Compare refractive changes across wavelengths with reliable precision. Measure group index and delay spread instantly. Support cleaner optical calculations for research, labs, and validation.
| Material | λ1 (nm) | n1 | λ2 (nm) | n2 | λ3 (nm) | n3 | Target λ (nm) | Δλ (nm) | L (km) | D ps/(nm·km) |
|---|---|---|---|---|---|---|---|---|---|---|
| Fused Silica Example | 1500 | 1.444618 | 1550 | 1.444024 | 1600 | 1.443419 | 1550 | 10 | 25 | 21.884169 |
This example produces about 5471.042 ps pulse broadening over 25 km.
Quadratic interpolation: The calculator uses three refractive index samples and a second-order interpolation model around the target wavelength.
Group index: ng = n - λ (dn/dλ)
Material dispersion coefficient: D = -(λ/c) × (d2n/dλ2)
Pulse broadening: Δτ = D × Δλ × L
Units used: λ in meters for calculation, D reported in ps/(nm·km), and broadening reported in ps and ns.
Material dispersion describes how a material changes refractive behavior as wavelength changes. This effect matters in optical chemistry, spectroscopy, photonics, glass analysis, and laser delivery systems. A small wavelength shift can change refractive index, group index, pulse speed, and total delay. This calculator helps estimate those linked values from three wavelength samples. It is useful when you need a practical engineering style estimate without building a full refractive model.
Many transparent media do not bend all wavelengths equally. Shorter and longer wavelengths travel with different group velocities. That difference broadens pulses and changes timing accuracy. In chemical optics, this can affect instrument calibration, sensing resolution, and signal interpretation. In fiber and glass evaluation, it helps compare materials, operating windows, and expected transmission behavior. Reliable dispersion estimates support better design choices and cleaner validation work.
The tool estimates the first derivative and second derivative of refractive index with respect to wavelength. It then calculates group index, group velocity, the material dispersion coefficient, and pulse broadening over a chosen spectral width and path length. You can also enter a known refractive index at the target wavelength for better group calculations. When that value is left blank, the calculator uses quadratic interpolation from the three data points.
Use wavelength points near the operating wavelength. Keep units consistent. Enter refractive index values with enough decimal precision for stable results. Distinct wavelength spacing improves interpolation quality. If your data comes from literature, confirm temperature and composition because both can shift refractive index. Wide wavelength gaps may exaggerate curvature and distort the local estimate near your chosen operating point during checks. For serious laboratory work, compare results with measured dispersion data whenever available.
This material dispersion calculator supports research screening, teaching, optical material comparison, and process checks. It can help evaluate glasses, polymers, liquids, and transparent solids used in guided light systems or measurement devices. The result section is placed above the form for faster review. CSV export supports reporting, while PDF export supports documentation. Together, these options make the page useful for quick calculations and repeatable records.
Material dispersion describes how refractive index changes with wavelength. Because of that variation, different wavelengths travel at different speeds and arrive at different times.
Three points let the calculator build a quadratic curve. That curve is needed to estimate the first and second refractive index derivatives used in dispersion calculations.
Yes. When left blank, the calculator interpolates refractive index at the target wavelength from the three wavelength-index samples you provided.
The main result is reported in ps/(nm·km). That unit shows pulse delay change per nanometer of spectral width and per kilometer of material length.
Pulse broadening estimates how much a signal spreads in time after traveling through the selected material length with the given spectral width.
No. It can also help compare glasses, liquids, polymers, and other transparent media when refractive index changes with wavelength are known.
Accuracy depends on your input data quality and spacing. Values close to the target wavelength usually give better local estimates than widely separated samples.
Use CSV for spreadsheet analysis and batch records. Use PDF when you need a clean report for documentation, sharing, or lab notes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.