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  • Received: Mar. 16, 2020

    Accepted: Apr. 30, 2020

    Posted: May. 26, 2020

    Published Online: May. 27, 2020

    The Author Email: Ying Chen (, Yineng Liu (, Huanyang Chen (

    DOI: 10.3788/COL202018.072401

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    Zhanlei Hao, Yawen Zhuang, Ying Chen, Yineng Liu, Huanyang Chen. Effective medium theory of checkboard structures in the long-wavelength limit[J]. Chinese Optics Letters, 2020, 18(7): 072401

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Chinese Optics Letters, Vol. 18, Issue 7, 072401 (2020)

Effective medium theory of checkboard structures in the long-wavelength limit

Zhanlei Hao, Yawen Zhuang, Ying Chen*, Yineng Liu**, and Huanyang Chen***

Author Affiliations

  • Institute of Electromagnetics and Acoustics and Key Laboratory of Electromagnetic Wave Science and Detection Technology, Xiamen University, Xiamen 361005, China


Effective medium theory is a powerful tool to solve various problems for achieving multifarious functionalities and applications. In this article, we present a concise empirical formula about effective permittivity of checkboard structures for different directions. To verify our empirical formula, we perform simulations of checkboard periodic structures in squares, rectangles, and sectors in two dimensions. Our results show that the formula is valid in a large range of parameters. This work provides a new way to understand and design composite materials, which might lead to further optical applications in transformation optics.


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