标题： 宏观电磁学的Ω理论：各向异性介质的更绿色的振动 显示英文标题

标题： Om-Theory of Macroscopic Electromagnetism: Greener Vibes for Isotropy-Broken Media

摘要： 宏观电磁学和微观电磁学的应用范围是相反的。 微观电磁学处理点源、奇异场和离散原子材料，而宏观电磁学则涉及源、场以及均质化有效超材料的平滑平均分布。 格林函数法（GFM）包括寻找点源的场，并应用叠加原理来求解分布式源的场。 当用于解决微观问题时，GFM完全在其适用范围内。 将GFM扩展到简单的宏观问题虽然方便，但并不完全合乎逻辑，因为点源和奇异场在技术上不属于宏观电磁学的研究范畴。 这解释了为什么在复杂的各向异性破坏介质中，找到格林函数并应用叠加原理会如此困难，因为这些环境与微观环境有很大的不同。 在本文中，我们提出了一种绕过GFM的方法来求解分布式源的宏观麦克斯韦方程组，通过引入逆向方法和基于奥姆势的方法，我们在文中对此进行了描述。 对于电磁学研究人员来说，这提供了强大的分析工具以及麦克斯韦方程的新广度解决方案空间。 显示英文摘要

摘要： The applicability ranges of macroscopic and microscopic electromagnetisms are opposite. While microscopic electromagnetism deals with point sources, singular fields, and discrete atomistic materials, macroscopic electromagnetism concerns smooth average distributions of sources, fields, and homogenized effective metamaterials. Greens function method - GFM - involves finding fields of point sources and applying superposition principle to find fields of distributed sources. When utilized to solve microscopic problems GFM is perfectly within the applicability range. Extension of GFM to simple macroscopic problems is convenient, but not fully logically sound, since point sources and singular fields are technically not a subject of macroscopic electromagnetism. This explains the difficulty of both finding the Greens functions and applying superposition principle in complex isotropy-broken media, which are very different from microscopic environments. In this manuscript, we lay out a path to solution of macroscopic Maxwells equations for distributed sources bypassing GFM, by introducing inverse approach and a method based on Om-potential which we describe here. To the researchers of electromagnetism this provides access to powerful analytical tools and a broad new space of solutions for Maxwells equations.