Dispersion delay lines (DDLs) are used for dispersion compensation in ultrafast optics. Note that the correct determination of the time delay of DDLs is based on the tautochronism principle: in an optical system consisting of refracting and reflecting elements the time delay between any two wavefronts is the same for all rays. But for diffraction gratings this principle is not valid; the time delay between the wavefronts of incident and diffracted waves for different light rays is different. However, fortunately, a pair of diffraction gratings can be combined so that the input and the output wavefronts of the system still satisfy the tautochronism principle. There are only two such grating systems: Treacy’s system and Martinez’s system. Both these systems are closely related to each other: in Martinez’s system one can see virtual Treacy’s system. Note that according to the tautochronism principle, dispersion Martinez’s system and virtual Treacy’s system are equal in value but opposite in sign.
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