Negative Index Metamaterial Lens for Subwavelength Microwave Detection

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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 refractive 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- crowavetime-reversal time-reversal imaging resolutionimaging resolution using a homogenized using a homogenized model of model a metamaterial of a metamaterial lens [33]. lensPreliminary [33]. Preliminary studies on studies the physical on the physical design of design a metamaterial of a metamaterial lens were lens presented were presented by the authors in [34]. The present contribution focuses on detailed numerical and experimental

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characterization of the lens design and its feasibility for far-field subwavelength defect detection. Existing literature on using LHMs in the far field employs electromagnetic windowing techniques to realize subwavelength focusing or defect detection. In this paper, a homodyne receiver-based architecture is proposed to be used in conjunction with the metamaterial lens for far-field measurements. The high SNR associated with such synchronous detection allows the lens to be characterized in free space and, hence, provides a system that can be used in the field under practical conditions. The theory governing the working principles of metamaterials is briefly discussed in the Section2. The Section3 provides a numerical study and EM parameter retrieval of the lens design using the commercial software HFSS. The Section4 presents the experimental characterization of the metamaterial lens and its implementation for detection of subwavelength defects using the homodyne system.

2. Theory A periodic array of conducting elements can act as an effective medium for EM scattering when the wavelength is much longer than the element dimensions, i.e.,

a λ (1)

where a is the dimension of a unit cell of the periodic array, and λ is the operating wavelength in the effective medium. The EM response of an effective medium is determined by the configuration of the unit cell and can be characterized by an effective relative permeability µe f f and effective relative permittivity ee f f . Metamaterials with simultaneous negative µe f f and ee f f over a specific range of frequencies are termed as “double negative” metamaterials. One typical example of a unit cell comprises two distinct structures: an SRR element with dominant magnetic response and a thin wire element with dominant electric response. A periodic array of the SRR elements can exhibit an effective magnetic behavior, similar to that of magnetic plasmas, in the microwave regime [35]. Under excitation by an external magnetic field parallel to the axis of the SRRs, the array behaves as a bulk medium having an effective relative permeability given by

Fω2 µ (ω) = 1 − (2) e f f 2 2 ω − ω0 + jωΓ where F is the fractional volume of the unit cell occupied by the rings, Γ is the dissi- pation factor, ω0 is the resonant frequency of the SRRs, and ω is the frequency of the excitation field. Equation (2) shows that the real part of µe f f is negative for frequencies ω greater than√ resonant frequency ω0 and less than magnetic plasma frequency ωmp given by ωmp = ω0/ 1 − F. Propagating wave modes are prohibited in this frequency band due to negative µe f f of the SRR medium. A periodic array of the thin metallic wire elements, under the influence of a time- varying electric field, can mimic an electric plasma at microwave frequencies [36]. The effective relative permittivity of such an array in the presence of an external electric field parallel to the wires is given by

2 ωep e (ω) = 1 − (3) e f f ω2

where ωep is the electric plasma frequency, and ω is the frequency of the excitation ﬁeld. Equation (3) shows that the real part of ee f f has negative values for frequencies ω < ωep. This causes the wire medium to prohibit propagating modes in that frequency regime. Combining both the SRR and wire elements in a periodic array gives rise to a metamaterial medium having simultaneous negative µe f f and ee f f over a certain range of Sensors 2021, 21, 4782 4 of 16

frequencies. Assuming that there is no direct interaction between the SRR and wire media, the refractive index n of the resulting metamaterial is given through

2 n = µe f f (ω)ee f f (ω) (4)

The negative square root in the calculation of n is chosen in (4) when both µe f f (ω) and ee f f (ω) are negative to account for propagation of left-handed waves in a metamaterial [37]. A left-handed transmission band occurs within the previously overlapping forbidden bands of negative µe f f and negative ee f f . The combined array behaves as a medium having an effective negative refractive index in this transmission band, and the transmission peak is referred to as a left-handed peak. Such a negative index medium not only focuses propagating waves but also enhances the evanescent wave component of the angular spectrum of the incident ﬁeld, which contains high-resolution information. Subwavelength focusing beyond the diffraction limit is, thus, made possible by using a negative index metamaterial lens. As shown in Figure1a, for an ideal lossless LHM lens of thickness t and refractive index n = −1, a diverging beam from a point source at a distance d1 from the lens focuses ﬁrst inside the lens and, then, outside the lens at a distance d2 given by [12]

d2 = t − d1 (5)

Although the presence of losses associated with fabricated LHMs causes them to deviate from perfect focusing capabilities of an ideal metamaterial lens, subwavelength focusing is still achievable using a lossy negative index lens [38].

3. Simulation A metamaterial can be designed by simulating an infinite array of metamaterial unit cells using periodic boundary conditions. Figure2a shows an HFSS model of the proposed unit cell along with incident field polarization and direction of propagation. The Perfect E and Perfect H boundary conditions of HFSS were applied on the y-z and x-y boundaries, respectively, to mimic an infinite array of unit cells and ensure correct polarization of the incident wave. FR4 (er = 4.4, tan δ = 0.02) of thickness 1.6 mm was used as the substrate for the PCB. Copper of thickness 35 micron was used as the conducting material. Wave ports were assigned on the z-x boundary to excite the model with a plane wave and obtain the S-parameters of the metamaterial medium. Figure2b shows the dimensions of the unit cell. The dimensional parameters for the proposed design at 3.45 GHz are as follows: r = 1.5 mm, c = g = 0.2 mm, t = w = 0.9 mm, and a = 9.3 mm. The distance between consecutive PCB layers (length of unit cell model along z direction) is 6.5 mm. The dimensions were adapted from previous works by Aydin et al., where they demonstrated negative refraction and left handed focusing by a metamaterial lens in the 3–4 GHz regime [39]. Although the principal objective of designing a negative index LHM lens is high spatial resolution, which can be achieved by improving the losses in the design, the primary purpose of this work is to demonstrate the viability of using an LHM lens for subwavelength defect detection. Hence, optimization of the performance of the unit cell by parameterizing its dimensions was left for future work. Sensors 2021, 21, 4782 5 of 16 Sensors 2021, 21, x FOR PEER REVIEW 5 of 18

(a) (b)

FigureFigure 2. (a) 2. HFSS (a) HFSS unit unit cell cell model. model. (b ()b Schematic) Schematic of of thethe metamaterial unit unit cell cell showing showing both both sides sides of the of PCB. the PCB.

