Calculator Inputs
Plotly Graph
The chart compares phase index and group index across wavelength. Submitted inputs drive the plotted trend or material model.
Example Data Table
| Case | Material | Wavelength | Phase Index n | dn/dλ | Group Index ng | Notes |
|---|---|---|---|---|---|---|
| 1 | Fused Silica | 1550 nm | 1.4440 | -1.18×10-5 per nm | 1.4623 | Telecom wavelength example. |
| 2 | BK7 Glass | 632.8 nm | 1.5151 | -8.80×10-5 per µm | 1.5708 | Visible optics example. |
| 3 | Sapphire | 1064 nm | 1.7545 | -1.02×10-4 per µm | 1.8630 | High-index crystal example. |
Formula Used
The calculator primarily uses the group refractive index relation below.
ng = n - λ(dn/dλ)
Here, n is the phase refractive index, λ is wavelength, and dn/dλ is the refractive-index slope with respect to wavelength.
Additional derived outputs use these relations.
vg = c / ng
Group delay per length = ng / c
When the material preset mode is selected, the script evaluates a Sellmeier model to estimate both n and its derivative.
How to Use This Calculator
- Select a method: direct derivative, two-point estimate, or Sellmeier material model.
- Enter the target wavelength and choose the matching wavelength unit.
- For direct mode, enter phase index and slope dn/dλ.
- For two-point mode, enter two wavelength-index pairs to estimate the derivative.
- For Sellmeier mode, choose a preset material and keep wavelength inside the valid range.
- Press Calculate Group Index to show results above the form.
- Review the graph, example table, and derived values like velocity and delay.
- Use the CSV or PDF buttons to export the current calculation summary.
Frequently Asked Questions
1. What is group refractive index?
Group refractive index describes how an optical pulse envelope travels through a material. It differs from phase refractive index because it includes dispersion, which changes velocity as wavelength changes.
2. Why is group index different from phase index?
Phase index tracks wavefront speed, while group index tracks pulse or energy-packet speed. When refractive index varies with wavelength, the derivative term changes the final result.
3. Which input method should I use?
Use direct mode when you already know n and dn/dλ. Use two-point mode for measured data. Use Sellmeier mode for standard optical materials with known dispersion models.
4. What does a negative dn/dλ mean?
A negative slope means refractive index decreases as wavelength increases. In many transparent optical materials, this makes group index larger than phase index over common operating wavelengths.
5. Can I use this for fiber optics?
Yes. The calculator is useful for pulse propagation, link timing, and delay estimation in optical fiber work, especially when you know wavelength-dependent refractive index behavior.
6. What does the delay per kilometer output mean?
It estimates how long a pulse takes to travel one kilometer in the chosen material. This helps with timing design, synchronization, and optical path comparisons.
7. Are the material presets exact for every condition?
No. Presets are model-based approximations and may vary with temperature, purity, polarization, and manufacturer data. Use measured values when your application requires tighter accuracy.
8. Why does the graph change with the selected method?
Direct and two-point modes build a local trend from your entered data. Sellmeier mode builds a material-model curve across wavelength, so the plotted shape becomes more realistic.