Calculator
Formula Used
This calculator estimates total grating-to-fiber coupling efficiency by multiplying independent sensitivity terms:
Total efficiency
η = ηpeak · ηxy · ηang · ηλ · ηF · ηpol
- Peak: ηpeak from percent or dB (η = 10dB/10).
- Misalignment: ηxy = exp[−2(Δx²+Δy²)/w²] using a Gaussian mode radius w.
- Angle: ηang = exp[−2(Δθ/θ0)²] with tolerance θ0.
- Wavelength: ηλ = exp[−2(Δλ/λ0)²] where Δλ = λ − λdesign.
- Fresnel: ηF = 1 − R, with R = [(n1−n2)/(n1+n2)]².
- Polarization: ηpol = cos²(Δψ) for polarization angle error Δψ.
Note: Real grating couplers can have correlated effects. This model is a practical engineering approximation for tolerance planning.
How to Use This Calculator
- Enter your best-case peak coupling efficiency from measurement or simulation.
- Set mode radius and alignment errors (Δx, Δy) for packaging tolerances.
- Provide angular misalignment and a reasonable angular tolerance θ0.
- Enable wavelength detuning if you expect laser drift or process shifts.
- Enable Fresnel if a planar interface dominates reflection loss in your setup.
- Enable polarization mismatch when polarization rotation is possible.
- Click Calculate to view efficiency (%) and insertion loss (dB) above the form.
- Use Download CSV or Download PDF to save the report.
Example Data Table
| Case | Peak (%) | Δx (μm) | Δy (μm) | w (μm) | Δθ (deg) | θ0 (deg) | λdesign / λ (nm) | λ0 (nm) | n1 / n2 | Δψ (deg) |
|---|---|---|---|---|---|---|---|---|---|---|
| Lab alignment | 65 | 0.2 | 0.2 | 5.0 | 0.3 | 2.0 | 1550 / 1550 | 40 | 1.44 / 1.00 | 2 |
| Packaging tolerance | 65 | 1.0 | 0.8 | 5.0 | 1.0 | 2.0 | 1550 / 1545 | 40 | 1.44 / 1.00 | 10 |
| Detuned wavelength | 55 | 0.5 | 0.5 | 4.5 | 0.7 | 1.8 | 1310 / 1320 | 25 | 1.44 / 1.00 | 5 |
Technical Article
1) Why grating coupler efficiency matters
Grating couplers connect planar photonic circuits to fibers, so coupling efficiency directly sets your link budget. Every 3 dB of insertion loss halves delivered power, tightening receiver margin and driving higher laser output. Quantifying tolerance‑driven penalties early helps reduce rework during assembly.
2) Interpreting peak efficiency in percent or dB
The peak term represents best alignment under ideal conditions and should come from your strongest measurement or trusted simulation. If you enter dB, the calculator converts using η = 10^(dB/10). For instance, −4 dB corresponds to η ≈ 0.398 (39.8%).
3) Lateral alignment sensitivity from Δx, Δy, and w
Lateral mismatch is modeled as a Gaussian overlap with 1/e2 mode radius w. With w = 5 μm and a 1 μm offset in one axis, ηxy = exp(−2·1²/25) ≈ 0.923. A combined 1 μm in x and 1 μm in y gives exp(−0.16) ≈ 0.852, showing how 2D placement adds quickly.
4) Angular misalignment and fiber tilt tolerance
Angle selectivity is captured with ηang = exp[−2(Δθ/θ0)²]. If θ0 = 2° and Δθ = 1°, ηang ≈ exp(−0.5) ≈ 0.607, which is roughly 2.17 dB of additional loss from tilt alone.
5) Wavelength detuning and process bandwidth
Detuning covers shifts between the design center wavelength and the laser or fabricated peak. With λ0 = 40 nm and Δλ = 5 nm, ηλ ≈ exp(−2·25/1600) ≈ 0.969. A 20 nm offset drops to about 0.607, emphasizing the role of process control and temperature drift.
6) Fresnel transmission at interfaces
When a planar interface is present, reflections reduce transmitted power. The approximation uses R = [(n1−n2)/(n1+n2)]² and ηF = 1−R. For silica (1.44) to air (1.00), ηF ≈ 0.9675, about 0.14 dB.
7) Polarization mismatch and cos² overlap
Polarization rotation is modeled with ηpol = cos²(Δψ). A 10° mismatch gives cos²(10°) ≈ 0.970, while 30° gives 0.750. This makes it easy to judge whether polarization control, stress relief, or a polarization‑tolerant design is required.
8) Using the model for packaging decisions
Because the terms multiply, moderate penalties can combine into large insertion loss. Start from a measured peak, then sweep realistic offsets, tilt, and wavelength shift based on your assembly process. Use the factor breakdown to identify the dominant contributor and target it with tighter mechanical tolerances, active alignment, or broader‑band coupler designs.
FAQs
1) What peak efficiency should I enter?
Use your best measured or simulated coupling at ideal alignment. Typical peaks range from roughly 20% to 80% depending on platform, wavelength band, and fiber type.
2) How do I estimate the mode radius w?
Start from the effective spot size at the coupler plane. For standard single‑mode fiber near 1550 nm, a radius around 5 μm is a common first estimate, then refine using overlap or alignment-sweep data.
3) Why does efficiency in dB appear negative?
Efficiency dB is 10·log10(η). Because η is below 1, the logarithm is negative. Insertion loss is −10·log10(η) and is positive.
4) When should I enable Fresnel transmission?
Enable it when a planar interface reflection is a known contributor, such as an air gap or window. If you use index matching or an optimized interface stack, Fresnel may be a smaller term.
5) What does θ0 mean?
θ0 is the 1/e2 angular width in this Gaussian model. Estimate it from an angle sweep measurement or from your optical simulation of the coupler response.
6) How accurate is this calculator?
It is a practical approximation for tolerance planning. Calibrate w, θ0, and λ0 using measured sweeps to align predictions with your specific design and assembly method.
7) Can I use it for two couplers in a fiber‑to‑fiber path?
Yes. Multiply the efficiencies of both couplers, or add their insertion losses in dB. Use matching tolerance assumptions if both assemblies are similar.