3.1.3.1. Scattering Scattering Parameters Parameters FigureFigure3 shows 3 shows the the simulated simulated S-parametersS-parameters for for three three cases—an cases—an SRR-only SRR-only medium, medium, a a wire-onlywire-only medium, medium, and and a a mediummedium that that combin combineses both both wires wires and and SRRs. SRRs. For the For SRR-only the SRR-only medium, a dip in the transmission parameter S21 is observed around the resonant fre- medium, a dip in the transmission parameter S is observed around the resonant frequency quency of 3.45 GHz of the SRR (Figure 3a). This21 is due to the prohibition of propagating of 3.45 GHz of the SRR (Figure3a). This is due to the prohibition of propagating waves waves by the negative of the medium. Figure 3b shows that the wire-only medium byallows the negative transmissionµe f f of (with the medium.less than 10 Figure dB of 3insertionb shows loss) that above the wire-only 5.5 GHz, which medium is the allows transmissionelectric plasma (with frequency less than 10. Propagating dB of insertion waves loss) below above this 5.5 frequency GHz, which are prohibited is the electric plasmadue to frequency the negativeωep . Propagating of the wire wavesmedium. below Figure this 3c frequencyshows that areafter prohibited combining dueboth to the negativethe SRRee and f f of wire, the wirea transmission medium. band Figure is observed3c shows around that after 3.45 combiningGHz. Left-handed both the waves SRR and

Sensorswire, 2021are, a21 allowed, transmission x FOR PEER to REVIEW propagate band isin observedthe frequency around region 3.45 where GHz. both Left-handed and waves are are simulta-6 allowedof 18 to

propagateneously innegative. the frequency region where both µe f f and ee f f are simultaneously negative.

(a) (b)

(c) Figure 3. HFSS S-parameter results for (a) SRR-only medium, (b) wire-only medium, and (c) SRR and wire combined Figure 3. HFSS S-parameter results for (a) SRR-only medium, (b) wire-only medium, and (c) SRR metamaterial medium. The respective HFSS models are shown in the insets of the figures. and wire combined metamaterial medium. The respective HFSS models are shown in the insets of 3.2. Electromagnetic Parameter Retrieval the ﬁgures. Extraction of the EM parameters from S-parameter data of the metamaterial design was done to verify left-handed nature of the transmission band. The procedure to determine the EM properties of the metamaterials is presented in Appendix A. The extracted material properties for the combined SRR and wire medium simulation results are shown in Figure 4. From the normalized impedance curve in Figure 4a, a resonance near the two plasma frequencies (3.45 GHz and 5.5 GHz) of the metamaterial medium is observed as expected. Figure 4b shows that the real part of the extracted refractive index is negative, thus verifying the left-handed transmission band in this frequency region. The value of real part of n at the resonant frequency of 3.45 GHz is −2.18. The real parts of the extracted and are also simultaneously negative in the frequency region, as expected (Figure 4c,d). It should be noted that above 5.5 GHz, both and are simultaneously positive, rendering the refractive index to be positive above this frequency.

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3.2. Electromagnetic Parameter Retrieval Extraction of the EM parameters from S-parameter data of the metamaterial design was done to verify left-handed nature of the transmission band. The procedure to determine the EM properties of the metamaterials is presented in AppendixA. The extracted material properties for the combined SRR and wire medium simulation results are shown in Figure4. From the normalized impedance curve in Figure4a, a resonance near the two plasma frequencies (3.45 GHz and 5.5 GHz) of the metamaterial medium is observed as expected. Figure4b shows that the real part of the extracted refractive index is negative, thus verifying the left-handed transmission band in this frequency region. The value of real part of n at the resonant frequency of 3.45 GHz is −2.18. The real parts of the extracted µe f f and ee f f are also simultaneously negative in Sensors 2021, 21, x FOR PEER REVIEWthe frequency region, as expected (Figure4c,d). It should be noted that above 5.5 GHz,7 of 18

both µe f f and ee f f are simultaneously positive, rendering the refractive index to be positive above this frequency.

5 8 Impedance (real) Refractive Index (real) 4 Impedance (imag) 6 Refractive Index (imag) 3 2 4 1 2 0 0 -1

-2 -2 -3 -4 -4 -5 -6 2 2.5 3 3.5 4 4.5 5 5.5 6 2 2.5 3 3.5 4 4.5 5 5.5 6 Frequency (GHz) Frequency(GHz) (a) (b)

-2 Relative Permittivity (real) Relative Permittivity (imag) -4

-6

-10

-12

-14 22.533.544.555.56 Frequency (GHz) (c) (d)

FigureFigure 4.4. Extracted simulatedsimulated EMEM parametersparameters of of the the metamaterial metamaterial design: design: (a ()a impedance,) impedance, (b ()b refractive) refractive index, index, (c )(c permeabil-) permeability, and (d) permittivity. ity, and (d) permittivity. 4. Experiment

A metamaterial lens, consisting of =20, =10 and =31 unit cells, was fabricated for experimental validation. Figure 5 presents the fabricated metamaterial lens. An amount of 20 × 10 unit cells in the x-y plane were printed in a single FR4 PCB of thickness 1.6 mm, and 31 such boards were stacked in the z direction at an interval of 6.5 mm. The magnetic and electric field vectors are polarized along the z and x axes, respectively, while the wave propagation vector is along the y axis. The thickness of the lens, t, in direction of propagation is 100 mm. Frequency sweep measurements were done to confirm the presence of left-handed transmission peak. A homodyne detection-based scheme was used to experimentally validate the negative refractive index and determine the subwavelength focal spot at the left-handed transmission peak frequency. NDE results for a set of dielectric test samples are presented in Section 4.2.3 to show the feasibility of using an LHM lens for the detection of subwavelength defects.

