Metamaterials for surfaces and waveguides

1 211356/2

TITLEMETAMATERIALS FOR SURFACES AND WAVEGUIDESCROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority from provisionalapplication no. 61/091,337 filed August 22, 2008.

STATEMENT REGARDING FEDERALLY

SPONSORED RESEARCH OR DEVELOPMENT

[0002]

TECHNICAL FIELD

[0003] The technology herein relates to artificially-structured materials such asmetamaterials, which function as artificial electromagnetic materials. Someapproaches provide surface structures and/or waveguide structures responsive toelectromagnetic waves at radio-frequencies (RF) microwave frequencies, and/orhigher frequencies such as infrared or visible frequencies. In some approaches theelectromagnetic responses include negative refraction. Some approaches providesurface structures that include patterned metamaterial elements in a conductingsurface. Some approaches provide waveguide structures that include patternedmetamaterial elements in one or more bounding conducting surfaces of thewaveguiding structures (e.g. the bounding conducting strips, patches, or planes ofplanar waveguides, transmission line structures or single plane guided modestructures).

BACKGROUND AND SUMMARY

[0004] Artificially structured materials such as metamaterials can extend theelectromagnetic properties of conventional materials and can provide novelelectromagnetic responses that may be difficult to achieve in conventional materials. 2 211356/2

Metamaterials can realize complex anisotropies and/or gradients of electromagneticparameters (such as permittivity, permeability, refractive index, and waveimpedance), whereby to implement electromagnetic devices such as invisibilitycloaks (see, for example, J. Pendry et al, “Electromagnetic cloaking method,” U.S.Publication No. 2008/0024792 A1) and GRIN lenses (see, for example, D. R Smithet al, “Metamaterials,” U.S. Publication No. 2008/0165079 A1). Further, it is possibleto engineer metamaterials to have negative permittivity and/or negative permeability,e.g. to provide a negatively refractive medium or an indefinite medium (i.e. havingtensor-indefinite permittivity and/or permeability; see, for example, D. R. Smith et al,“Indefinite materials,” U.S. Publication No. 2006/0125681 A1).

[0005] The basic concept of a “negative index” transmission line, formed byexchanging the shunt capacitance for inductance and the series inductance forcapacitance, is shown, for example, in Pozar, Microwave Engineering (Wiley 3d Ed.).The transmission line approach to metamaterials has been explored by Itoh andCaloz (UCLA) and Eleftheriades and Balmain (Toronto). See for example Elek et al,“A two-dimensional uniplanar transmission-line metamaterial with a negative index ofrefraction”, New Journal of Physics (Vol. 7, Issue 1 pp. 163 (2005); and US PatentNo. 6,859,114.

[0006] The transmission lines (TLs) disclosed by Caloz and Itoh are based onswapping the series inductance and shunt capacitance of a conventional TL toobtain the TL equivalent of a negative index medium. Because shunt capacitanceand series inductance always exist, there is always a frequency dependent dualbehavior of the TLs that gives rise to a “backward wave” at low frequencies and atypical forward wave at higher frequencies. For this reason, Caloz and Itoh havetermed their metamaterial TL a “composite right/left handed” TL, or CRLH TL. TheCRLH TL is formed by the use of lumped capacitors and inductors, or equivalentcircuit elements, to produce a TL that functions in one dimension. The CRLH TLconcept has been extended to two dimensional structures by Caloz and Itoh, and byGrbic and Eleftheriades. WO 2010/021736 PCT/US2009/004772 3 [0007] Use of a complementary split ring resonator (CSRR) as a microstripcircuit element was proposed in F. Falcone et al,, “Babinet principle applied to thedesign of metasurfaces and metamaterials," Phys, Rev. Lett, V93, Issue 19, 197401.The CSRR was demonstrated as a filter in the microstrip geometry by the same 5 group. See e.g., Marques et al, “Ab initio analysis of frequency selective surfacesbased on conventional and complementary split ring resonators", Journal of Optics A:Pure and Applied Optics, Volume 7, Issue 2, pp. S38-S43 (2005), and Bonache et al.,“Microstrip Bandpass Filters With Wide Bandwidth and Compact Dimensions"(Microwave and Optical Tech. Letters (46:4, p. 343 2005). The use of CSRRs as 10 patterned elements in the ground plane of a microstrip was explored. These groupsdemonstrated the microstrip equivalent of a negative index med.ium, formed usingCSRRs patterned in the ground plane and capacitive breaks in the upper conductor.This work was extended to coplanar microstrip lines as well.

