Stochastic optimization of broadband dispersion controlled mirrors

Summary form only given. Since their recent introduction dispersion-controlled mirrors (DCM) or chirped mirrors have proved to be essential devices for the production of ultrashort laser pulses directly from the oscillator. They have found their main applications in Ti:sapphire femtosecond oscillators. Using only DCMs in the cavity, 7.5-fs pulses were obtained, and in combination with a prism pair and a semiconductor saturable-absorber mirror (SESAM), pulses as short as 6.5 fs were demonstrated. The starting point for the design of a broadband DCM is a standard single-stack quarter-wave laser mirror, i.e., a multilayer dielectric coating with alternate layers with very different indices of refraction, e.g., SiO/sub 2/ and TiO/sub 2/. The thicknesses of the layers are then optimized numerically in order to attain the desired dispersion in the target bandwidth, while keeping the reflectance above a certain threshold. The approach to the DCM optimization problem that we propose consists of a random search around the initial quarter-wave mirror design. More precisely, in each iteration the thicknesses of the layers are randomly varied, and the modifications are accepted only if the global energy decreases. The search range is controlled by a temperature parameter that is continuously decreased as the design converges. We show with some examples discussed that this algorithm leads to efficient solutions. In addition, we introduce a new objective function based on the group delay rather than on the group delay dispersion.