Abstract
The higher-order correction terms of the electric field vector of a Gaussian beam are derived explicitly from the magnetic vector potential that is assumed to be Gaussian and linearly polarized at the z=0 plane. The correction terms are proved to satisfy exactly Lax’s recurrence equations [Phys. Rev. A11, 1365 (1975)]. The electric field vector with correction terms of orders up to 3 is compared with the exact electric field vector of an integral form that is also derived from the magnetic vector potential.
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