Group Refractive Index Calculator

Calculator Inputs

Choose a method, enter values, and compute the group refractive index. Results appear above this form after submission.

Calculation Method

Switch modes to reveal the relevant fields.

Wavelength λ (nm)

Use the same wavelength unit assumed by the slope.

Phase Refractive Index n

Typical values are above 1 for transparent media.

dn/dλ (per nm)

Negative values commonly represent normal dispersion regions.

Group Velocity v_g (m/s)

This mode converts pulse speed into group index.

Path Length L (m)

Used for optical path and transit calculations.

Transit Time t (ns)

Enter the measured pulse travel time through the medium.

Plotly Graph

Enter values and calculate to replace this example chart with your own trend.

Example Data Table

These sample values illustrate how wavelength dispersion changes the group index and group velocity.

Material Example	Wavelength (nm)	Phase Index n	dn/dλ (per nm)	Group Index n_g	Group Velocity (m/s)
Optical glass sample A	532	1.5190	-0.000120	1.58284	1.89417e+8
Optical glass sample B	633	1.5150	-0.000090	1.57197	1.90728e+8
Fiber-like sample	850	1.5100	-0.000050	1.55250	1.93100e+8

Formula Used

Dispersion relation: n_g = n - λ(dn/dλ)

Group velocity relation: n_g = c / v_g

Measured timing relation: n_g = ct / L

Delay per meter: τ = n_g / c

Keep wavelength and slope units consistent. If λ is entered in nanometers, then dn/dλ must be entered per nanometer.

How to Use This Calculator

Select the calculation method that matches your available data.
For dispersion mode, enter wavelength, phase index, and the slope dn/dλ.
For velocity mode, enter the measured or assumed group velocity.
For timing mode, enter the physical path length and the measured transit time.
Optionally keep a path length entered to derive optical path and travel time.
Press Calculate Group Index to display results above the form.
Review the graph to see how the index trend changes with your method.
Use the CSV or PDF buttons to export the last calculation.

Frequently Asked Questions

1. What is group refractive index?

It describes how an optical pulse envelope travels through a medium. It links pulse speed to the vacuum light speed using n_g = c / v_g.

2. How is it different from phase refractive index?

Phase index describes how a single-frequency wave phase moves. Group index describes how a pulse or wave packet travels. They match only when dispersion is zero.

3. Why does the dispersion slope matter?

The slope tells how refractive index changes with wavelength. That change shifts pulse speed, making the group index larger or smaller than the phase index.

4. Which wavelength units should I use?

Use any wavelength unit you like, but keep it consistent with the derivative unit. This page assumes nanometers when you enter dn/dλ in per nanometer.

5. Can the group index be smaller than one?

It can, especially in unusual dispersive regions. That does not automatically violate relativity, because information speed and signal front speed follow stricter physical limits.

6. Why can group velocity exceed c sometimes?

In strongly dispersive media, calculated group velocity may exceed vacuum light speed or become negative. This reflects pulse reshaping effects, not faster-than-light information transfer.

7. When should I use path length and transit time mode?

Use it when you measured how long a pulse took to travel through a known distance. It is practical for laboratory timing and fiber characterization.

8. Do the exports use my latest calculation?

Yes. The CSV and PDF downloads are generated from the most recent result currently displayed above the form.