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4. Experiment

A metamaterial lens, consisting of Nx = 20, Ny = 10 and Nz = 31 unit cells, was fabricated for experimental validation. Figure5 presents the fabricated metamaterial lens. An amount of 20 × 10 unit cells in the x-y plane were printed in a single FR4 PCB of thickness 1.6 mm, and 31 such boards were stacked in the z direction at an interval of 6.5 mm. The magnetic and electric ﬁeld vectors are polarized along the z and x axes, respectively, while the wave propagation vector is along the y axis. The thickness of the lens, t, in direction of propagation is 100 mm. Frequency sweep measurements were done to conﬁrm the presence of left-handed transmission peak. A homodyne detection-based scheme was used to experimentally validate the negative refractive index and determine the subwavelength focal spot at the left-handed transmission peak frequency. NDE results Sensors 2021, 21, x FOR PEER REVIEWfor a set of dielectric test samples are presented in Section 4.2.3 to show the feasibility8 of of18

using an LHM lens for the detection of subwavelength defects.

Figure 5. Fabricated metamaterial lens.

4.1.4.1. Transmission Transmission Characteristics AA large metallic screen (~10 λλ)) with with an an aperture was used to obtain the transmission characteristicscharacteristics of of the the fabricated metamaterial lens. The The metallic screen was implemented byby attaching aluminum aluminum sheets sheets to to a a Styrofoam board. An An aperture aperture of of the the size of the lens was cut in the middle of of the the board board to to allow fo forr waves waves to to pass pass through through the the lens lens only only [40]. [40]. Wideband (675 MHz to 12 GHz) Vivaldi antennasantennas were used as transmitter and receiver toto illuminate illuminate the the lens lens with with a a uniform plane wave. The The antennas antennas were were placed 40 cm apart toto ensure ensure far-field far-ﬁeld measurements. The The frequency sweep measurements were done using anan Agilent Agilent EB070B EB070B vector vector network network analyzer analyzer (V (VNA).NA). Figure Figure 6a6 showsa shows the the schematic schematic of ex- of experimental set up. The measurements of S clearly indicate the presence of a left-handed perimental set up. The measurements of S2121 clearly indicate the presence of a left-handed transmissiontransmission band band with with a peak transmission of −1616 dB dB around around 3.5 3.5 GHz (Figure 66b).b). TheThe slightslight shift shift in in frequency frequency between between the the simulat simulateded and experimental experimental results can be attributed toto fabrication fabrication tolerances. tolerances. Above Above 5.5 5.5 GHz, GHz, the the metamaterial metamaterial acts acts as as a a conventional conventional medium medium having positive µe f f and ee f f . Conventional right handed waves are allowed to propagate having positive and . Conventional right handed waves are allowed to propa- in this frequency regime, and hence, the transmission band is observed. gate in this frequency regime, and hence, the transmission band is observed.

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(a) (a) (b) (b)

Figure 6. (a) FreeFigure spaceFigure 6. transmission( 6.a) ( Freea) Free space space experiment transmission transmission schematic. experiment experiment (b) Experimental schematic. schematic. (b )transmission ( Experimentalb) Experimental response transmission transmission of the responsemetamaterial response of theof the metamaterial metamaterial lens. The measurementslens.lens. The The were measurements measurements calibrated werewith were calibratedrespect calibrated to withtransmission with respect respect to in transmission tofree transmission space. in freein free space. space.

4.2. Left-Handed4.2. Characteristics4.2. Left-Handed Left-Handed Characteristics Characteristics After experimentallyAfterAfter experimentally confirming experimentally the conﬁrming left-han confirmingded the transmission the left-handed left-handed peak transmission transmission at 3.5 GHz, peak peaksingle at 3.5at 3.5 GHz, GHz, single single frequency measurementsfrequencyfrequency measurements using measurements a homodyne using using receiv a homodynea homodyneer architecture receiver receiv wereer architecture architecture used to facilitate were were used used to facilitateto facilitate fast characterizationfastfast characterization characterizationof the metamaterial of of the the lens metamaterial metamaterial at 3.5 GHz. lens Thelens at schematic 3.5at 3.5 GHz. GHz. The of The the schematic schematichomodyne of theof the homodyne homodyne architecture isarchitecture shownarchitecture in Figure is shown is shown7. The in Figure RFin Figuresignal7. The generator7. The RF signal RF signalproduces generator generator a continuous produces produces a continuoussinusoi- a continuous sinusoidal sinusoidal wave of frequencywavedal ofwave 3.5 frequency GHz.of frequency The 3.5 generated GHz. 3.5 GHz. The signal generatedThe generatedis passed signal throughsignal is passed is apassed splitter through through with a one splitter a splitter with with one one channel to the channeltransmittingchannel to theto theantenna transmitting transmitting and the antenna otheantennar channel and and the the otherto othethe channelLOr channel port toof thetothe the LOmixer. LO port port The of theof the mixer. mixer. The The RF port of the RFmixerRF port port is of connected of the the mixer mixer to is the connectedis connected receiver to antenna. theto the receiver re Theceiver DC antenna. antenna. signal The produced The DC DC signal signalat the produced produced at theat the IF of the mixerIF isIF of read of the the by mixer mixera digital is readis readmultimet by by a digital a erdigital (DMM) multimeter multimet and is (DMM)er proportional (DMM) and and is to proportionalis the proportional strength to theto the strength strength of the receivedof signal.of the the received Thereceived high signal. signal.SNR The associ The high atedhigh SNR withSNR associated suchassoci synchronousated with with such such detection synchronous synchronous allows detection detection allows allows the lens to be characterizedthethe lens lens to to be be characterizedin characterizedfree space without in in free free space the space need without without for the the windowingthe need need for for the usedthe windowing windowing in the used used in thein the frequency sweepfrequencyfrequency measurements. sweep sweep measurements. Moreover,measurements. using Moreover, Moreover, homodyne using using detection homodyne homodyne circumnavigates detection detection circumnavigates circumnavigates the use of expensivethethe use use RF of instrumentsof expensive expensive RF suchRF instruments instruments as a VNA. such such as as a VNA. a VNA.

