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A highly dispersive mirror for dispersion compensation in femtosecond lasers is designed by inverse spectral theory. The design of a simple quarter-wave Bragg reflector can be modified by moving the poles in the optical impedance found in the photonic stop band. These spectral quantities are used as independent variables in the numerical optimization because they have no effect on the location of the photonic stop band, and so the design requirements to obtain a high reflectivity and a specific delay spectrum are decoupled. The design was fabricated by ion-beam sputtering. A group delay dispersion of -300 fs2 was measured over a bandwidth of 28 nm, with a remaining reflectivity of greater than 99% in this range. The mirrors were used to make two Ti:sapphire lasers with 10- and 4-mm-long crystals, both of which generated near-transform-limited pulses of 35-fs duration. Because of the high dispersion of the mirrors, the laser cavities needed only five and three bounces from the mirrors, thus keeping reflection losses to a minimum.
© 1999 Optical Society of America
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