[0008) A split-ring resonator (SRR) substantially responds to an out-of-plane 15 magnetic field (i.e. directed along the axis of the SRR). The complementary SRR(CSRR), on the other hand, substantially responds to an out-of~plane electric field(i.e. directed along the CSRR axis). The CSRR may be regarded as the “Babinet”dual of the SRR and embodiments disclosed herein may include CSRR elementsembedded in a conducting surface, e.g. as shaped apertures, etchings, or perforation 20 of a metal sheets. In some applications as disclosed herein, the conducting surfacewith embedded CSRR elements is a bounding conductor for a waveguide structuresuch as a planar waveguide, microstrip line, etc.

[0009] While split-ring resonators (SRRs) substantially couple to an out-of-plane magnetic field, some metamaterial applications employ elements that 25 substantially couple to an in-plane electric field. These alternative elements may bereferred to as electric LC (ELC) resonators, and exemplary configurations aredepicted in D. Schurig et al, “Electric-field coupled resonators for negative permittivitymetamaterials,” Appl. Phys. Lett 88, 041109 (2006). While the electric LC (ELC)resonator substantially couples to an in-plane electric field, the complementary electric 30 LC (CELC) resonator substantially responds to an in-plane magnetic field. The CELCresonator may be regarded the “Babinet” dual of the ELC resonator, and WO 2010/021736 PCT/US2009/004772 4 embodiments disclosed herein may include CELC resonator elements (alternatively oradditionally to CSRR elements) embedded in a conducting surface, e.g. as shapedapertures, etchings, or perforations of a metal sheet. In some applications asdisclosed herein, a conducting surface with embedded CSRR and/or CELC elementsis a bounding conductor for a waveguide structure such as a planar waveguide,microstrip line, etc.

[0010] Some embodiments disclosed herein employ complementary electric LC(CELC) metamaterial elements to provide an effective permeability for waveguidestructures, in various embodiments the effective (relative) permeability may begreater then one, iess than one but greater than zero, or less than zero. Alternativelyor additionally, some embodiments disclosed herein employ complementary split-ring-resonator (CSRR) metamaterial elements to provide an effective permittivity for planarwaveguide structures. In various embodiments the effective (relative) permittivity maybe greater then one, less than one but greater than zero, or less than zero [0011] Exemplary non-limiting features of various embodiments include: • Structures for which an effective permittivity, permeability, or refractiveindex is near zero ® Structures for which an effective permittivity, permeability, or refractive index is less than zero ® Structures for which an effective permittivity or permeability is an indefinite tensor (i.e. having both positive and negative eigenvalues) • Gradient structures, e.g. for beam focusing, collimating, or steering ® Impedance matching structures, e.g. to reduce insertion loss ® Feed structures for antenna arrays ® Use of complementary metamaterial elements such as CELCs and CSRRs to substantially independently configure the magnetic and electric WO 2010/021736 PCT/US2009/004772 5 responses, respectively, of a surface or waveguide, e.g. for purposes ofimpedance matching, gradient engineering, or dispersion control » Use of complementary metamaterial elements having adjustable physical parameters to provide devices having correspondingly adjustable 5 electromagnetic responses (e.g. to adjust a steering angle of a beam steering device or a focal length of a beam focusing device) • Surface structures and waveguide structures that are operable at RF, microwave, or even higher frequencies (e.g. millimeter, infrared, and visiblewavelengths)