FigureFigure 7. 7. SchematicSchematicFigure of of homodyne homodyne 7. Schematic archit architecture-based ofecture-based homodyne archit setup setupecture-based for for sing singlele frequency frequency setup for measurements. measurements.single frequency measurements.

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4.2.1.4.2.1. Negative Negative Refraction Refraction AnAn imaging experiment was was carried out to demonstrate negative refraction by the metamaterialmetamaterial lens lens and and calculate its effective refractive index [33]. [33]. A A standard gain horn antennaantenna at 3.53.5 GHzGHz waswas used used as as the the transmitter, transmitter, while while a quarter a quarter wavelength wavelength monopole monopole was wasused used as the as receivingthe receiving probe. probe. Outgoing Outgoing spherical spherical waves waves from from the the horn horn are are incident incident at anat angle θi at the ﬁrst air-LHM interface. After undergoing negative refraction through the an angle at the first air-LHM interface. After undergoing negative refraction through LHM of thickness t, the waves are shifted towards the side of the transmitter by a distance the LHM of thickness t, the waves are shifted towards the side of the transmitter by a d at the second LHM–air interface. The angle of refraction can be determined by scanning distance d at the second LHM–air interface. The angle of refraction can be determined by the received signal amplitude can be calculated as θ = tan−1(d/t). The top view of the scanning the received signal amplitude can be calculatedr as =tan(⁄ ). The top experimental setup is shown schematically in Figure8. view of the experimental setup is shown schematically in Figure 8.

Figure 8. Negative refraction experiment schematic top view. Figure 8. Negative refraction experiment schematic top view.

TheThe receiving receiving probe probe was was mounted on on a a 2D scanner, moved in the y-z plane, and the receivedreceived amplitude amplitude distribution distribution was was measured. measured. A Astep step size size of 5 of mm 5 mm was was used used in both in both the zthe andz yand directions.y directions. The transmitting The transmitting horn was horn placed was at placed a distance at adistance of 12 cm of(1.4 12λ) cmfrom (1.4 theλ) ◦ firstfrom air–LHM the ﬁrst air–LHMinterface with interface an angle with of an incidence angle of incidence = 10°. Theθi = normalized 10 . The normalized measured amplitudemeasured distribution amplitude distribution is shown in isFigure shown 9a. in The Figure outgoing9a. The wave outgoing from the wave metamaterial from the lensmetamaterial has a beam lens profile has centered a beam proﬁletowards centered the transmitting towards antenna. the transmitting The angle antenna. of refraction, The angle, through of refraction, the fabricatedθr, through lens of the thickness fabricated t = lens 100 ofmm thickness and beamt = shift 100 mmd = 15 and mm beam is calcu- shift latedd = 15 to mm be is8.53 calculated°. The real to bepart 8.53 of◦ effective. The real refrac parttive of effective index is refractive thereby computed index is thereby using Snell’scomputed law usingand is Snell’s equal to law −1.17 and at is 3.5 equal GHz. to −1.17 at 3.5 GHz.

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(a)

(b)

FigureFigure 9. ( 9.a)( aNormalized) Normalized received received signal signal amplitude amplitude scan. scan. The The outgoing outgoing wave wave from from the the LHM LHM has has a a beambeam profile proﬁle centered centered at at85 85mm. mm. (b) ( bNormalized) Normalized line line scan scan of ofthe the received received signal signal amplitude amplitude at y at =y 0.= 0. TheThe beam beam shift shift d isd measuredis measured to tobe beequal equal to to15 15mm. mm.

4.2.2.4.2.2. Subwavelength Subwavelength Focusing Focusing TheThe presence presence of ofnegative negative refraction refraction allows allows the the possibility possibility of of using using the the fabricated fabricated met- meta- amaterialmaterial structure structure as as a alens lens for for subwavelen subwavelengthgth focusing. focusing. A Amonopole monopole antenna antenna produces produces anan azimuthally azimuthally symmetric symmetric field ﬁeld pattern, pattern, as asdoes does an an ideal ideal isotropic isotropic radiator. radiator. Therefore, Therefore, a a monopolemonopole with with a aresonant resonant frequency frequency of of 3.5 GHz waswas usedused as as the the transmitter transmitter to to demonstrate demon- stratesubwavelength subwavelength focusing. focusing. Due Due to theto the negative negative refractive refractive index index of theof the metamaterial metamaterial lens, lens,diverging diverging beams beams from from the the monopole monopole antenna, antenna, placed placed at at an an appropriate appropriate distance, distance, will will be bebrought brought toto focusfocus outside the lens lens according according to to (5). (5). Figure Figure 10 10 presents presents the the schematic schematic top top viewview of ofthe the experimental experimental setup. setup. A Aquarter quarter wavelength wavelength monopole monopole was was used used as asthe the probe probe for for measuring measuring the the received received signal.signal. The The receiving receiving probe probe was was mounte mountedd on ona 2D a 2D scanner scanner and and moved moved on on the the y-zy-z planeplane andand the the received received amplitude amplitude distribution distribution was was me measured.asured. A Astep step size size of of5 mm 5 mm was was used used in in z y d bothboth the the z andand y directions.directions. The The transmitting transmitting mo monopolenopole was was placed placed at at60 60 mm mm (d1 () 1from) from the the air–LHMair–LHM interface. interface. Figure Figure 11a 11 showsa shows normalized normalized received received signal signal amplitude. amplitude. A Afocal focal point point is observed at a distance 30 mm (d ) from the second LHM–air interface. The measured is observed at a distance 30 mm (d2) 2from the second LHM–air interface. The measured focalfocal spot spot distance distance satisfies satisﬁes the the relation relation in in (5) (5) for for the the fabricated fabricated lens ofof thicknessthickness 100100 mmmm ( t).

