# Effective complex permittivity tensor of a periodic array of cylinders

@article{Godin2013EffectiveCP, title={Effective complex permittivity tensor of a periodic array of cylinders}, author={Yuri A. Godin}, journal={Journal of Mathematical Physics}, year={2013}, volume={54}, pages={053505-053505} }

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex…

## 23 Citations

Transport properties of periodic metamaterials

- Materials Science2014 8th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics
- 2014

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, whose…

Long-wave approximation for the effective dielectric tensor of periodic materials

- Mathematics2016 URSI International Symposium on Electromagnetic Theory (EMTS)
- 2016

We describe a method to calculate the effective dielectric tensor of a periodic array of dielectric cylinders embedded in a host matrix for transverse electromagnetic waves whose wavelength is much…

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

- Materials ScienceWaves in Random and Complex Media
- 2018

ABSTRACT The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a…

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- Physics, MedicineProceedings of the Royal Society A
- 2019

This work considers transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders and obtains explicit formulae for the effective dielectric tensor and the dispersion relation with the rigorously justified error of order O.

Gain and loss enhancement of passive and active materials in a square periodic array of cylinders

- 2018

The asymptotic homogenization method is applied to complex dielectric two-phase fibrous composites. Under continuity conditions at the interfaces, we derive closed-form formulas for the complex…

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- Mathematics, Physics
- 2016

A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodic functions for…

Unified complex variable solution for the effective transport properties of composites with a doubly-periodic array of fibers

- Materials Science
- 2017

We present a complex variable method to evaluate the transverse effective transport properties of composites with a doubly-periodic array of fibers. The obtained complex variable solution is derived…

Effect of Microgeometry on the Effective Dielectric Property of Anisotropic Composites

- 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO)
- 2020

Composite Material is ubiquitous in both natural and engineered systems. Electromagnetic responses of these systems are determined by the effective properties of the composites, e.g. permittivity and…

Enhanced inertia from lossy effective fluids using multi-scale sonic crystals

- Materials Science, Physics
- 2014

In this work, a recent theoretically predicted phenomenon of enhanced permittivity with electromagnetic waves using lossy materials is investigated for the analogous case of mass density and acoustic…

Effective transport properties for periodic multiphase fiber-reinforced composites with complex constituents and parallelogram unit cells

- Materials Science
- 2020

Abstract The two-scale asymptotic homogenization method is used to find closed-form formulas for effective properties of periodic multi-phase fiber-reinforced composites where constituents have…

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