Statistical regimes of electromagnetic wave propagation in randomly time-varying media
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908596428603392 |
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| author | Kim, Seulong Kim, Kihong |
| author_facet | Kim, Seulong Kim, Kihong |
| contents | Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder-random fluctuations in material parameters-can suppress propagation and induce localization, analogous to Anderson localization. However, the statistical nature of this process remains incompletely understood. We present a comprehensive analytical and numerical study of electromagnetic wave propagation in spatially uniform media with randomly time-varying permittivity. Using the invariant imbedding method, we derive exact moment equations and identify three distinct statistical regimes for initially unidirectional input: gamma-distributed energy at early times, negative exponential statistics at intermediate times, and a quasi-log-normal distribution at long times, distinct from the true log-normal. In contrast, symmetric bidirectional input yields genuine log-normal statistics across all time scales. These findings are validated using two complementary disorder models--delta-correlated Gaussian noise and piecewise-constant fluctuations--demonstrating that the observed statistics are robust and governed by input symmetry. Momentum conservation constrains the long-time behavior, linking the statistical outcome to the initial conditions. Our results establish a unified framework for understanding statistical wave dynamics in time-modulated systems and offer guiding principles for the design of dynamically tunable photonic and electromagnetic devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical regimes of electromagnetic wave propagation in randomly time-varying media Kim, Seulong Kim, Kihong Optics Disordered Systems and Neural Networks Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder-random fluctuations in material parameters-can suppress propagation and induce localization, analogous to Anderson localization. However, the statistical nature of this process remains incompletely understood. We present a comprehensive analytical and numerical study of electromagnetic wave propagation in spatially uniform media with randomly time-varying permittivity. Using the invariant imbedding method, we derive exact moment equations and identify three distinct statistical regimes for initially unidirectional input: gamma-distributed energy at early times, negative exponential statistics at intermediate times, and a quasi-log-normal distribution at long times, distinct from the true log-normal. In contrast, symmetric bidirectional input yields genuine log-normal statistics across all time scales. These findings are validated using two complementary disorder models--delta-correlated Gaussian noise and piecewise-constant fluctuations--demonstrating that the observed statistics are robust and governed by input symmetry. Momentum conservation constrains the long-time behavior, linking the statistical outcome to the initial conditions. Our results establish a unified framework for understanding statistical wave dynamics in time-modulated systems and offer guiding principles for the design of dynamically tunable photonic and electromagnetic devices. |
| title | Statistical regimes of electromagnetic wave propagation in randomly time-varying media |
| topic | Optics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2507.11062 |