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Sensors 2021, 21, x FOR PEER REVIEW 12 of 18

Figure 11b shows the normalized line scan at the focal plane (y = 30 mm). The full width at half(t). Figure maxima 11b shows (FWHM) the normalized for the focal line scan spot at is the found focal plane to be ( 70y = mm30 mm). (0.82 Theλ). full width at half maxima (FWHM) for the focal spot is found to be 70 mm (0.82λ).

Figure 10. Subwavelength focusing experiment schematic top view. Sensors 2021, 21, x FOR PEER REVIEW 13 of 18 Figure 10. Subwavelength focusing experiment schematic top view.

(a)

(b)

Figure 11. (a) Normalized received signal amplitude. A focal spot is observed at a distance of d2 = 30 Figuremm from the 11. lens.(a ()b) Normalized Normalized line scan received at y = 30 mm. signal The dashed amplitude. lines indicate A − focal3 dB point. spot is observed at a distance of d = 30 mm from the lens. (b) Normalized line scan at y = 30 mm. The dashed lines indicate 4.2.3.2 Microwave NDE −Next,3 dB the point. capability of the LHM lens for detection of subwavelength defects with far- field microwave NDE data is demonstrated. The experimental setup is shown in Figure 12, and the schematic top view is shown in Figure 13a. Figure 13b shows the schematic of the sample under test. Teflon samples are used as the dielectrics for testing. A groove of size 15mm (0.17λ) × 5 mm (0.06λ) is machined along the length of the sample. A similar Teflon sample with no machined groove is treated as the healthy sample. The samples are placed at the focal spot of the lens, and line scans are performed to obtain the scattered data. The contribution due to the defect is measured by the changes in the test signal relative to the baseline signal (found by measuring the healthy sample). The calibration and detection procedure is shown in Figure 14. The position of the defect can be determined by the minima in the line scans [26]. Three sets of measurements were taken at three positions of the sample. The distance p between consecutive defect positions was set to be 20 mm (0.23λ).

Sensors 2021, 21, 4782 12 of 16

4.2.3. Microwave NDE Next, the capability of the LHM lens for detection of subwavelength defects with far- field microwave NDE data is demonstrated. The experimental setup is shown in Figure 12, and the schematic top view is shown in Figure 13a. Figure 13b shows the schematic of the sample under test. Teflon samples are used as the dielectrics for testing. A groove of size 15 mm (0.17λ) × 5 mm (0.06λ) is machined along the length of the sample. A similar Teflon sample with no machined groove is treated as the healthy sample. The samples are placed at the focal spot of the lens, and line scans are performed to obtain the scattered data. The contribution due to the defect is measured by the changes in the test signal relative to the baseline signal (found by measuring the healthy sample). The calibration and detection procedure is shown in Figure 14. The position of the defect can be determined by the minima in the line scans [26]. Three sets of measurements were taken at three positions Sensors 2021, 21, x FOR PEER REVIEWof the sample. The distance p between consecutive defect positions was set to be 2014 mmof 18 (0.23λ).

Figure 12. Proposed microwave NDE sensor. The sample is kept at the focal point of the LHM lens to allow for subwave- Figure 12. Proposed microwave NDE sensor. The sample is kept at the focal point of the LHM lens to allow for subwavelength defect detection. length defect detection.

(a) (b) Figure 13. (a) NDE experiment schematic top view. (b) Sample under test schematic. All dimensions are given in mm.

Sensors 2021, 21, x FOR PEER REVIEW 14 of 18

Sensors 2021, 21, 4782 13 of 16 Figure 12. Proposed microwave NDE sensor. The sample is kept at the focal point of the LHM lens to allow for subwavelength defect detection.

(a) (b)

SensorsSensors 20212021Figure,, 2121,, x13.x FORFOR (a) PEER PEERNDE REVIEW REVIEWexperiment schematic top view. (b) Sample under test schematic. All dimensions are given in mm.1515 ofof 1818 Figure 13. (a) NDE experiment schematic top view. (b) Sample under test schematic. All dimensions are given in mm.

Figure 14. Calibration and defect detection flowchart. FigureFigure 14. 14.Calibration Calibration andand defect detection detection flowchart. flowchart. Figure 15a shows the defect signal for the three measurements. The received line FigureFigure 15 15aa shows shows thethe defectdefect signal signal for for th thee three three measurements. measurements. The received The received line line scans were fitted with smooth curves to obtain the minima. The minima in the three line scansscans were were fitted fitted with with smoothsmooth curves to to obtain obtain the the minima. minima. The The minima minima in the in three the threeline line scansscans areare shiftedshifted withwith repositioningrepositioning ofof thethe defecdefectt location,location, thusthus indicatingindicating thethe positionposition ofof scansthe aresubwavelength shifted with defect. repositioning This demonstrates of the defectthe proposed location, system thus is indicatingsensitive to thea 0.17 positionλ ofthe subwavelength subwavelength defect. defect. This Thisdemonstrates demonstrates the proposed the proposed system issystem sensitive is to sensitive a 0.17λ to a ×× 0.060.06λλ defectdefect andand cancan determinedetermine consecutiveconsecutive defectdefect positionspositions withwith aa separationseparation ofof 0.230.23λλ.. 0.17λ × 0.06λ defect and can determine consecutive defect positions with a separation of TheThe NDENDE measurementsmeasurements werewere repeatedrepeated withoutwithout thethe LHMLHM lenslens toto illuillustratestrate thatthat thethe sub-sub- λ 0.23wavelengthwavelength. The NDE defectsdefects measurements areare notnot detectabledetectable were repeated withouwithoutt thethe without lens.lens. FigureFigure the LHM 15b15b lensshowsshows to thethe illustrate resultingresulting that the subwavelengthreceivedreceived lineline scanscan defects signalssignals are without notwithout detectable thethe lens.lens. without SinceSince waveswaves the lens. fromfrom Figure thethe monopolemonopole 15b shows transmittertransmitter the resulting receivedareare notnot line focused,focused, scan thethe signals receivedreceived without signalsignal the strengthsstrengths lens. Since areare dominateddominated waves from byby edgeedge the monopoleeffectseffects andand scattering transmitterscattering are notfromfrom focused, thethe background.background. the received Therefore,Therefore, signal strengths nono minima,minima, are asas dominated inin thethe casecase by ofof thethe edge LHMLHM effects lens,lens, and areare scatteringobserved.observed. from theHence,Hence, background. thesethese initialinitial Therefore, resultsresults clcl noearlyearly minima, demonstratedemonstrate as in the thatthat case subwavsubwav of theelengthelength LHM defects,defects, lens, are whichwhich observed. areare un-un- Hence, thesedetectabledetectable initial results inin freefree clearlyspacespace inin demonstrate thethe farfar field,field, that cacann subwavelengthbebe detecteddetected usingusing defects, aa properlyproperly which designeddesigned are undetectable met-met- in freeamaterialamaterial space lens.lens. in the far field, can be detected using a properly designed metamaterial lens.

