  Shaped pulses obtained by optimal control theory often possess unphysically
broad spectra. In principle, the spectral width of a pulse can be restricted by
an additional constraint in the optimization functional. However, it has so far
been impossible to impose spectral constraints while strictly guaranteeing
monotonic convergence. Here, we show that Krotov's method allows for
simultaneously imposing temporal and spectral constraints without perturbing
monotonic convergence, provided the constraints can be expressed as positive
semi-definite quadratic forms. The optimized field is given by an integral
equation which can be solved efficiently using the method of degenerate
kernels. We demonstrate that Gaussian filters suppress undesired frequency
components in the control of non-resonant two-photon absorption.
