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Angular Momentum Density of the Vectorial Terms for a Laguerre-Gaussian Beam
Y-Q. Xu, G-Q. Zhou and G-Y. Ru

The description of the linearly polarized Laguerre-Gaussian beam is directly derived from the Maxwell’s equations, and the method of the vectorial angular spectrum is applied to resolve the Maxwell’s equations. The linearly polarized Laguerre-Gaussian beam is uniquely decomposed into the transverse electric (TE) and transverse magnetic (TM) terms, which are referred to as the vectorial structure. Analytical expressions of the TE term, the TM term and the whole beam of the Laguerre-Gaussian beam in free space are derived by using only one omission of an integral, which is verified to be valid for the case of n+m/2≤15 and f≤0.055. By using the expressions of the electromagnetic fields, the expressions of the orbital angular momentum density are presented. The effects of the angular mode number, the linearly polarized angle, the radial mode number, and the axial propagating distance on the distribution of the orbital angular momentum density are investigated in detail. The optimal choice of the linearly polarized angle is that the linearly polarized angle is not equal to zero. To acquire the maximum orbital angular momentum density in a given reference plane, the optimal choice is to increase the angular mode number, and the second priority is to increase the radial mode number. The present research is very useful for the optical trapping, the optical guiding, and the optical manipulation by using a Laguerre-Gaussian beam.

Keywords: Laser beam, angular momentum density, Laguerre-Gaussian beam, vectorial structure, orbital angular momentum density, analytical model

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