Efficient analytic computation of dispersion from multilayer structures

We demonstrate an inductive method for computing exact derivatives of reflection phase for layered media by using the transfer-matrix formalism. The algorithm scales linearly with the number of layers. We show a physically realistic approximation that leads to an efficient procedure for accurately computing dispersion significantly faster than with standard finite-difference methods. We discuss the theory behind the approximation and show results for a dispersion-compensating chirped mirror from a Ti:sapphire laser.