Special Issue on Metamaterials LHM

Microwave focusing and beam collimation usingnegative index of refraction lenses

R.B. Greegor, C.G. Parazzoli, J.A. Nielsen, M.A. Thompson, M.H. Tanielian, D.C. Vier,S. Schultz, D.R. Smith and D. Schurig

Abstract: Negative index of refraction materials (NIMs) were first postulated by Veselago in 1968and have recently been realised using structures formed with rings and wires deposited on printedcircuit boards. The proof of the existence of negative index of refraction was established using aSnell’s law experiment with a wedge. The predicted and measured refraction angles were foundto be consistent for a negative index material and in excellent agreement with the theoretical expec-tations. For microwave lenses NIMs have the advantage of being lighter, having better focusingproperties and potentially lower aberrations. Simulation and experimental results on NIM configur-ations including gradient index of refraction and spherical 3D lenses are presented. Both focusingand beam collimating applications will be considered. These results will be compared to normalpositive index of refraction material lenses.

1 Introduction

In 1968, Veselago [1] discussed the likelihood of a negativeindex of refraction material NIM. Recently, these NIMswere realised in practice by the appropriate combinationof conductive elements deposited on a dielectric substrate[2]. In the microwave regime, NIMs are fabricated frommetallic wires and rings assembled in a periodic cell struc-ture. The rings are generally referred to as split ring resona-tors. NIMs have the property that the effective permittivity1eff and permeability meff are both negative resulting in aneffective negative index of refraction, n ¼

pm

p1. Initially

there was some controversy regarding the existence ofNIMs, but more recently the effect has been conclusivelydemonstrated [2, 3] using a Snell’s law experiment.Lenses built with NIMs reduced aberrations comparedwith an equivalent one made of a positive index of refrac-tion material (PIM) [4]. Plano-concave NIM lenses havebeen built using NIM and photonic crystals with constantindex of refraction, namely a cylindrical geometry lens at14.7 GHz [5] and a similar lens at 9.265–9.490 GHz [6].It was shown that an NIM lens in the RF regime can beeasily manufactured with a gradient index of refraction(GRIN) [7] in the absence of any physical curved surfaces.Subsequently, a GRIN lens in cylindrical geometry has beenbuilt and tested [8, 9].

In this paper, we will discuss the performance of spheri-cal NIM lenses with physical curvature and flat GRINlenses. We will compare their performance to an equivalent

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-map:20060071

Paper first received 6th April and in revised form 19th July 2006

R.B. Greegor, C.G. Parazzoli, J.A. Nielsen, M.A. Thompson and M.H.Tanielian are with Boeing Company, Seattle, WA 98124, USA

D.C Vier and S. Schultz are with the Department of Physics, University ofCalifornia, San Diego, La Jolla, CA 92093, USA

D.R. Smith and D. Schurig are with the Department of ECE, Duke University,Durham, NC 27708, USA

E-mail: robert.b.greegor@boeing.com

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PIM lens. Specifically we will address four major areas: (a)characterisation of the free space test setup used for ourspherical lenses, (b) a plano–convex PIM lens, (c) aplano–concave NIM lens and (d) a plano–plano GRINlens using an NIM medium. The PIM lens was modelled,designed and fabricated to observe the performance differ-ences between lenses made of normal materials andNIMs. Also, we were interested in comparable GRINlenses since they are easy to fabricate, are of uniformthickness and lighter than either the PIM or NIM lensessince they are effectively thinner. All of the lenses weredesigned to operate having the same nominal focal length(�12.7 cm) and aperture (�12.7 cm), giving an F numberapproximately equal to 1.0. Since the dispersion curvesare steep in the negative index region, the lenses onlyhave the desired focal length at the designed frequencyof �14.8 GHz. The bandwidth of the negative indexregion was �10%. The individual unit cells were designedby modelling the details of the rings, wires andsubstrates. However, for simulations of the entire NIMand GRIN lenses, an effective medium approximation wasused, that is, the individual rings and wires were notmodelled.

