Dispersive mirror in AlGaAs designed by inverse spectral theory.

We introduce a new mathematical method, based on the inverse spectral theory of Gel'fand and Levitan, of designing dispersive coatings for use in femtosecond lasers. We fabricated an example in AlGaAs by metal-organic chemical-vapor deposition. The mirror has a high value of group delay dispersion over a bandwidth of 10 nm, reaching an extreme of -1200 fs(2) at the center (805 nm) and falling to -800 fs(2) at the edge of this range. In the same band the reflectivity remains over 95%. We created the design by identifying parameters in the spectral domain, numerically optimizing these parameters, and solving the resulting inverse problem to recover the refractive-index profile. Because we performed the optimization in the spectral domain, we needed only four parameters to obtain a good result. Numerical analysis shows that the excess optical delay at the red end of the stop band can be achieved by use of a mild optical resonance, with the optical field approximately twice the magnitude of that at the blue end.