10 BRIEF DESCRIPTION OF THE DRAWINGS

[0012] These and other features and advantages will be better and morecompletely understood by referring to the following detailed description of exemplarynon-limiting illustrative implementations in conjunction with the drawings of which: [0013] Figures 1-1D depict a wave-guided complementary ELC (magnetic 15 response) structure (Figure 1) and associated plots of effective permittivity,permeability, wave impedance, and refractive index (Figures 1A-1D); [0014] Figures 2-2D depict a wave-guided complementary SRR (electricresponse) structure (Figure 2) and associated plots of effective permittivity,permeability, wave impedance, and refractive index (Figures 2A-2D);

20 [0015] Figures 3-3D depict a wave-guided structure with both CSRR and CELC elements (e.g. to provide an effective negative index) (Figure 3) and associated plotsof effective permittivity, permeability, wave impedance, and refractive index (Figures3A-3D);

[0016] Figures 4-4D depict a wave-guided structure with both CSRR and CELC 25 elements (e.g. to provide an effective negative index) (Figure 4) and associated plotsof effective permittivity, permeability, wave impedance, and refractive Index (Figures4A-4D); WO 2010/021736 PCT/US2009/004772 6 [0017] Figures 5-5D depict a microstrip complementary ELC structure (Figure5) and associated plots of effective permittivity, permeability, wave impedance, andrefractive index (Figures 5A-5D); [0018] Figures 6-6D are depict a microstrip structure with both CSRR and 5 CELC elements (e.g. to provide an effective negative index) (Figure 6) and associatedplots of effective permittivity, permeability, wave impedance, and refractive index(Figures 6A-6D); [0019] Figure 7 depicts an exemplary CSRR array as a 2D planar waveguidestructure;

10 [0020] Figure 8-1 depicts retrieved permittivity and permeability of a CSRR element, and Figure 8-2 depicts the dependence of the retrieved permittivity andpermeability on a geometrical parameter of the CSRR element; [0021] Figures 9-1, 9-2 depict field data for 2D implementations of the planarwaveguide structure for beam-steering and beam-focusing applications, respectively; 15 [0022] Figures 10-1,10-2 depict an exemplary CELC array as a 2D planar waveguide structure providing an indefinite medium; and [0023] Figures 11-1, 11-2 depict a waveguide based gradient index lensdeployed as a feed structure for an array of patch antennas.

DETAILED DESCRIPTION 20 [0024] Various embodiments disclosed herein include “complementary” metamaterial elements, which may be regarded as Babinet complements of originalmetamaterial elements such as split ring resonators (SRRs) and electric LCresonators (ELCs).

[0025] The SRR element functions as an artificial magnetic dipolar "atom,” 25 producing a substantially magnetic response to the magnetic field of anelectromagnetic wave. Its Babinet “dual,” the complementary split ring resonator(CSRR), functions as an electric dipolar “atom" embedded in a conducting surface and WO 2010/021736 PCT/US2009/004772 7 producing a substantially electric response to the electric field of an electromagneticwave. While specific examples are described herein that deploy CSRR elements invarious structures, other embodiments may substitute alternative elements. Forexample, any substantially planar conducting structure having a substantially 5 magnetic response to an out-of-plane magnetic field (hereafter referred to as a “M-type element," the SRR being an example thereof) may define a complement structure(hereafter a "complementary M-type element," the CSRR being an example thereof),which is a substantially-equivalently-shaped aperture, etching, void, etc. within aconducting surface. The complementary M-type element will have a Babinet-dual 10 response, i.e. a substantially electric response to an out-of-plane electric field.

Various M-type elements (each defining a corresponding complementary M-typeelement) may include: the aforementioned split ring resonators (including single splitring resonators (SSRRs), double split ring resonators (DSRRs), split-ring resonatorshaving multiple gaps, etc.), omega-shaped elements (cf. C.R. Simovski and S. He, 15 arXiv:physics/0210049), cut-wire-pair elements (cf. G. Dolling et al, Opt. Lett. 30, 3198 (2005)), or any other conducting structures that are substantially magnetically *polarized (e.g. by Faraday induction) in response to an applied magnetic field.

