Properties of an elegant Laguerre-Gaussian beam in the receiver plane of Airy transformation

Abstract

As the superposition of an even and odd modes constitutes an elegant Laguerre-Gaussian beam (ELGB), Airy transformation of the even mode, the odd mode, and the ELGB is studied. Analytical expressions of the even mode, the odd mode, and the ELGB in the receiver plane of Airy transformation are derived, respectively. Also, the analytical centroid and the analytical beam width for the arbitrary even mode, the arbitrary odd mode, and the arbitrary ELGB in the receiver plane of Airy transformation are concluded by numerical calculations. Moreover, the relationship of the centroids and the beam widths among the even mode, the odd mode, and the ELGB in the receiver plane of Airy transformation are presented. As typical examples, the properties of the even, the odd, and the whole beam for E01, E02, E11, and E12 are demonstrated in the receiver plane of Airy transformation. The above two subscripts correspond to the radial and the angular moduli, respectively. The effects of the transform coefficients on the normalized light intensity, the centroid, and the beam width of the even, the odd, and the whole beam for E01, E02, E11, and E12 in the receiver plane of Airy transformation are analyzed. Furthermore, the effect of the transform coefficients on the orbital angular momentum (OAM) density of E01, E02, E11, and E12 are examined. The OAM of the ELGB in the receiver plane of Airy transformation is conserved, which is not subject to influence of the transform coefficients. This study provides an optional scheme for obtaining peculiar laser beams, and also it expands applications of the even mode, the odd mode, and the ELGB.

Keywords

• Elegant Laguerre-Gaussian beam
• Airy transformation
• Centroid
• Beam width
• Orbital angular momentum density