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An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials with Negative Permittivity and Permeability

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An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials with Negative Permittivity and Permeability University of Pennsylvania ScholarlyCommons Departmental Papers (ESE) Department of Electrical & Systems Engineering 1-1-2002 An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials With Negative Permittivity and Permeability Nader Engheta University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/ese_papers Part of the Electrical and Computer Engineering Commons Recommended Citation Nader Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials With Negative Permittivity and Permeability", . January 2002. Copyright 2002 IEEE. Reprinted from IEEE Antennas and Wireless Propagation Letters, Volume 1, Issue 1, 2002, pages 10-13. Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=21952&puNumber=7727 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/ese_papers/12 For more information, please contact [email protected]. An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials With Negative Permittivity and Permeability Abstract In this letter, we present and analyze theoretically some ideas for thin one-dimensional (1-D) cavity resonators in which a combination of a conventional dielectric material and a metamaterial possessing negative permittivity and permeability has been inserted. In this analysis, it is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, thus, by combining such a slab with another slab made of a conventional dielectric material one can, in principle, have a 1-D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses. In other words, one can, in principle, conceptualize a 1-D cavity resonator with the total thickness far less than the conventional λ/2. Mathematical steps and physical intuitions relevant to this problem are presented. Keywords Cavity resonator, metamaterials, negative index of refraction, negative permeability, negative permittivity, phase compensator, phase conjugation. Disciplines Electrical and Computer Engineering Comments Copyright 2002 IEEE. Reprinted from IEEE Antennas and Wireless Propagation Letters, Volume 1, Issue 1, 2002, pages 10-13. Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=21952&puNumber=7727 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This journal article is available at ScholarlyCommons: https://repository.upenn.edu/ese_papers/12 10 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 1, 2002 An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials With Negative Permittivity and Permeability Nader Engheta, Fellow, IEEE Abstract—In this letter, we present and analyze theoretically permittivity and permeability in omega media for a certain some ideas for thin one-dimensional (1-D) cavity resonators in range of frequencies [23]. For metamaterials with negative which a combination of a conventional dielectric material and a permittivity and permeability, several names and terminologies metamaterial possessing negative permittivity and permeability has been inserted. In this analysis, it is shown that a slab of have been suggested such as “left-handed” media [17]–[22], metamaterial with negative permittivity and permeability can media with negative refractive index [17]–[22] “backward act as a phase compensator/conjugator and, thus, by combining media” (BW media) [24], “double negative metamaterials” such a slab with another slab made of a conventional dielectric [25], [26], to name a few. The anomalous refraction at the material one can, in principle, have a 1-D cavity resonator whose boundary of such media and the fact that for a plane wave dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the direction of the Poynting vector is antiparallel with the the ratio of these thicknesses. In other words, one can, in principle, direction of phase velocity, provide us with features that can conceptualize a 1-D cavity resonator with the total thickness far be advantageous in design of novel devices and components. less than the conventional /2. Mathematical steps and physical Recently, we introduced and presented in a symposium [27] intuitions relevant to this problem are presented. one of our ideas for a compact cavity resonator. Here in this Index Terms—Cavity resonator, metamaterials, negative index letter, we describe the details of this idea and the mathematical of refraction, negative permeability, negative permittivity, phase steps behind our analysis. compensator, phase conjugation. A. Metamaterials With Negative and as Phase I. INTRODUCTION Compensators/Conjugators N the past several decades, the electromagnetic (EM) When a lossless metamaterial possesses negative real permit- I properties of complex media have been the subject of tivity and permeability at certain frequencies, the index of re- research study for many research groups [1]–[16]. Several fraction in such a medium attains real values. So as theoreti- types of EM complex media such as chiral materials, omega cally predicted by Veselago, the EM wave can propagate in such media, bianisotropic media, local, and nonlocal media to name a medium [22]. However, for a monochromatic uniform plane a few, have been studied. Recently, the idea of composite wave in such a medium the phase velocity is in the opposite di- materials in which both permittivity and permeability possess rection of the Poynting vector. negative values at certain frequencies has gained considerable Consider a slab of conventional lossless material with real attention [17]–[21]. In 1967, Veselago theoretically investi- permittivity , real permeability , and the index of gated plane wave propagation in a material whose permittivity refraction , where and are the per- and permeability were assumed to be simultaneously negative mittivity and permeability of the free space. Here, is taken [22]. His theoretical study showed that for a monochromatic to be a positive real quantity. The slab is infinitely extent in the uniform plane wave in such a medium, the direction of the - plane and has the thickness along the axis. We tem- Poynting vector is antiparallel with the direction of phase porarily assume that the intrinsic impedance of the dielectric velocity, contrary to the case of plane wave propagation in material is the same as that of the outside re- conventional simple media. Recently, Smith et al. constructed gion , i.e., , but its refractive index is such a composite medium for the microwave regime and different from that of outside, i.e., . (We will soon re- demonstrated experimentally the presence of anomalous re- move the first part of this assumption.) Let us assume that a fraction in this medium [17], [18], [20], [21]. It is also worth monochromatic uniform plane wave is normally incident on this noting that previous theoretical study of EM wave interaction slab. The wave propagates through the slab without any reflec- with omega media reveals the possibility of having negative tion (because for now we are still assuming ). As this wave traverses this slab, the phase at the end of the slab is obvi- Manuscript received December 20, 2001; revised February 11, 2002. This ously different from the phase at the beginning of the slab by the work was presented in part at the International Conference on Electromagnetics amount , where . Now, consider a slab of in Advanced Applications (ICEAA), Torino, Italy, September 10–14, 2001. a lossless metamaterial with negative real permittivity and per- The author is with the Department of Electrical Engineering, University of Pennsylvania, Philadelphia, PA 19104 USA (e-mail: [email protected]). meability, i.e., and at certain frequencies. For Digital Object Identifier 10.1109/LAWP.2002.802576 this slab, the index of refraction is a real quantity denoted by 1536-1225/02$17.00 © 2002 IEEE ENGHETA: THIN SUBWAVELENGTH CAVITY RESONATORS WITH NEGATIVE PERMITTIVITY AND PERMEABILITY 11 Fig. 1. A two-layer structure in which the left layer is assumed to be a Fig. 2. An idea for a compact, subwavelength, thin cavity resonator. The 4 b H " b H two-layer structure discussed in Fig. 1 is sandwiched between the two conventional lossless dielectric material
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