2 Characterisation of the empty aperturetest setup

The experimental setup for the lens measurements incorpor-ated a network analyser that was controlled by a computerrunning Labview. The setup utilises a source antenna illu-minating a 6.20-cm radius aperture made of aluminiumthat is shielded by eccosorb to reduce reflections.Microwave studio (MWS) simulations of this setup weremade for two cases: (a) the aperture illuminated by aplane wave and (b) the aperture illuminated by a smalldipole on the optical axis approximating a point source.Line plot comparisons for the plane wave case of theMWS simulation and an analytical calculation were made.The analytical expression for the time averaged planewave diffracted power per unit solid angle by a circular

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aperture is proportional to

dP

dV/

2J1ðka sin uÞ

ka sin u

����

����

2

ð1:1Þ

where J1 is a Bessel function of first order, k the wavevector, a the aperture radius and u the angle with respectto the propagation direction. We found that the far fieldcomparison between the FDTD and analytical methodswas in good agreement. We estimate the far fieldapproximation to be valid at approximately Zff ¼ 2D2/l ¼2(2 � 6.19 cm)2/(3e10 cm s21/15e9 s21) ¼ 153 cm, whereD is the diameter of the aperture.

The electric near field downstream from the aperture wasmeasured. The comparisons of the MWS FDTD simulationto the experimental results are shown in Fig. 1. These exper-imental results are in excellent agreement with the simu-lations and indicate that we are able to adequately modelthe setup used to test our lenses. We also measuredsurface plots in the far field at 2.0 m from the empty aper-ture illuminated by a small dipole source placed at theapproximate focal spot of the lenses to be tested. Thesemeasurements were made to determine the gain of thelenses in the far field as compared to the empty aperture.

3 Design and characterisation of PIM lens

A PIM lens was fabricated to compare the NIM and GRINlenses to be discussed later. This lens was made of Rexolitehaving 1 ¼ 2.53 (n ¼ 1.59). The designed focal length ofthe lens was 12.7 cm. This lens along with a simple raytracing analysis is shown in Fig. 2. Note that for the full aper-ture not all of the rays intersect at the same point due to aber-ration effects that cause the focal spot to be elongated.

A comparison of the experimental and simulated electricnear field focusing characteristics for the PIM lens is shownin Fig. 3. The line plots in this figure show excellentagreement between the experiment and simulation. The

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oscillations along the z propagation direction for the exper-imental data are due to interference between the receivingantenna and the mounting fixture. Also, the experimentalprofile is broader than the simulated profile due to thefinite dimensions of the receiving antenna.

We also measured the far field pattern/gain with respect tothe empty aperture. We define gain with respect to the emptyaperture as G(dB) ¼ 10 log (EPIM

2 /EAPT2 ). The gain for the

PIM lens is approximately 10 dB above the empty aperture.

4 Design and characterisation of NIM lens

We have fabricated an NIM lens with a designed focallength of 12.2 cm and a 24.4 cm radius of curvature. Thisdesign assumes that the NIM index of refraction n ¼ 21.0at an operating frequency of �14.8 GHz. The smoothspherical lens surface is replaced by a stepwise approxi-mation with steps the size of the unit cell dimension at0.254 cm as shown in Fig. 4.

The unit cell dimensions for the 2E2H NIM (2E2H indi-cates that the structure couples with two polarisations of theE and H fields) are shown in Fig. 5. Note that this unit cell isindefinite so that 1 ¼ m ¼ (21.0, 21.0, 1.0) Our ray tracingand effective media simulations have shown that this inde-finite unit cell will perform nearly as well as a full 3E3Hunit cell having 1 ¼ m ¼ (21.0, 21.0, 21.0) [9]. The2E2H unit cell lends itself to simpler fabrication techniquesand reduces the need for cut wires in the propagation direc-tion. Impedance matching with Z ¼ 1.0 is achieved bydesigning 1 ¼ m at the operating frequency. A comparisonof the simulated and measured S21 for the pathfinder2E2H unit cell is also shown in Fig. 5. Note that at the oper-ating frequency the experimental transmission is �0.90 fora single unit cell due to dissipative losses and impedancemismatch of the material. This unit cell loss has animpact on the lens performance where multiple unit cellsare required in the propagation direction.

