Tight focusing of femtosecond radially polarized light pulses through a dielectric interface

Based on the Richards-Wolf vector diffraction theory, we have derived the expressions for the electric field and the propagation velocity of femtosecond radially polarized light pulses focused by a high numerical aperture (NA) objective. The intensity distribution in the focus, wavefront spacings, and propagation velocity variation near the focus are investigated in detail by using numerical calculations. It is found that the propagation velocity of focused ultrashort light pulses changes dramatically near the focus, and the propagation velocity of the focused laser pulse is strongly dependent on the NA of an objective and the refractive index of media. Moreover, the usual propagation velocity of light pulses, as expected, decreases as the refractive index of media increases.