[0026] The ELC element functions as an artificial electric dipolar “atom,"producing a substantially electric response to the electric field of an electromagnetic 20 wave. Its Babinet “dual,” the complementary electric LC (CELC) element, functions asa magnetic dipolar "atom” embedded in a conducting surface and producing asubstantially magnetic response to the magnetic field of an electromagnetic wave.While specific examples are described herein that deploy CELC elements in variousstructures, other embodiments may substitute alternative elements. For example, any 25 substantially planar conducting structure having a substantially electric response to anin-plane electric field (hereafter referred to as a "E-type element," the ELC elementbeing an example thereof) may define a complement structure (hereafter a"complementary E-type element," the CELC being an example thereof), which is asubstantially-equivalently-shaped aperture, etching, void, etc. within a conducting 30 surface. The complementary E-type element will have a Babinet-dual response, i.e. asubstantially magnetic response to an in-plane magnetic field. Various E-typeelements (each defining a corresponding complementary E-type element) may WO 2010/021736 PCT/US2009/004772 8 include: capacitor-like structures coupled to oppositely-oriented loops (as in Figures 1,3, 4, 5, 6, and 10-1, with other exemplary varieties depicted in □. Schurig et al,“Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys.Lett. 88, 041109 (2006) and in H.-T. Cen et al, "Complementary planar terahertzmetamaterials,” Opt. Exp. 15, 1084 (2007)), closed-ring elements (cf. R, Liu et al,"Broadband gradient index optics based on non-resonant metamaterials,”unpublished; see attached Appendix), l-shaped or “dog-bone” structures (cf. R. Liu etal, "Broadband ground-plane cloak,” Science 323, 366 (2009)), cross-shapedstructures (cf. H.-T. Cen et al, previously cited), or any other conducting structuresthat are substantially electrically polarized in response to an applied electric field. Invarious embodiments, a complementary E-type element may have a substantiallyisotropic magnetic response to in-plane magnetic fields, or a substantially anisotropicmagnetic response to in-plane magnetic fields.

[0027] While an M-type element may have a substantial (out-of-plane) magneticresponse, in some approaches an M-type element may additionally have an (in-plane)electric response that is also substantial but of lesser magnitude than (e.g. having asmaller susceptibility than) the magnetic response. In these approaches, thecorresponding complementary M-type element will have a substantial (out-of-plane)electric response, and additionally an (in-plane) magnetic response that is alsosubstantial but of lesser magnitude than (e.g. having a smaller susceptibility than) theelectric response. Similarly, while an E-type element may have a substantial (in-plane) electric response, in some approaches an E-type element may additionallyhave an (out-of-plane) magnetic response that is also substantial but of lessermagnitude than (e.g. having a smaller susceptibility than) the electric response. Inthese approaches, the corresponding complementary E-type element will have asubstantial (in-plane) magnetic response, and additionally an (out-of-plane) electricresponse that is also substantial but of lesser magnitude than (e.g. having a smallersusceptibility than) the magnetic response.

[0028] Some embodiments provide a waveguide structure having one or morebounding conducting surfaces that embed complementary elements such as thosedescribed previously. In a waveguide context, quantitative assignment of quantities 9 211356/2 typically associated with volumetric materials—such as the electric permittivity,magnetic permeability, refractive index, and wave impedance—may be defined forplanar waveguides and microstrip lines patterned with the complementary structures.For example, one or more complementary M-type elements such as CSRRs,patterned in one or more bounding surfaces of a waveguide structure, may becharacterized as having an effective electric permittivity. Of note, the effectivepermittivity can exhibit both large positive and negative values, as well as valuesbetween zero and unity, inclusive. Devices can be developed based at least partiallyon the range of properties exhibited by the M-type elements, as will be described.The numerical and experimental techniques to quantitatively make this assignmentare well-characterized.

