# Grating pair dispersion calculator

## About this calculator

This calculator computes the second order (GDD) and third order (TOD) dispersion of a double-pass grating pair compressor in Treacy configuration. Additionally, the calculator gives the Littrow angle, which is the incidence angle optimized for highest diffraction efficiency in blazed transmission gratings. The angle of diffraction $\theta_d$ for diffraction order $m=-1$ is calulated using the sign convention for transmission gratings. Finally, the calculator also gives the angular dispersion, i.e. how many degrees the diffracted beam spreads per nanometer of spectral width.

The formulas for second and third order dispersion are

Littrow angle is calculated as

and the angle of diffraction is computed from the grating equation as

Finally, the angular dispersion is found by differentiating the grating equation with respect to wavelength