Analytic Expressions for the Fourth- and the Fifth-Order Dispersions of Crossed Prisms Pairs

In case of tunable ultrashort-pulse lasers, besides the prism material, separation, and insertion, one may choose the central wavelength providing a better high-order dispersion compensation. Because of errors that accumulate in numerical iterations, the analytic approach may be preferable for high-order dispersion examination. Analytic expressions for the fourth- and the fifthorder dispersions of crossed prisms pairs, both at arbitrary and Brewster-angle incidences are presented. Examples are given for e-sapphire slabs and for one or two pairs of fused-silica prisms. Results are shown providing compensation of both the second- and the third-order dispersions, by keeping as low as possible the higher-order ones.