[0029] Alternatively or additionally, in some embodiments complementary E-type elements such as CELCs, patterned into a waveguide structure in the samemanner as described above, have a magnetic response that may be characterizedas an effective magnetic permeability. The complementary E-type elements thuscan exhibit both large positive and negative values of the effective permeability, aswell as effective permeabilities that vary between zero and unity, inclusive.(throughout this disclosure, real parts are generally referred to in the descriptions ofthe permittivity and permeability for both the complementary E-type andcomplementary M-type structures, except where context dictates otherwise as shallbe apparent to one of skill in the art) Because both types of resonators can beimplemented in the waveguide context, virtually any effective material condition canbe achieved, including negative refractive index (both permittivity and permeabilityless than zero), allowing considerable control over waves propagating through thesestructures. For example, some embodiments may provide effective constitutiveparameters substantially corresponding to a transformation optical medium (asaccording to the method of transformation optics, e.g. as described in J. Pendry etal, “Electromagnetic cloaking method,” U.S. Publication No. 2008/0024792 A1).

[0030] Using a variety of combinations of the complementary E- and/or M-typeelements, a wide variety of devices can be formed. For example, virtually all of thedevices that have been demonstrated by Caloz and Itoh using CRLH TLs have WO 2010/021736 PCT/VS2009/004772 10 analogs in the waveguiding metamaterial structures described here. Most recently,Silvereinha and Engheta proposed an interesting coupler based on creating a regionin which the effective refractive index (or propagation constant) is nearly zero (CITE).The equivalent of such a medium can be created by the patterning of complementaryE- and/or M-type elements into the bounding surfaces of a waveguide structure. TheFigures show and describe exemplary illustrative non-limiting realizations of the zeroindex coupler and other devices with the use of patterned waveguides and severaldepictions as to how exemplary non-limiting structures may be implemented.

[0031] Figure 1 shows an exemplary illustrative non-limiting wave-guidedcomplementary ELC (magnetic response) structure, and Figures 1A-1D showassociated exemplary plots of the effective index, wave impedance, permittivity andpermeability. While the depicted example shows only a single CELC element, otherapproaches provide a plurality of CELC (or other complementary E-type) elementsdisposed on one or more surfaces of a waveguide structure.

[0032] Figure 2 shows an exemplary illustrative non-limiting wave-guidedcomplementary SRR (electric response) structure, and Figures 2A-2D showassociated exemplary plots ofthe effective index, wave impedance, permittivity andpermeability. While the depicted example shows only a single CSRR element, otherapproaches provide a plurality of CSRR elements (or other complementary M-type)elements disposed on one or more surfaces of a waveguide structure.

[0033] F igure 3 shows an exemplary illustrative non-limiting wave-guided structure with both CSRR and CELC elements (e.g. to provide an effective negativeindex) in which the CSRR and CELC are patterned on opposite surfaces of a planarwaveguide, and Figures 3A-3D show associated exemplary plots ofthe effectiveindex, wave impedance, permittivity and permeability. While the depicted exampleshows only a single CELC element on a first bounding surface of a waveguide and asingle CSRR element on a second bounding surface of the waveguide, otherapproaches provide a plurality of complementary E- and/or M-type elements disposedon one or more surfaces of a waveguide structure. WO 2010/021736 PCT/US2009/004772 11 [0034] Figure 4 shows an exemplary illustrative non-limiting wave-guidedstructure with both CSRR and CELC elements (e.g. to provide an effective negativeindex) in which the CSRR and CELC are patterned on the same surface of a planarwaveguide, and Figures 4A-4D show associated exemplary plots of the effective 5 index, wave impedance, permittivity and permeability. While the depicted exampleshows only a single CELC element and a single CSRR element on a first boundingsurface of a waveguide, other approaches provide a plurality of complementary E-and/or M-type elements disposed on one or more surfaces of a waveguide structure.

