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We present a detailed study of the fields and propagation characteristicsaround the focus of ultrashort radially-polarized laser beams (RPLBs) havinglow-order spatio-temporal couplings (STCs). The three STCs considered are thefocusing of the different frequencies to different positions along thelongitudinal coordinate, the focusing of the frequencies to different positionsalong one transverse coordinate, and the beam waist or Rayleigh range having apower-law frequency dependence. The STCs considered are deemed low-orderbecause they are generally linear in frequency. The combination of a low-ordervector beam, ultrashort pulse duration, and the three different STCs showspromise for exotic applications in dielectric or charged particle manipulationand potentially other strong-field phenomena. The STCs presented are alldeveloped in a standard frequency-domain model where each case involves adifferent chromatic term. We present the results unique to the vector nature ofthe RPLBs and compare them to the linearly polarized cases, opening upopportunities for control of the electric field around the focus with theadditional element of polarization.

Focused fields of ultrashort radially-polarized laser pulses having low-order spatio-temporal couplings