10-4 4 10-4 4 position 1 position 1 position 2 3 position 2 3 position 3 position 3 2 2

1 1

0 0

-1 -1 Received Signal (V) Signal Received Received Signal (V) Signal Received -2 -2

-3 -3

-4 -4 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 mm mm ((aa)) ((bb)) Figure 15. NDE line scan results. (a) Measurements using the LHM lens. The minimum of the plot gives the defect position. FigureFigure 15. NDE 15. NDE line line scan scan results. results. (a) (a Measurements) Measurements using using the LHM LHM lens. lens. The The minimu minimumm of the of plot the plotgives gives the defect the defect position. position. ((bb)) MeasurementsMeasurements withoutwithout thethe LHMLHM lens.lens. WavesWaves areare notnot focusedfocused inin freefree space.space. SubwavelengthSubwavelength defectsdefects positionposition cannotcannot bebe (b) Measurements without the LHM lens. Waves are not focused in free space. Subwavelength defects position cannot determined.determined. be determined. 5.5. DiscussionDiscussion ThisThis paperpaper presentspresents thethe designdesign ofof aa metamaterialmetamaterial lenslens andand itsits applicationapplication asas aa far-fieldfar-field microwavemicrowave sensor.sensor. NumericalNumerical studiesstudies ofof thethe memetamaterialtamaterial unitunit cellcell designdesign areare presented.presented. AA fabricatedfabricated metamaterialmetamaterial lenslens waswas usedused forfor experimentalexperimental verificationverification ofof thethe left-handedleft-handed propagationpropagation characteristicscharacteristics ofof thethe lens.lens. AA homodynehomodyne detectiondetection setupsetup waswas usedused withwith thethe LHMLHM lenslens forfor NDENDE ofof subwavelengthsubwavelength defects.defects. InitialInitial resultsresults demonstratedemonstrate thatthat aa negativenegative refractiverefractive indexindex metamaterialmetamaterial lenslens cancan achieveachieve resolutionresolution beyondbeyond thethe diffractiondiffraction limitlimit forfor far-fieldfar-field microwavemicrowave NDE.NDE. TheThe subwavelengthsubwavelength resoresolutionlution capabilitycapability ofof aa metamaterialmetamaterial lenslens isis limitedlimited byby thethe inherentinherent losseslosses associatedassociated wiwithth aa fabricatedfabricated LHM.LHM. Therefore,Therefore, futurefuture workwork

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5. Discussion This paper presents the design of a metamaterial lens and its application as a far-field microwave sensor. Numerical studies of the metamaterial unit cell design are presented. A fabricated metamaterial lens was used for experimental verification of the left-handed propagation characteristics of the lens. A homodyne detection setup was used with the LHM lens for NDE of subwavelength defects. Initial results demonstrate that a negative refractive index metamaterial lens can achieve resolution beyond the diffraction limit for far-field microwave NDE. The subwavelength resolution capability of a metamaterial lens is limited by the inherent losses associated with a fabricated LHM. Therefore, future work will involve the design of low loss LHMs to mitigate this issue. Moreover, work is in progress to design active metamaterials that can provide tunability that is lacking in passive metamaterial lens designs such as the one reported in this study. Finally, more extensive testing of experimental imaging of subwavelength defects is also underway to demonstrate the full potential of LHMs.

Author Contributions: Conceptualization, S.M. and L.U.; design, S.D.; fabrication, X.S. and S.D.; experiment, S.D., X.S., and E.R.; resources, Y.D., L.U., and M.H.; writing—original draft prepara- tion, S.D.; writing—review and editing, E.R. and L.U.; supervision, L.U., E.R., and Y.D.; funding acquisition, M.H., S.M., Y.D., and L.U. All authors have read and agreed to the published version of the manuscript. Funding: This work was sponsored by the National Science Foundation under the Manufacturing USA Award number 1762331. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to thank Deepak Kumar of Michigan State University for his valuable contributions with the homodyne receiver system. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A Estimation of permittivity and permeability of an engineered material from its S- parameters is a well-established method, ﬁrst proposed in the original work of Nicolson and Ross [41] and Weir [42]. Using this approach, an inhomogeneous metamaterial structure, assumed to be a homogenous medium under the effective medium theory, can be characterized by a refractive index n and normalized impedance z [43,44]. The normalized impedance z of a metamaterial unit cell is related to its S parameters by the equation v u 2 2 u (1 + S11) − S z = ±t 21 (A1) 2 2 (1 + S11) + S21 Since the metamaterial is a passive device, the reﬂected power cannot exceed the incident power. Therefore, the real part of z is positive, which in turn resolves the sign ambiguity in (A1). The refractive index of a metamaterial unit cell of dimension d is related to the S- parameters by the following equation

