Nonparaxial analysis of vectorial Laguerre-Bessel-Gaussian beams.

The concept of vectorial Laguerre-Bessel-Gaussian (LBG) beams is proposed. On the basis of vectorial Rayleigh-Sommerfeld formulas, the analytical formulas for the nonparaxial propagation of vectorial LBG beams are derived and applied to study the nonparaxial propagation properties of vectorial LBG beams. The far field and paraxial approximation are dealt with as special cases of our general results. Some detailed comparisons of the obtained results with the paraxial results are made, which show the propagation of paraxial and nonparaxial LBG beams is all instable in the near field and the f parameter plays the important role in determining the nonparaxiality of vectorial LBG beams. The beam parameter alpha also affects the propagation behavior of nonparaxial LBG beams. Under certain conditions, the obtained results can be reduced to those of the cases for vectorial Laguerre-Gaussian and Bessel Gaussian beams.