Title: Beyond Fresnel Wave Surfaces: Off-Shell Photonic Density of States and Near-Fields in Isotropy-Broken Materials with Loss or Gain Show Chinese title

Title: 超越菲涅尔波面：各向异性破坏材料中非壳光子态密度和近场

Abstract: Fresnel wave surfaces, or isofrequency light shells, provide a powerful framework for describing electromagnetic wave propagation in anisotropic media, yet their applicability is restricted to reciprocal, lossless materials and far-field radiation. This paper extends the concept by incorporating near-field effects and non-Hermitian responses arising in media with loss, gain, or non-reciprocity. Using the Om-potential approach to macroscopic electromagnetism, we reinterpret near fields as off-shell electromagnetic modes, in analogy with off-shell states in quantum field theory. We show that photonic density of states (PDOS) distributions near Fresnel surfaces acquire Lorentzian broadening in non-reciprocal media, directly linking this effect to the Beer-Bouguer-Lambert law of exponential attenuation or amplification. Furthermore, we demonstrate how Abraham and Minkowski momenta, locked to light shells in the far field, naturally shift to characterize source structures in the near-field regime. This unified treatment bridges the gap between sources and radiation, on-shell and off-shell modes, and reciprocal and non-reciprocal responses. The framework provides both fundamental insight into structured light and practical tools for the design of emitters and metamaterial platforms relevant to emerging technologies such as 6G communications, photonic density-of-states engineering, and non-Hermitian photonics. Show Chinese abstract

Abstract: 弗朗霍夫波面，或等频率光壳，为描述各向异性介质中的电磁波传播提供了一个强有力的框架，但其适用性仅限于互易、无损耗材料和远场辐射。 本文通过引入近场效应以及在具有损耗、增益或非互易性的介质中出现的非厄米响应，扩展了这一概念。 利用宏观电磁学的Om势方法，我们将近场重新解释为非壳电磁模式，类似于量子场论中的非壳态。 我们表明，在非互易介质中，靠近弗朗霍夫面的光子态密度（PDOS）分布会获得洛伦兹展宽，直接将这种效应与指数衰减或增强的Beer-Bouguer-Lambert定律联系起来。 此外，我们展示了阿布拉罕动量和米氏动量，在远场中与光壳锁定，自然地转移到近场区域来表征源结构。 这种统一的处理方式弥合了源与辐射、壳上模式与非壳模式，以及互易与非互易响应之间的差距。 该框架不仅为结构光提供了基本见解，还为设计与新兴技术如6G通信、光子态密度工程和非厄米光子学相关的发射器和超材料平台提供了实用工具。