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Thursday, May 28, 2009

Angular momentum of focused beams: Beyond the paraxial approximation

Paula B. Monteiro, Paulo A. Maia Neto, and H. Moysés Nussenzveig

We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam [[h-bar][script-l] orbital angular momentum per photon; sigma=1(−1) for left- (right-) handed polarization] by a high-numerical-aperture objective. The diffraction-limited focused beam has unexpected properties resulting from a strong interplaybetween the angular spatial structure and the local polarization in the nonparaxial regime. In the region near the beam axis, and provided that |[script-l]|=" align="bottom" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 100%; ">2 and [script-l] and sigmahave opposite signs, the energy locally counterpropagates and the projection of the electric field onto the focal plane counter-rotates with respect to the circular polarization of the incident beam. We explicitly show that the total angular momentum flux per unit power is conserved after focusing, as expected by rotational symmetry, but the spin and orbital separate contributions change.

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