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Multiple-prism dispersion theory


The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book Opticks. Prism pair expanders were introduced by Brewster in 1813. A modern mathematical description of the single-prism dispersion was given by Born and Wolf in 1959. The generalized multiple-prism dispersion theory was introduced by Duarte and Piper in 1982.

The generalized mathematical description of multiple-prism dispersion, as a function of the angle of incidence, prism geometry, prism refractive index, and number of prisms, was introduced as a design tool for multiple-prism grating laser oscillators by Duarte and Piper, and is given by

which can also be written as

using

Also,

Here, is the angle of incidence, at the mth prism, and its corresponding angle of refraction. Similarly, is the exit angle and its corresponding angle of refraction. The two main equations give the first order dispersion for an array of m prisms at the exit surface of the mth prism. The plus sign in the second term in parentheses refers to a positive dispersive configuration while the minus sign refers to a compensating configuration. The k factors are the corresponding beam expansions, and the H factors are additional geometrical quantities. It can also be seen that the dispersion of the mth prism depends on the dispersion of the previous prism (m - 1).


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