Figure 1

(Color online) Multipolar decomposition of a Gaussian beam. First column: Right circular polarization $(p=+1)$. Second column: Left circular polarization $(p=-1)$. First row: weight of the multipolar components $C_{j0p}^2$. Second, third, and last rows represent the different components (respectively, right circular, longitudinal, and left circular) of the field at $z=0$, after performing the summation of the multipole components. Note the different scales of the components.Reuse & Permissions

Figure 2

(Color online) Multipolar decomposition of Laguerre-Gaussian beams. First column: Right circular polarization $(p=+1)$ and azimuthal index negative $(l=-1)$. Second column: Left circular polarization $(p=-1)$ and azimuthal index positive $(l=+1)$. First row: weight of the multipolar components: $C_{j\pm 1\mp 1}^2$. In this case $C_{j+1-1}=-C_{j-1+1}$. Second, third, and last rows are as in Fig. 1.Reuse & Permissions

Figure 3

(Color online) Total angular momentum of paraxial beams. (a) Dependence of the density of total angular momentum of a paraxial beam vs the beam width. Open circles represent the calculated value of the angular momentum for a LG beam with right circular polarization. The label of each set of data is the azimuthal index $l$ of the LG beam. Continuous line follow the rule of $\sqrt{(\Vert l\Vert +1)∕2}{w}_0$. (b) Steepness of the kind of curves shown in (a) with respect to the azimuthal index of the LG beam. The data are extracted by a linear regression of the calculated angular momentum. Open circles: Right circular polarization. Crosses: Left circular polarization. Error bars in the linear regression are smaller than the size of the spot. Continuous line: expected value of $\sqrt{(\Vert l\Vert +1)∕2}$.Reuse & Permissions