Do vector plane waves form complete basis of solutions to Maxwell's equations? Introduction to Generalized Plane Wave Solutions
2018-04-27
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Do vector plane waves form complete basis of solutions to Maxwell's equations? Introduction to Generalized Plane Wave Solutions
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2018-04-27
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As the title says, this article questions the well established belief that the vector plane waves form a complete basis of solutions to Maxwell's equations. Vector solutions to Maxwell's equations are presented here, which have planar wave-fronts and transverse electric and magnetic fields but spatially varying polarization. They form a one-parameter family specified by integer $n$, and are termed as \textit{generalized vector plane waves}. The known vector plane wave solution with spatially uniform polarization, referred to as \textit{conventional vector plane waves} in this article, is a subset of this family obtained for $n = 0$. In contradiction to the established belief, it is shown that these \textit{generalized vector plane waves} with spatially varying polarization (for $n \neq 0$) cannot be expressed as superposition of conventional vector plane waves. The family of solutions also includes the interesting cases of radially and azimuthally polarized plane waves for $n=1$.
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The article is preprint version of a manuscript submitted for publication in a journal. The author is the sole creator of the ideas presented here. Please see the copyright notice in the document.
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Aryan, Saurav. (2018). Do vector plane waves form complete basis of solutions to Maxwell's equations? Introduction to Generalized Plane Wave Solutions. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/196090.
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