Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit
Open accessAbstract
We present an effective medium theory that simultaneously determines the effective permittivity and effective permeability of a magnetodielectric composite beyond the long-wavelength limit. In the long-wavelength limit, our theory reproduces previous results obtained in two and three dimensions. To verify our theory, we performed band-structure calculations on a periodic composite in two dimensions for a specific configuration with complicated Mie resonances in the microstructure. Our results show that our theory can be valid even when the wavelength in the background medium, ${\ensuremath{\lambda}}_{0}$, is as small as 1.3 times the lattice constant, $a$, whereas the long-wavelength theory breaks down when ${\ensuremath{\lambda}}_{0}<3.5a$.
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In 2D photonic crystals, effective medium theory can be applied to extract εeff and μeff if the bands are derived from the monopole and dipole scattering of the building blocks.
“It can be shown that in 2D photonic crystals, effective medium theory can be applied to extract ε eff and μ eff if the bands are derived from the monopole and dipole scattering of the building blocks [68]”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [68]
Section III shows that effective-medium calculations of εeff and μeff reproduce bands associated with m = 0 and m = 1 resonances in a two-dimensional periodic composite. But it restricts the meaningful band-structure comparison to an isotropic region near the Γ point and says the equations become invalid beyond that range. The citing sentence omits this spatial-range limitation. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIf band dispersions in a 2D photonic crystal can be described by monopole and dipole interactions, an effective medium theory can be applied to extract effective constitutive parameters.
“It can be shown [68] that if the band dispersions in a 2D photonic crystal can be described by monopole and dipole interactions, an effective medium theory [68] can be applied to extract effective constitutive parameters”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [68]
As effective medium theory is not expected to work when the bands have a strong quadrupole character, the core-shell system should not behave like a zero-index medium even though it has a conical dispersion.
“As effective medium theory [68] is not expected to work when the bands have a strong quadrupole character, we expect that the system should not behave like a zero-index medium even though it has a conical dispersion.”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [68]
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Acoustic metamaterials with spinning components
Zhao, D., Wang, Y., Fung, K. H., Zhang, Z.-Q., & Chan, C. T. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.054107 · Cited by 24 · see citing works
Self-citationPLASMONIC RESONANT LIGHT SCATTERING BY A CYLINDER WITH RADIAL ANISOTROPY
Jin, Y., Gao, D., & Gao, L. (2010) · Electromagnetic waves · doi:10.2528/pier10060601 · Cited by 23 · see citing works
Physics of the zero‐ n photonic gap: fundamentals and latest developments
Zhou, L., Song, Z., Huang, X., & Chan, C. T. (2012) · Nanophotonics · doi:10.1515/nanoph-2012-0020 · Cited by 24 · see citing works
Self-citationZhang, X., & Forrest, S. R. (2011) · Physical Review B · doi:10.1103/physrevb.84.045427 · Cited by 23 · see citing works
Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres
Zhang, L., Shi, Y., & Liang, C. (2016) · Optics Express · doi:10.1364/oe.24.023333 · Cited by 23 · see citing works
Coherent perfect absorber and laser modes in purely imaginary metamaterials
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Pseudospin-1 Physics of Photonic Crystals
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Configurable Dirac-like conical dispersions in complex photonic crystals
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Effective-medium theory for multilayer metamaterials: Role of near-field corrections
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Effective-medium properties of metamaterials: A quasimode theory
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Effective dynamic constitutive parameters of acoustic metamaterials with random microstructure
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Breakdown of Maxwell Garnett theory due to evanescent fields at deep-subwavelength scale
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A new type of artificial structure to achieve broadband omnidirectional acoustic absorption
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- Authors
- Wu, Y., Li, J., Zhang, Z.-Q., & Chan, C. T.
- Affiliations
- Hong Kong University of Science and Technology (HK)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-08-15
- Volume
- 74
- Issue
- 8
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1998772394
- Cited by
- 231
- References
- 25
- Citations by year
- 2026: 3 · 2025: 7 · 2024: 10 · 2023: 8 · 2022: 9 · 2021: 12 · 2020: 15 · 2019: 17 · 2018: 16 · 2017: 19 · 2016: 21 · 2015: 28 · 2014: 14 · 2013: 9 · 2012: 13
- FWCI
- 3.58
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review B (publishedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Multiferroics and related materials
- Physical Sciences › Engineering › Biomedical Engineering › Dielectric materials and actuators
- Keywords
- effective medium theory, magnetic-dielectric composites, effective permittivity, effective permeability, long-wavelength limit, Mie resonance, periodic composites, electronic band structure, two-dimensional microstructures, electromagnetic wave propagation
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