Introduction to the Maxwell Garnett approximation: tutorial
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This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius-Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for isotropic and anisotropic media, multicomponent mixtures and the Bruggeman equation, the concept of smooth field, and Wiener and Bergman-Milton bounds.
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Maxwell-Garnett typically assumes spherical inclusions and works well for low-to-moderate inclusion concentrations.
“Examples of common EMTs include Maxwell-Garnett, which typically assumes spherical inclusions and works well for low-to-moderate inclusion concentrations, and Bruggeman, which is often preferred for higher concentrations or more symmetric mixtures [49, 55, 64, 65].”
From Tutorial: Accurate Determination of Refractive Index and Absorption Coefficient in Terahertz Time-Domain Spectroscopy (2025) · cites this paper as [65]
Bruggeman is often preferred for higher concentrations or more symmetric mixtures.
“Examples of common EMTs include Maxwell-Garnett, which typically assumes spherical inclusions and works well for low-to-moderate inclusion concentrations, and Bruggeman, which is often preferred for higher concentrations or more symmetric mixtures [49, 55, 64, 65].”
From Tutorial: Accurate Determination of Refractive Index and Absorption Coefficient in Terahertz Time-Domain Spectroscopy (2025) · cites this paper as [65]
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VII. Colours in metal glasses, in metallic films, and in metallic solutions.—II
Garnett, J. C. M. (1906) · Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character · doi:10.1098/rsta.1906.0007 · Cited by 1,246 · cited 1× · see citing works
“In 1904, Maxwell Garnett developed a simple but immensely successful homogenization theory [1,2].”
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Tutorial: An introduction to terahertz time domain spectroscopy (THz-TDS)
Neu, J., & Schmuttenmaer, C. A. (2018) · Journal of Applied Physics · doi:10.1063/1.5047659 · Cited by 675 · see citing works
The Bouguer-Beer-Lambert Law: Shining Light on the Obscure
Mayerhöfer, T. G., Pahlow, S., & Popp, J. (2020) · ChemPhysChem · doi:10.1002/cphc.202000464 · Cited by 618 · see citing works
Leung, C. K., Ward-Berry, J. N., Wanvig i Dot, E., Lee, J., & Zeitler, J. A. (2025) · Journal of Infrared, Millimeter and Terahertz Waves · doi:10.1007/s10762-025-01070-8 · Cited by 17 · see citing works
“Examples of common EMTs include Maxwell-Garnett, which typically assumes spherical inclusions and works well for low-to-moderate inclusion concentrations, and Bruggeman, which is often preferred for higher concentrations or more symmetric mixtures [49, 55, 64, 65].”
- Authors
- Markel, V. A.
- Corresponding author
- Markel, Vadim A.
- ORCID
- Markel, Vadim A.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 2016-06-06
- Volume
- 33
- Issue
- 7
- Pages
- 1244
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W2410624667
- Cited by
- 859
- References
- 1
- Citations by year
- 2026: 92 · 2025: 92 · 2024: 81 · 2023: 100 · 2022: 101 · 2021: 120 · 2020: 91 · 2019: 101 · 2018: 51 · 2017: 28 · 2016: 2
- FWCI
- 19.08
- Type
- journal article
- Language
- en
- Open access
- green
- hal.science
- Licence
- Locations
- Journal of the Optical Society of America A (publishedVersion)
- PubMed (publishedVersion)
- HAL (submittedVersion, other-oa)
- Funders
- Agence Nationale de la Recherche (ANR) (ANR-11-IDEX-0001-02)
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Engineering › Biomedical Engineering › Plasmonic and Surface Plasmon Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Electromagnetic Scattering and Analysis
- Keywords
- Maxwell-Garnett model, effective medium theory, Clausius-Mossotti relation, discrete dipole approximation, anisotropic materials, chemical mixtures, Bruggeman equation, effective permittivity
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