Accurate paraxial Maxwell beams
Abstract
In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy the full Maxwell equations up to the order of (λ/w0)2. The solutions contain some additional terms, which turn out to be relevant for polarization, especially in the case of beams endowed with orbital angular momentum.
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