Fig. 1 Experimental (top left) and MWS simulated (top right) electric near field amplitude of empty aperture at 14.6 GHz

Line plots (bottom) of the experimental (dash) and MWS simulated (solid) fields are in excellent agreement

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A detailed comparison between the MWS near fieldfocusing simulation and experimental data is shown inFig. 6 for the NIM lens. The line plots in this figure showexcellent agreement between the experiment and simu-lation. Note that for the simulation, the effective 1 and mwere adjusted to (20.8, 20.8, 1.0) which is within our

Fig. 2 Rexolite PIM lens (top) having dimensions shown in raytracing diagram (bottom)

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fabrication and experimental error. As mentioned pre-viously, the oscillations along the z propagation directionfor the experimental data are due to interference betweenthe receiving antenna and the lens/mounting fixture. Also,the experimental profile is broader than the simulated dueto the finite dimensions of the receiving antenna.

The electric far field pattern/gain with respect to theempty aperture was also experimentally determined. Thegain for the NIM lens was �5.0 dB above the emptyaperture.

5 Design and characterisation of GRIN lens

We have fabricated a GRIN lens having a designed focallength of 12.7 cm as shown in Fig. 7. The principle advan-tage of a GRIN lens is its uniform thickness, which onaverage is thinner than a physically curved NIM lens ascharacterised above. The GRIN lens is constructed byusing an NIM with a variable index of refraction in theradial direction, perpendicular to the direction of propa-gation z. To design the lens we used a ray-tracing calcu-lation based on an anisotropic eikonal equation [9]. Thegradient required for the 12.7 cm focal length lens is1 ¼ m ¼ 21.120.0501 r2

þ 0.0001 r4. The unit cell step-wise approximation to this smooth gradient is also shownin Fig. 7. The GRIN lens has 5 NIM unit cells in the propa-gation direction. Each unit cell is 0.20 cm in width for atotal thickness of 1.0 cm. The number of unit cells designedwas 19, labelled A–S as indicated in the figure. The detailsof the A–S unit cell designs are shown in Fig. 8. Note thatthis geometry corresponds to a 1E1H unit cell (1E1H indi-cates that only one polarisation for the electric and magneticfields are coupled by the structure), that is, 1 ¼ (21.0, 1.0,1.0) and m ¼ (1.0, 21.0, 1.0). The index of refraction andimpedance for the A–S type cells were calculated fromsimulated S parameters for normal incidence of the electro-magnetic wave. The unit cells were designed such that

Fig. 3 Experimental (top left) and MWS simulated (top right) focusing electric near field amplitude of PIM lens at 14.6 GHz

Line plots (bottom) of the experimental (dash) and MWS simulated (solid) fields are in excellent agreementFocal spot for this lens is at �9.0 cm

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0

1

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1 1.2 1.4Propagation Direction, Z(cm)

Tran

sver

se D

irect

ion,

Y(c

m)

StepSmooth

0

1

2

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4

5

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7

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Propagation Direction, Z(cm)

Tran

sver

se D

irect

ion,

Y(c

m)

StepSmooth

Fig. 4 Fabricated NIM lens (top) showing steps of the unit celldimension (0.254 cm) used to approximate the smooth 24.4 cmradius spherical surface (bottom) needed for a 12.2 cm focallength assuming an index of refraction n ¼ 21.0 at the operatingfrequency of �14.8 GHz

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impedance was matched to free space at the operatingfrequency.

