Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion
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2019-09-02
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The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion.
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Arrayás, M.; Rañada, A.F.; Tiemblo, A.; Trueba, J.L. Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion. Symmetry 2019, 11, 1105. https://doi.org/10.3390/sym11091105
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