Temporal widening of a short polarized pulse focused with a high numerical aperture aplanatic lens

We present a theoretical analysis of the field distribution in the focal plane of a dispersionless, high numerical aperture (NA) aplanatic lens for an x-polarized short pulse. We compare the focused pulse spatial distribution with that of a focused continuous wave (CW) field and its temporal distribution with the profile of the incident pulse. Regardless of the aberration free nature of the focusing aplanatic lens, the temporal width of the focused pulse widens considerably for incident pulses with durations on the order of a few cycles due to the frequency-dependent nature of diffraction phenomena, which imposes a temporal diffraction limit for focused short pulses. The spatial distribution of the focused pulse is also affected by this dependence and is altered with respect to the diffraction limited distribution of the CW incident field. We have analyzed pulses with flat top and Gaussian spatial irradiance profiles and found that the focused pulse temporal widening is less for the Gaussian spatial irradiance pulse, whereas the spatial distribution variation is similar in both cases. We present results of the focused pulsewidth as a function of the NA for the two spatial irradiance distributions, which show that the Gaussian irradiance pulse outperforms the flat top pulse at preserving the incident pulse duration.