Grating pair compressor

Dispersion parameters of grating pair compressor/stretcher for given distance between gratings $$L$$, angle of incidence $$\vartheta_0$$ and grooves density $$d^{-1}$$. Formulas for the double-pass GDD and TOD are, respectively: $$\mathrm{GDD}(\lambda)=-\frac{\lambda^{3}L}{\pi c^{2}d^{2}}\left[1-\left(\frac{\lambda}{d}-\sin\vartheta_0\right)^{2}\right]^{-\frac{3}{2}},$$ $$\mathrm{TOD}(\lambda)=-\frac{3\lambda}{2\pi c}\frac{\partial^{2}\phi_{g}}{\partial\omega^{2}}\frac{1+\frac{\lambda}{d}\sin\vartheta_0-\sin^{2}\vartheta_0}{1-\left(\frac{\lambda}{d}-\sin\vartheta_0\right)^{2}}.$$

mm
deg
/mm