Dispersion theory of multiple-prism beam expanders for pulsed dye lasers

The single pass dispersion of multiple-prism beam expanders of interest for practical pulsed dye laser cavities is calculated. The theory is extended to enable evaluation of the overall (outward and return pass) dispersion of multiple-prism-grating combinations. It is found that although the contribution to overall dispersion from the prisms can be minimized (though not eliminated for practical expanders) by arrangement of the prisms in compensating pairs, it is in any case small (≈2%) compared to the contribution to dispersion from the grating in practical cavities. Formulae for dispersion of multiple-prism-grating combinations including up to four prisms arranged in additive or compensating configurations are given; the dispersion of an arbitrary number of prisms arranged in conjunction with a grating can also be calculated. The implications for output linewidth of pulsed dye lasers incorporating prism beam expanders are discussed.