S jnk0d = 21 e z−1 (A2) 1 − S11 z+1

The value of refractive index n can be evaluated from (A2) as

1 hn o n oi n = Re ln ejnk0d + 2mπ − j Im ln ejnk0d (A3) k0d Sensors 2021, 21, 4782 15 of 16

where Re(.) and Im(.) are the real and imaginary operators, respectively, k0 is the free space wavenumber, and m is an integer. The ambiguity in the branch selection of the multi-valued complex logarithmic function in (A3) can be resolved by choosing correct integer value m, which is dependent on the electrical length of the unit cell. Due to the small electrical length of the proposed unit cell design (9.3 mm) compared to the homogenized wavelength (38 mm), the fundamental branch (m = 0) is chosen for calculation of material parameters from the simulation model [45]. The effective permittivity and permeability of the metamaterial are computed from z and n using the following relations

µe f f = nz; ee f f = n/z (A4)

References 1. Veselago, V.G. The electrodynamics of substances with simultaneously negative values of \epsilon and µ. Sov. Phys. Uspekhi 1968, 10, 509–514. [CrossRef] 2. Smith, D.R.; Padilla, W.; Vier, D.C.; Nemat-Nasser, S.C.; Schultz, S. Composite Medium with Simultaneously Negative Permeabil- ity and Permittivity. Phys. Rev. Lett. 2000, 84, 4184–4187. [CrossRef] 3. Shelby, R.A.; Smith, D.R.; Schultz, S. Experimental Verification of a Negative Index of Refraction. Science 2001, 292, 77–79. [CrossRef][PubMed] 4. Parazzoli, C.G.; Greegor, R.B.; Li, K.; Koltenbah, B.E.C.; Tanielian, M. Experimental Verification and Simulation of Negative Index of Refraction Using Snell’s Law. Phys. Rev. Lett. 2003, 90, 107401. [CrossRef] 5. Aydin, K.; Guven, K.; Soukoulis, C.M.; Ozbay, E. Observation of negative refraction and negative phase velocity in left-handed metamaterials. Appl. Phys. Lett. 2005, 86, 124102. [CrossRef] 6. Valanju, P.M.; Walser, R.M.; Valanju, A.P. Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous. Phys. Rev. Lett. 2002, 88, 187401. [CrossRef] 7. Munk, B.A. Metamaterials: Critique and Alternatives; Wiley: Hoboken, NJ, USA, 2009. 8. Houck, A.A.; Brock, J.B.; Chuang, I.L. Experimental Observations of a Left-Handed Material That Obeys Snell’s Law. Phys. Rev. Lett. 2003, 90, 137401. [CrossRef] 9. Ziolkowski, R. Design, fabrication, and testing of double negative metamaterials. IEEE Trans. Antennas Propag. 2003, 51, 1516–1529. [CrossRef] 10. Aydin, K.; Guven, K.; Kafesaki, M.; Zhang, L.; Soukoulis, C.M.; Ozbay, E. Experimental observation of true left-handed transmission peaks in metamaterials. Opt. Lett. 2004, 29, 2623–2625. [CrossRef] 11. Alù, A. First-principles homogenization theory for periodic metamaterials. Phys. Rev. B Condens. Matter Mater. Phys. 2011, 84, 075153. [CrossRef] 12. Pendry, J. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 2000, 85, 3966–3969. [CrossRef] 13. Grbic, A.; Eleftheriades, G.V. Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens. Phys. Rev. Lett. 2004, 92, 117403. [CrossRef][PubMed] 14. Aydin, K.; Bulu, I.; Ozbay, E. Subwavelength resolution with a negative-index metamaterial superlens. Appl. Phys. Lett. 2007, 90, 254102. [CrossRef] 15. Ozbay, E.; Li, Z.; Aydin, K. Super-resolution imaging by one-dimensional, microwave left-handed metamaterials with an effective negative index. J. Phys. Condens. Matter 2008, 20, 304216. [CrossRef] 16. Roy, T.; Rogers, E.; Zheludev, N. Sub-wavelength focusing meta-lens. Opt. Express 2013, 21, 7577–7582. [CrossRef] 17. Haxha, S.; Abdelmalek, F.; Ouerghi, F.; Charlton, M.D.B.; Aggoun, A.; Fang, X. Metamaterial Superlenses Operating at Visible Wavelength for Imaging Applications. Sci. Rep. 2018, 8, 16119. [CrossRef] 18. Mukherjee, S.; Tamburrino, A.; Haq, M.; Udpa, S.; Udpa, L. Far field microwave NDE of composite structures using time reversal mirror. NDT E Int. 2018, 93, 7–17. [CrossRef] 19. Savin, A.; Bruma, A.; Steigmann, R.; Iftimie, N.; Faktorova, D. Enhancement of Spatial Resolution Using a Metamaterial Sensor in Nondestructive Evaluation. Appl. Sci. 2015, 5, 1412–1430. [CrossRef] 20. Mukherjee, S.; Shi, X.; Udpa, L.; Udpa, S.; Deng, Y.; Chahal, P.; Shi, X. Design of a Split-Ring Resonator Sensor for Near-Field Microwave Imaging. IEEE Sens. J. 2018, 18, 7066–7076. [CrossRef] 21. Zhang, Y.; Zhao, J.; Cao, J.; Mao, B. Microwave Metamaterial Absorber for Non-Destructive Sensing Applications of Grain. Sensors 2018, 18, 1912. [CrossRef] 22. O’Hara, J.F.; Singh, R.; Brener, I.; Smirnova, E.; Han, J.; Taylor, A.J.; Zhang, W. Thin-film sensing with planar terahertz metamaterials: Sensitivity and limitations. Opt. Express 2008, 16, 1786–1795. [CrossRef] 23. Leggio, L.; Dadrasnia, E.; de Varona, O. Microwave Focusing within Arbitrary Refractive Index Media Using Left-Handed Metamaterial Lenses. Prog. Electromagn. Res. M 2016, 45, 51–58. [CrossRef] Sensors 2021, 21, 4782 16 of 16

