Generalized multiple-prism dispersion theory for laser pulse compression: higher order phase derivatives

An exact, and explicit, expression for the second derivative of the generalized multiple-prism angular dispersion is provided. This corresponds to the third derivative of the generalized exit angle with respect to the refractive index (∇ _n ³ φ _2,m ). Higher derivatives, in abstract notation, are also given. The generalized equations are presented in a format applicable to practical prismatic configurations utilized in laser pulse compression schemes in the femtosecond domain. Exact values, as a function of the refractive index, are given for the first, second, and third angular derivatives for compensating double-prism and four-prism configurations of practical interest.