sensors Article Negative Index Metamaterial Lens for Subwavelength Microwave Detection Srijan Datta 1,* , Saptarshi Mukherjee 2, Xiaodong Shi 1, Mahmood Haq 1, Yiming Deng 1, Lalita Udpa 1 and Edward Rothwell 1 1 Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected] (X.S.); [email protected] (M.H.); [email protected] (Y.D.); [email protected] (L.U.); [email protected] (E.R.) 2 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA; [email protected] * Correspondence: [email protected] Abstract: Metamaterials are engineered periodic structures designed to have unique properties not encountered in naturally occurring materials. One such unusual property of metamaterials is the ability to exhibit negative refractive index over a prescribed range of frequencies. A lens made of negative refractive index metamaterials can achieve resolution beyond the diffraction limit. This paper presents the design of a metamaterial lens and its use in far-field microwave imaging for subwavelength defect detection in nondestructive evaluation (NDE). Theoretical formulation and numerical studies of the metamaterial lens design are presented followed by experimental demonstration and characterization of metamaterial behavior. Finally, a microwave homodyne receiver-based system is used in conjunction with the metamaterial lens to develop a far-field microwave NDE sensor system. A subwavelength focal spot of size 0.82λ was obtained. The system is shown to be sensitive to a defect of size 0.17λ × 0.06λ in a Teflon sample. Consecutive positions of Citation: Datta, S.; Mukherjee, S.; the defect with a separation of 0.23λ was resolvable using the proposed system. Shi, X.; Haq, M.; Deng, Y.; Udpa, L.; Rothwell, E. Negative Index Keywords: metamaterial; lenses; refractive index; microwave sensors; nondestructive testing Metamaterial Lens for Subwavelength Microwave Detection. Sensors 2021, 21, 4782. https:// doi.org/10.3390/s21144782 1. Introduction In 1968, V. Veselago theoretically introduced the electrodynamics of materials having Academic Editor: Anthony N. Sinclair simultaneous negative values of permittivity and permeability µ [1]. He showed that such materials will exhibit unusual properties such as negative refraction, reversal of Doppler Received: 1 June 2021 shift and backward Cherenkov radiation. The electric field, magnetic field, and wave vector Accepted: 10 July 2021 of a plane wave form a left-handed triplet in such a medium, instead of the conventional Published: 13 July 2021 right-handed one. The word “metamaterial” was coined for such materials, alluding to their unusual properties, not generally encountered in nature. The first left-handed metamaterial Publisher’s Note: MDPI stays neutral (LHM) structure was realized by Smith et al., in their seminal paper of 2000, where they with regard to jurisdictional claims in published maps and institutional affil- showed that an alternating periodic array of split-ring resonators (SRRs), and thin wires iations. can produce an effective medium having a negative refractive index in the microwave regime [2]. Extensive research demonstrating and characterizing the left-handed behavior of such structures followed [3–5]. Early on, negative refractive index structures were a controversial topic, and their existence was disputed by researchers [6,7]. However, over the past two decades, there has been significant evidence that certain periodic structures can Copyright: © 2021 by the authors. indeed have an effective negative refractive index over a limited range of frequencies [8–10]. Licensee MDPI, Basel, Switzerland. Such periodic structures, even though inhomogeneous, can behave as a homogeneous This article is an open access article distributed under the terms and medium in response to electromagnetic (EM) waves with appropriately long wavelength. conditions of the Creative Commons The homogenized negative index behavior of inhomogeneous metamaterial structures has Attribution (CC BY) license (https:// been described by an effective negative and µ of the periodic arrays [11]. creativecommons.org/licenses/by/ Metamaterials have inspired many novel applications based on their negative refrac- 4.0/). tive index. One of the most ingenious applications of LHM structures was put forward Sensors 2021, 21, 4782. https://doi.org/10.3390/s21144782 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 18 Sensors 2021, 21, 4782 2 of 16 Metamaterials have inspired many novel applications based on their negative refrac- tive index. One of the most ingenious applications of LHM structures was put forward by J.B.by J.B.Pendry, Pendry, where where he showed he showed that a that negative a negative refractive refractive index indexmaterial material can