It is shown that in a rotational coordinate system the elementary solutions of Maxwell's equations can be derived from two scalar functions. These two functions are the azimuthal (angular) components E phi and H phi of an electromagnetic field and satisfy a differential equation of fourth order, which in particular cases can be factorized. This result follows from a theorem which states that in a wide class of rotational coordinates the azimuthal component F phi satisfies the following differential equation: (2 -2 h 3 4 ( Delta +k 2 -h 3 -2 ) 2 +( delta 2 / delta phi 2 ))F phi =0, if the field F satisfies the vector Helmholtz equation.
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J. Zagrodziński (1977) studied this question.