The MWS near field effective medium focusing simu-lation and experimental data for a 1E1H unit cell GRINlens are compared in Fig. 9. This analysis indicates thatthe 1E1H unit cell performs well for this GRIN application.The 1E1H unit cell has the distinct advantage of beingsimple to fabricate and assemble into a GRIN lens. Notethat the index gradient for the simulation was adjusted(i.e. 1 ¼ m ¼ 21.1 2 0.03 r2

þ 0.0001 r4) to better matchthe experimental data. This effectively reduces the indexgradient in the lens so that at the centre A type unit cellthe refractive index is 21.1 and at the edges the S typeunit cell refractive index is �22.4. This indicates that forthe fabricated lens the gradient achieved was somewhatlower than the design goal as shown in Fig. 7.

The measured electric far field pattern/gain with respectto the empty aperture indicated that the gain for the GRINlens was �10.0 dB above the empty aperture.

6 Comparison of experimental data foraperture, PIM, NIM and GRIN lenses

We have compared the performance of our PIM, NIM andGRIN lenses to each other at the approximate design fre-quency (14.8 + 0.3 GHz) as well as below (13.1 GHz)and above (16.3 GHz) the design point. As shown inFig. 5 (S21 magnitude against frequency for NIM unitcell), we expect the NIM lens to have little transmissionat 13.1 GHz, perform best at �14.8 GHz (where unit cellis matched to free space) and have degraded performanceat 16.3 GHz (where the NIM has good transmission but isnot matched to free space). Indeed, this is what we observed

Fig. 5 NIM 2E2H unit cell design (top) and comparison of simulated and measured S21 values showing �0.90 transmission at the operat-ing frequency of �14.8 GHz (bottom)

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Fig. 6 Experimental (top left) and MWS simulated (top right) focusing electric near field amplitude of NIM lens at 14.6 GHz

Line plots (bottom) of the experimental (dash) and MWS simulated (solid) fields are in excellent agreementFocal spot for this lens is at �11.0 cm

in our experimental measurements as shown in Fig. 10. Inthis figure, we plot the electric field values in the far fieldfor the empty aperture PIM, NIM and GRIN lenses at13.1, 14.8 and 16.3 GHz, respectively. The aperture and

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lenses were illuminated by a small dipole point sourceplaced at the focal spot for each lens and the correspondinglocation for the empty aperture. Note that the electric fieldvalue for the NIM is �50% of the value for the PIM lens.

Fig. 7 Fabricated GRIN lens (top), location of various cell types (bottom left) and step wise approximation to smooth1 ¼ m ¼ 21.1 2 0.0501 r2

þ 0.0001 r4 gradient (bottom right) needed for 12.7 cm focal length

Note that each unit cell A–S has a different index of refraction ranging from n ¼ 21.1 to 23.2

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This is due to losses in the NIM unit cell. If the transmissionis �0.90 for a single unit cell at the design frequency, thenthe transmission through the �5 unit cell thick NIM lens isS21NIM � (0.9)5 ¼ 0.59. For the PIM lens the transmissionis higher. For this case S11PIM ¼ Er/Eo � (n 2 1)/(nþ 1) ¼ (1.59 2 1.00)/(1.59þ 1.00) ¼ 0.23, where Eo isthe incident field, Er the reflected field and n therefractive index of Rexolite. For one interfaceS21PIM ¼ (1 2 S112)1/2 ¼ (1 2 0.232)1/2 ¼ 0.97, thatbecomes 0.94 for two interfaces, so we expect thatS21NIM/S21PIM �0.59/0.94 ¼ 0.63 which is approximately

Fig. 8 1E1H NIM unit cell design for 19 step GRIN lens

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what we observe experimentally. The experimental value(�0.50) is probably lower due to fabrication tolerancesand the resulting increased impedance mismatch. Wenote, however, that the FWHM of the NIM lens (�12.5 8)is smaller than the GRIN lens (�148) and PIM lens (�158),which was expected based on an aberration analysis [9].

