Study of dispersion compensation in femtosecond lasers

Abstract

We present a formal analysis of dispersion compensation in femtosecond lasers and provide a detailed examination of the relevant features in Ti: sapphire and Cr: LiSAF lasers. It is shown that the essential of dispersion compensation up to the fourth order consists of searching for the solutions of a group of three linear equations. With the use of a prism pair, complete compensation of both the second- and the third-order dispersion corresponds to solving two of the three equations with the prism separation and the intraprism beam path length as variables. Owing to the limitations on the practically achievable prism separation and the intraprism path length in a laser set-up, only some of these solutions are physically meaningful; hence both zero second- and third-order cavity dispersion may be realized merely within a certain specific spectral range. The fourth-order dispersion, however, cannot be completely compensated for in this case unless a third control variable is introduced. It is also shown that the dominant parameter in determining the spectral region where dispersion is minimized is the difference between the ratio of the third-order dispersion to the second-order dispersion of the laser rod and that of the selected prism pair material. This also explains the major differences between Ti: sapphire and Cr: LiSAF lasers in terms of dispersion compensation.