THEORY OF DOUBLE-CHIRPED MIRRORS

A theory of double-chirped mirrors (DCM's) for dispersion Compensation in ultrashort pulse laser sources is presented. We describe the multi layer interference coating by exact coupled-mode equations. They show that the analysis and synthesis of a coating with a slowly varying chi rp in the layer thicknesses can be mapped onto a weakly inhomogeneous transmission line problem. Solutions of the transmission line equation s are given using the WKB-method, Analytic expressions for reflectivit y and group delay are derived, The solutions show that the main proble m in chirped mirror design is the avoidance of spurious reflections, t hat lead to Gires-Tournois-like interference effects responsible for t he oscillations in the group delay. These oscillations are due to an i mpedance matching problem of the equivalent transmission line. The imp edance matching can be achieved by simultaneously chirping the strengt h of the coupling coefficient and the Bragg wavenumber of the mirror, An adiabatic increase in the coupling coefficient removes the typical oscillations in the group delay and results in broad-band mirrors with a controlled dispersion, Finally, the mirror is matched to air with a broadband antireflection coating. We discuss a complete design of a l aser mirror with a reflectivity larger than 99.8% and a controlled dis persion over 400-nm bandwidth. Using such mirrors in a Ti:sapphire las er, we have demonstrated approximate to 30-fs pulses, tunable over 300 nm, as well as 8-fs pulses from the same setup. A different design re sulted in 6.5-fs pulses.