The GRIN lens exhibits a normalised electric far fieldvalue that is �75% that of the PIM lens. This is higherthan the NIM lens due to the lower losses of the 1E1H unitcell structure. The GRIN lens FWHM maximum (�148) issmaller than the PIM lens but larger than the NIM lens.

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Fig. 9 Experimental (top left) and MWS simulated (top right) focusing electric near field amplitude of GRIN lens at 15.0 GHz

Line plots (bottom) of the experimental (dash) and MWS simulated (solid) fields are in excellent agreementFocal spot for this lens is at �10.0 cmNote that the index gradient for the simulation was adjusted, within the range of the fabrication uncertainties, to match the experimental data

0.0

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Fig. 10 Normalised electric field magnitude for aperture, PIM,NIM and GRIN lenses at 13.1, 14.8 + 0.3 and 16.3 GHz

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7 Conclusion

We have simulated, designed, fabricated and tested avariety of lenses operating in the microwave region.These lenses include PIM, NIM and GRIN lenses. Thetest setup in which these lenses were measured was alsocharacterised. Our results indicate that in general thelenses made of NIMs are lighter than the normal PIMlenses. This is due to the honeycomb-like techniques usedfor NIM fabrication. The NIM lens exhibited a gain lessthan the GRIN and PIM lenses due to the inherent highermaterial losses. The GRIN lens, however, had a gain com-parable to the PIM lens. On the basis of these results,further development and testing of lenses made of NIMsis warranted.

8 Acknowledgments

We thank B.E.C. Koltenbah and T. Lam for software assist-ance with the eikonal and aberration analysis. This workwas supported by DARPA Contract MDA972-01-2-0016.

9 References

1 Veselago, V.G.: ‘The electrodynamics of substances withsimultaneously negative values of 1 and m’, Sov. Phys. Usp., 1968,10, (4), pp. 509–514

2 Shelby, R.A., Smith, D.R., and Schultz, S.: ‘Experimental verificationof a negative index of refraction’, Science, 2001, 292, (5514),pp. 77–79

3 Parazzoli, C.G., Greegor, R.B., Li, K., Koltenbah, B.E.C., andTanielian, M.: ‘Experimental verification and simulation of negative

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I

index of refraction using Snell’s law’, Phys. Rev. Lett., 2003, 90, (10),pp. 107401(1)–107401(4)

4 Shurig, D., and Smith, D.R.: ‘Negative index lens aberrations’, Phys.Rev. E, 2004, 70, pp. 065601(1)–065601(4)

5 Parazzoli, C.G., Greegor, R.B., Nielsen, J.A., Thompson, M.A., Li, K.,Vetter, A.M., Taniliean, M.H., and Vier, D.C.: ‘Performance of anegative index of refraction lens’, Appl. Phys. Lett., 2004, 84, (17),pp. 3232–3234

6 Vodo, P., Parimi, P.V., Lu, W.T., and Sridar, S.: ‘Focusing by aplanoconcave lens using negative refraction’, Appl. Phys. Lett.,2005, 86, pp. 201108(1)–2001108(2)

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7 Smith, D.R., Mock, J.J., Starr, A.F., and Schurig, D.: ‘Gradient indexmetamaterials’, Phys. Rev. E, 2005, 71, pp. 036609(1)–036609(6)

8 Greegor, R.B., Parazzoli, C.G., Nielsen, J.A., Thompson, M.A.,Tanielian, M.H., and Smith, D.R.: ‘Simulation and testing of agraded negative index of refraction lens’, Appl. Phys. Lett., 2005,87, pp. 091114(1)–091114(3)

9 Parazzoli, C.G., Koltenbah, B.E.C., Greegor, R.B., Lam, T.A., andTanielian, M.H.: ‘Eikonal equation for a general anisotropic orchiral medium: application to a negative-graded index-of-refractionlens with an anisotropic material’, J. Opt. Soc. Am. B, 2006, 23, (3),pp. 439–450

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