Based on the vectorial Debye theory, the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically, including the intensity, the phase and the orbital angular momentum properties. Then the influence of certain parameters on the focusing properties is also investigated. It is shown that sub-wavelength elliptical light spots can be obtained. And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam, indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.
This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.
