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arXiv · 2504.05735

Anomalous Maxwell-Garnett theory for photonic time crystals

Zheng Gong·Ruoxi Chen·Hongsheng Chen·Xiao Lin
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Abstract

Maxwell-Garnett theory, dating back to James Clerk Maxwell-Garnett's foundational work in 1904, provides a simple yet powerful framework to describe the inhomogeneous structure as an effective homogeneous medium, which significantly reduces the overall complexity of analysis, calculation, and design. As such, the Maxwell-Garnett theory enables many practical applications in diverse realms, ranging from photonics, acoustics, mechanics, thermodynamics, to material science. It has long been thought that the Maxwell-Garnett theory of light in impedance-mismatched periodic structures is valid only within the long-wavelength limit, necessitating either the temporal or spatial period of light to be much larger than that of structures. Here, we break this long-held belief by revealing an anomalous Maxwell-Garnett theory for impedance-mismatched photonic time crystals beyond this long-wavelength limit. The key to this anomaly lies in the Fabry-Perot resonance. We discover that under the Fabry-P\'erot resonance, the impedance-mismatched photonic time crystal could be essentially equivalent to a homogeneous temporal slab simultaneously at specific discrete wavelengths, despite the temporal period of these light being comparable to or even much smaller than that of photonic time crystals.

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Zheng Gong, Ruoxi Chen, Hongsheng Chen, Xiao Lin. 2025-04-08. Anomalous Maxwell-Garnett theory for photonic time crystals. https://arxiv.org/abs/2504.05735

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