlap model used by this calculator

The calculator treats both the incident beam and the fiber mode as Gaussian fields. The geometric efficiency is the product of size mismatch, lateral offset, angular tilt, and a simple NA acceptance term. This is useful for quick tolerance studies and alignment planning, and the intermediate factors show what dominates.

3) Mode field diameter and waist selection

MFD specifies the effective 1/e² intensity width of the guided mode. Aim for a beam radius at the facet close to MFD/2 after accounting for lens working distance. At 1550 nm, MFD ≈ 10.4 μm implies a target radius ≈ 5.2 μm. Use the fiber datasheet MFD or a mode-field measurement to set realistic inputs for your wavelength.

4) Sensitivity to lateral misalignment

Transverse offsets reduce overlap rapidly. With matched spot sizes, the penalty behaves roughly like exp(-r²/w²). For w ≈ 5 μm, a 1 μm offset can produce a noticeable drop, and 2 μm can become a double-digit loss. High-performance setups often rely on sub-micrometer translation steps and low thermal drift to maintain repeatability.

5) Sensitivity to angular tilt

Tilt creates a phase gradient at the facet that the mode cannot match. The model uses a small-angle approximation where loss scales with (w·θ/λ)². Larger waists and shorter wavelengths therefore require tighter angular control. Check tilt by observing far-field symmetry or by monitoring coupling while steering with small controlled steps.

6) Defocus, Rayleigh range, and working distance

If the waist is not at the facet, the spot grows as w(z)=w0√(1+(z/zR)²) with zR=πw0²/λ. When |Δz| approaches zR, size mismatch increases quickly. The reported Rayleigh range helps judge longitudinal tolerance. Increasing w0 increases zR, trading a larger spot for easier focus placement and less sensitivity to dz.

7) Numerical aperture and acceptance limits

NA sets the acceptance half-angle for guided power. The tool estimates beam NA from divergence and applies a conservative clipping factor when NA_beam exceeds fiber NA. This is most relevant for very small waists or coupling in higher-index media. Typical single-mode fiber NA is about 0.11–0.14.

8) Practical measurement and optimization tips

Use the model for what-if comparisons: sweep dx, dy, tilt, and Δz to see dominant sensitivity. During alignment, maximize power with translation, reduce tilt with steering, then fine-tune focus. Exported results help document tolerances and improvements. Attach the CSV/PDF report with test conditions and coupling margin.

1) What does MFD mean in this calculator?

MFD is the mode field diameter of the guided fundamental mode. The tool converts it to a mode radius (MFD/2) and uses it for Gaussian overlap with the incident beam at the fiber facet.

2) Why does the tool assume Gaussian fields?

Single-mode fibers and well-corrected focused beams are often close to Gaussian near the facet. Gaussian overlap gives a fast, reliable first-order estimate for alignment tolerances and expected coupling loss.

3) How should I choose the beam waist w0?

Start by matching the beam radius at the facet to the fiber mode radius (MFD/2). If you know your lens and working distance, use them to estimate the waist, then refine with measured coupling versus focus position.

4) What is the difference between geometric efficiency and total efficiency?

Geometric efficiency includes size, offset, tilt, and NA factors only. Total efficiency multiplies the geometric result by any extra losses you enter in dB, such as connectors, reflections, or splices.

5) Does this include polarization effects?

No. The calculator assumes polarization is matched and stable. If polarization-dependent loss exists, model it as an additional loss term in dB or measure it separately using a polarization controller and power meter.

6) How accurate is the NA factor?

It is a simplified power-clipping approximation meant for quick screening. For high-NA focusing, multimode behavior, or complex lens aberrations, use a full physical optics model or measure coupling experimentally.

7) Why can very small offsets cause large changes?

Single-mode spots are only a few micrometers wide. Because overlap depends exponentially on normalized offset, sub-micrometer motion can cause measurable power changes, especially when the beam and mode are tightly matched.