Extension of effective permittivity for metallic elements on the substrates interface

Abstract

Previously, the influence of substrate interface on the metallic element is always described by the specific effective permittivity. Here, the metallic element on the substrate interface can be converted into that in a homogenized equivalent substrate with almost arbitrary permittivity. Specifically, according to the definition of the permittivity, the substrate interface with a small thickness can be regarded as a homogenized equivalent substrate. Based on the tangential components of the electrical fields, it can be derived that the equivalent permittivity is strongly related to the thickness of the equivalent substrate. Finally, the simulation results demonstrate that the electromagnetic response of the metallic element placed in the homogenized equivalent substrate keeps unchanged as that on the substrate interface. Thus, the proposed method not only provides a generalized means to describe the electromagnetic influence of the substrate interface on the metallic element, but also greatly simplifies the analytical design of multi-layered metasurface.

KEYWORDS:

• Equivalent substrate
• metallic elements
• radiation
• relative permittivity
• scattering
• substrate interface
• metasurface

Disclosure statement

No potential conflict of interest was reported by the author(s).

Author contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Data availability statement

All data that support the findings of this study are included within the article.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants Nos. 62101428 and 62171362, and in part by the Postdoctoral Science Foundation of China under grant number 2021M692530, and in part by the Fundamental Research Funds for the Central Universities under grant number xzy012022089.

Notes on contributors

Peidong Yang

Peidong Yang received the B.S. degree in electronic engineering from Xidian University, Xi'an, China, in 2022, and he is currently pursuing the M.S. degree in electronic information from Xi'an Jiao tong University, Xi'an. His current research interests include metasurface design, antenna and transmitting array design.

Xiaobo Liu

Xiaobo Liu (Member, IEEE) was born in Baoji, China, in 1992. He received the B.Eng. degree in information engineering and the Ph.D. degree in electronic science and technology from Xi'an Jiaotong University, Xi'an, China, in 2014 and 2018, respectively. From 2018 to 2020, he has been a Research Associate at Xi'an Jiaotong University. Since 2020, he has been a Postdoctoral Fellow in applied mathematics and an Assistant Professor with Xi'an Jiaotong University. He has authored or coauthored more than 30 papers in international and domestic journals and conferences. His research interests include electromagnetic and microwave theory, metasurface, and over-the-air (OTA) testing.

Anxue Zhang

Anxue Zhang received the B.S. degree in electrical and electronics engineering from Henan Normal University, Xinxiang, China, in 1996, and the M.S. and Ph.D. degrees in electromagnetic and microwave engineering from Xi'an Jiaotong University, Xi'an, China, in 1999 and 2003, respectively. He is currently a Professor and the Director with the Institute of Electromagnetics and Information Technology, Xi'an Jiaotong University. He has coauthored one book, more than 300 journal articles on the topics of his research interests, which include antenna and electromagnetic wave propagation, RF and microwave circuit designs, and metamaterials. Prof. Zhang is a member of the Academic Committee of the Key Laboratory of Ultrahigh Speed Circuit Design and Electromagnetic Compatibility, Ministry of Education.

Xiaoming Chen

Xiaoming Chen (Senior Member, IEEE) received the B.Sc. degree in electrical engineering from Northwestern Polytechnical University, Xi'an, China, in 2006, and the M.Sc. and Ph.D. degrees in electrical engineering from the Chalmers University of Technology, Gothenburg, Sweden, in 2007 and 2012, respectively. From 2013 to 2014, he was a Postdoctoral Researcher at the Chalmers University of Technology. From 2014 to 2017, he was at Qamcom Research and Technology AB, Gothenburg. Since 2017, he has been a Professor with Xi'an Jiaotong University, Xi'an. His research areas include MIMO antennas, over-the-air testing, and reverberation chambers, and has published more than 150 journal articles on these topics. Prof. Chen received the IEEE Outstanding Associate Editor Award five times from 2018 to 2022 and the International Union of Radio Science (URSI) Young Scientist Award in 2017 and 2018. He was the General Chair of the IEEE International Conference on Electronic Information and Communication Technology (ICEICT) 2021. He currently serves as a Senior Associate Editor (AE) for IEEE Antennas and Wireless Propagation Letters and an AE for IEEE Transactions on Antennas and Propagation.