act can as a act “super as a “superlens”, capable lens”,capable of achieving of achieving subwavelength subwavelength focusing focusing in the far in field the farby fieldrestoring by restoring the am- plitudethe amplitude of evanescent of evanescent wave components wave components [12]. The [ 12highest]. The resolution highest resolution that can be that obtained can be usingobtained a conventional using a conventional lens in the lens far in field the faris limited field is by limited the operating by the operating wavelength, wavelength, due to thedue physics to the physics of diffraction. of diffraction. The breaking The breaking of this diffraction of this diffraction limit using limit point using source point focusing source (Figurefocusing 1a) (Figure and evanescent1a) and evanescent wave amplification wave amplification of a LHM oflens a LHMhas been lens one has of been the onesignifi- of cantthe significant driving factors driving for factorsmetamaterial for metamaterial research. Various research. metamaterial Various metamaterial designs, operating designs, fromoperating radio from to optical radio frequencies, to optical frequencies, have been havedeveloped been developed and shown and to achieve shown tosubwave- achieve lengthsubwavelength focusing focusing[13–17]. [13–17]. (a) (b) Figure 1.1. (a) RayRay diagramdiagram showingshowing reversalreversal ofof Snell’sSnell’s lawlaw inin aa metamaterialmetamaterial medium.medium. For a conventionalconventional medium,medium, the diverging beams from from a a point point source source will will not not come come into into focus. focus. (b) (Printedb) Printed circuit circuit board board (PCB) (PCB) implementation implementation of a met- of a amaterial consisting of alternating periodic arrangement of SRRs and wires. The structure will exhibit an effective negative metamaterial consisting of alternating periodic arrangement of SRRs and wires. The structure will exhibit an effective refractive index over a range of frequencies under specific incident wave polarization. negative refractive index over a range of frequencies under specific incident wave polarization. This paper reports thethe designdesign ofof aa metamaterialmetamaterial lens lens and and its its experimental experimental implementa- implemen- tationtion for for far-field far-field microwave microwave detection detection of subwavelength of subwavelength defects. defects. Far-field Far-field microwave microwave NDE NDEoffers offers the advantage the advantage of rapid of scanrapid times, scan buttimes, is constrained but is constrained by the diffraction by the diffraction limit from limit de- fromtecting detecting smaller subwavelengthsmaller subwavelength defects [18 defects]. A single [18]. SRRA single coupled SRR with coupled a transmission with a trans- line missionbehaves line as a LCbehaves tank circuit,as a LC whose tank resonantcircuit, whose frequency resonant can be frequency changed incan the be presence changed of in a theload. presence Although of a extensive load. Although research extensive on such metamaterial-inspiredresearch on such metamaterial-inspired near-field sensors near- have fieldbeen sensors described have in literature,been described they do innot literature, offer the they advantages do not offer of far-field the advantages systems [ 19of– far-22]. Whilefield systems numerical [19–22]. studies While of LHMsnumerical as lenses studies in of the LHMs far field as lenses have been in the undertaken far field have [23 been–26], undertakenthe practical [23–26], feasibility the ofpractical their use feasibility has not of been their widely use has demonstrated. not been widely One demonstrated. study of far- Onefield study microwave of far-field imaging microwave is reported imaging by Shrieber is reported et al., by who Shrieber present et subwavelength al., who present defect sub- wavelengthdetection in defect fiberglass detection composites in fiberglass [27]. composites An LHM lens-based [27]. An LHM microwave lens-based hyperthermia microwave hyperthermiascheme for treatment scheme offor tumors treatment is proposed of tumors in is[ proposed28]. The metamaterial in [28]. The metamaterial lens concept lens has conceptbeen extended has been to extended ultrasonics to ultrasonics as well [29], as with well various [29], with studies various demonstrating studies demonstrating subwave- subwavelengthlength imaging imaging using acoustic using acoustic LHM lenses LHM being lenses reported being reported [30–32]. [30–32]. The authors The authors of the ofpresent the present paper recentlypaper recently reported reported a numerical a numerical study on study enhancement on enhancement of far-field of far-field microwave mi-