This analysis demonstrates novel solutions of Maxwell equations using Riemann–Silberstein vectors, highlighting their impact on polarization and angular momentum.
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 ( λ / w 0 ) 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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Tomasz Radożycki (2025) studied this question.
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