Simulations of the secondary maxima of highly focused ultrashort optical pulses in the focal plane

Nowadays, ultrashort optical pulses have quite a few applications, e.g. in the measuring technology, in the processing of materials, and also in the medical science. Like in the stationary (continuous wave) case, secondary maxima appear in the focal plane, when optical pulses are focused by an aplanatic lens (without aberrations). These can be simulated by adding frequency dependent Debye integrals, where each of them can be considered as a superposition of plane waves travelling from the exit pupil to the focus. By changing the order of integrations this corresponds to a superposition of waves with plane wavefront, but time-dependent amplitude. The secondary maxima are highly dependent on the duration of the pulse. Depending on the parameters of the pulse and the lens, they have a maximum intensity at a certain duration, and seemingly vanish as the duration of the pulse grows shorter. The latter results from the fact, that at any non-axial point in the focal plane the amplitude of the envelope of some of these "plane waves" diminishes. Via simulations the effects of certain parameters, such as polarisation, numerical aperture, and initial amplitude profile can be analysed.