Abstract
Following a brief survey of the theory of Laguerre-Gaussian beam modes, expressions are derived for the paraxial vector electric and magnetic fields for wave modes of arbitrary order. The variation of field amplitude in the plane transverse to the axis of propagation is illustrated by three-dimensional graphs, and constant-amplitude contours are obtained. Also, the electric and magnetic fields in longitudinal (xz and yz) planes are plotted for some low-order modes.
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