Calculator
Units: wavelength in nm, distances in µm, angles in mrad. The model assumes a near-Gaussian input beam and a single-mode fiber fundamental mode.
Formula Used
This calculator uses a practical Gaussian overlap approximation for coupling into a single-mode fiber fundamental mode.
- Mode-size mismatch: ηsize = ( 2 wb wf / (wb2 + wf2) )2
- Lateral offset: ηoff = exp( -2 Δ2 / (wb2 + wf2) ), where Δ = sqrt(Δx2 + Δy2)
- Angular tilt: ηtilt = exp( - (π weff α / λ )2 ), with weff = sqrt( (wb2 + wf2) / 2 )
- Defocus: ηz = 1 / ( 1 + (Δz / zR)2 ), zR = π wb2 / λ
- Fresnel transmission: T = 1 - ((n1 - n2)/(n1 + n2))2 (optional)
- Total: η = ηsize ηoff ηtilt ηz T
For high-NA systems, non-Gaussian beams, or multimode fibers, a full overlap integral or wave optics model may be required.
How to Use
- Enter the wavelength and your beam radius at the fiber facet.
- Enter the fiber mode field diameter for that wavelength.
- Provide measured offsets, tilt, and defocus from alignment data.
- Enable Fresnel transmission if the facet is uncoated.
- Click Calculate to view efficiency and loss.
- Use CSV or PDF export for reporting and comparisons.
Example Data Table
These examples are generated using the same equations as the calculator.
| λ (nm) | wb (µm) | MFD (µm) | Δx, Δy (µm) | αx, αy (mrad) | Δz (µm) | Fresnel | η (%) | IL (dB) |
|---|---|---|---|---|---|---|---|---|
| 1550 | 5.20 | 10.40 | 1.00, 0.00 | 1.00, 0.00 | 0.0 | On | 93.108 | 0.310 |
| 1310 | 4.50 | 9.20 | 2.00, 1.00 | 2.00, 1.00 | 50.0 | On | 36.802 | 4.341 |
| 850 | 3.00 | 5.00 | 0.50, 0.50 | 0.50, 0.50 | 20.0 | Off | 66.546 | 1.769 |
Notes
- Beam radius is the 1/e2 intensity radius at the fiber facet.
- Mode field diameter varies with wavelength and fiber type.
- Defocus uses the Rayleigh range computed from wb and λ.
- Angular factor uses a small-angle phase tilt approximation.
- For best results, validate against a measured coupling curve.