24. Chen, J.J.; Grzegorczyk, T.M.; Wu, B.-I.; Kong, J.A. Limitation of FDTD in simulation of a perfect lens imaging system. Opt. Express 2005, 13, 10840–10845. [CrossRef] 25. Lu, J.; Grzegorczyk, T.M.; Wu, B.-I.; Pacheco, J.; Chen, M.; Kong, J.A. Effect of poles on subwavelength focusing by an LHM slab. Microw. Opt. Technol. Lett. 2005, 45, 49–53. [CrossRef] 26. Tassin, P.; Veretennicoff, I.; Van Der Sande, G. Veselago’s lens consisting of left-handed materials with arbitrary index of refraction. Opt. Commun. 2006, 264, 130–134. [CrossRef] 27. Shreiber, D.; Gupta, M.; Cravey, R. Microwave nondestructive evaluation of dielectric materials with a metamaterial lens. Sens. Actuators A Phys. 2008, 144, 48–55. [CrossRef] 28. Tao, Y.; Yang, E.; Wang, G. Left-handed metamaterial lens applicator with built-in cooling feature for superficial tumor hyperthermia. Appl. Comput. Electromagn. Soc. J. 2017, 32, 1029–1034. 29. Zhang, S.; Yin, L.; Fang, N. Focusing Ultrasound with an Acoustic Metamaterial Network. Phys. Rev. Lett. 2009, 102, 194301. [CrossRef] 30. Amireddy, K.K.; Rajagopal, P.; Balasubramaniam, K.; Nadu, T. Holey-structured metalens for deep sub-wavelength resolution of delamination in layered materials using ultrasound. In Proceedings of the 15th Asia Pacific Conference for Non-Destructive Testing (APCNDT2017), Singapore, 13–17 November 2017; pp. 1–5. 31. Walker, E.L.; Jin, Y.; Reyes, D.; Neogi, A. Sub-wavelength lateral detection of tissue-approximating masses using an ultrasonic metamaterial lens. Nat. Commun. 2020, 11, 5967. [CrossRef] 32. Zaman, A.-U.-Z.; Song, K.; Lee, D.-G.; Hur, S. A novel approach to Fabry–Pérot-resonance-based lens and demonstrating deep-subwavelength imaging. Sci. Rep. 2020, 10, 10769. [CrossRef] 33. Mukherjee, S.; Su, Z.; Udpa, L.; Udpa, S.; Tamburrino, A. Enhancement of Microwave Imaging Using a Metamaterial Lens. IEEE Sens. J. 2019, 19, 4962–4971. [CrossRef] 34. Datta, S.; Shi, X.; Mukherjee, S.; Deng, Y.; Udpa, L. Model-Based Study of a Metamaterial Lens for Nondestructive Evaluation of Composites. J. Nondestruct. Eval. Diagn. Progn. Eng. Syst. 2020, 3, 041001. [CrossRef] 35. Pendry, J.; Holden, A.; Robbins, D.; Stewart, W. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 1999, 47, 2075–2084. [CrossRef] 36. Pendry, J.B.; Holden, A.J.; Stewart, W.J.; Youngs, I. Extremely Low Frequency Plasmons in Metallic Mesostructures. Phys. Rev. Lett. 1996, 76, 4773–4776. [CrossRef] 37. Smith, D.R.; Kroll, N. Negative Refractive Index in Left-Handed Materials. Phys. Rev. Lett. 2000, 85, 2933–2936. [CrossRef] 38. Smith, D.R.; Schurig, D.; Rosenbluth, M.; Schultz, S.; Ramakrishna, S.A.; Pendry, J.B. Limitations on subdiffraction imaging with a negative refractive index slab. Appl. Phys. Lett. 2003, 82, 1506–1508. [CrossRef] 39. Aydin, K.; Bulu, I.; Ozbay, E. Focusing of electromagnetic waves by a left-handed metamaterial flat lens. Opt. Express 2005, 13, 8753–8759. [CrossRef][PubMed] 40. Wilson, P.; Ma, M.; Adams, J. Techniques for measuring the electromagnetic shielding effectiveness of materials. I. Far-field source simulation. IEEE Trans. Electromagn. Compat. 1988, 30, 239–250. [CrossRef] 41. Nicolson, A.M.; Ross, G.F. Measurement of the Intrinsic Properties of Materials by Time-Domain Techniques. IEEE Trans. Instrum. Meas. 1970, 19, 377–382. [CrossRef] 42. Weir, W. Automatic measurement of complex dielectric constant and permeability at microwave frequencies. Proc. IEEE 1974, 62, 33–36. [CrossRef] 43. Chen, X.; Grzegorczyk, T.M.; Wu, B.-I.; Pacheco, J.J.; Kong, J.A. Robust method to retrieve the constitutive effective parameters of metamaterials. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 2004, 70, 016608. [CrossRef] 44. Arslanagic, S.; Hansen, T.V.; Mortensen, N.A.; Gregersen, A.H.; Sigmund, O.; Ziolkowski, R.; Breinbjerg, O. A Review of the Scattering-Parameter Extraction Method with Clarification of Ambiguity Issues in Relation to Metamaterial Homogenization. IEEE Antennas Propag. Mag. 2013, 55, 91–106. [CrossRef] 45. Rothwell, E.J.; Frasch, J.L.; Ellison, S.M.; Chahal, P.; Ouedraogo, R.O. Analysis of the Nicolson-Ross-Weir Method for Characteriz- ing the Electromagnetic Properties of Engineered Materials. Prog. Electromagn. Res. 2016, 157, 31–47. [CrossRef]