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.