[0035] Figure 5 shows an exemplary illustrative non-limiting microstrip 10 complementary ELC structure, and Figures 5A-5D show associated exemplary plotsof the effective index, wave impedance, permittivity and permeability. While thedepicted example shows only a single CELC element on the ground plane of amicrostrip structure, other approaches provide a plurality of CELC (or othercomplementary E-type) elements disposed on one or both of the strip portion of the 15 microstrip structure or the ground plane portion of the microstrip structure.

[0036] Figure 6 shows an exemplary illustrative non-limiting micro-strip linestructure with both CSRR and CELC elements (e.g. to provide an effective negativeindex), and Figures 6A-6D show associated exemplary plots of the effective index,wave impedance, permittivity and permeability. While the depicted example shows 20 only a single CSRR element and two CELC elements on the ground plane of amicrostrip structure, other approaches provide a plurality of complementary E- and/orM-type elements disposed on one or both of the strip portion of the microstripstructure or the ground plane portion of the microstrip structure.

[0037] Figure 7 illustrates the use of a CSRR array as a 2D waveguide 25 structure. In some approaches a 2D waveguide structure may have boundingsurfaces (e.g. the upper and lower metal places depicted in Figure 7) that arepatterned with complementary E- and/or M-type elements to implement functionalitysuch as impedance matching, gradient engineering, or dispersion control.

[0038] As an example of gradient engineering, the CSRR structure of Figure 30 7has been utilized to form both gradient index beam-steering and beam-focusing WO 2010/021736 PCT7US2009/004772 12 structures. Figure 8-1 illustrates a single exemplary CSRR and the retrievedpermittivity and permeability corresponding to the CSRR (in the waveguide geometry).By changing parameters within the CSRR design (in this case a curvature of eachbend ofthe CSRR), the index and/or the impedance can be tuned, as shown in Figure8-2.

[0039] A CSRR structure laid out as shown in Figure 7, with a substantiallylinear gradient of refractive index imposed along the direction transverse to theincident guided beam, produces an exit beam that is steered to an angle different fromthat of the incident beam. Figure 9-1 shows exemplary field data taken on a 2Dimplementation of the planar waveguide beam-steering structure. The field mappingapparatus has been described in considerable detail in the literature [B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, D. R. Smith, “Spatial mapping of the internaland external electromagnetic fields of negative index metamaterials,*’ Optics Express,vol. 14, p. 8694 (2006)]. Likewise, implementing a parabolic refractive index gradientalong the direction transverse to the incident beam within the CSRR array produces afocusing lens, e.g. as shown in Figure 9-2. More generally, a transverse index profilethat is a concave function (parabolic or otherwise) will provide a positive focusingeffect, such as depicted in Figure 9-2 (corresponding to a positive focal length); atransverse index profile that is a convex function (parabolic or otherwise) will provide anegative focusing effect (corresponding to a negative focal length, e.g. to receive acollimated beam and transmit a diverging beam). For approaches wherein themetamaterial elements include adjustable metamaterial elements (as discussedbelow), embodiments may provide an apparatus having an electromagnetic function(e.g. beam steering, beam focusing, etc.) that is correspondingly adjustable. Thus, forexample, a beam steering apparatus may be adjusted to provide at least first andsecond deflection angles; a beam focusing apparatus may be adjusted to provide atleast first and second focal lengths, etc. An example of a 2D medium formed withCELCs is shown in Figures 10-1, 10-2. Here, an in-plane anisotropy of the CELCs isused to form an Indefinite medium/ in which a first in-plane component of thepermeability is negative while another in-plane component is positive. Such amedium produces a partial refocusing of waves from a line source, as shown in theexperimentally obtained field map of Figure 10-2. The focusing properties of a bulk WO 2010/021736 PCT/US2009/004772 13 indefinite medium have previously been reported [D. R. Smith, D. Schurig, J. J. Mock,P. Kolinko, P. Rye, “Partial focusing of radiation by a slab of indefinite media,” AppliedPhysics Letters, vol. 84, p. 2244 (2004)]. The experiments shown in this set of figuresvalidate the design approach, and show that waveguide metamaterial elements canbe produced with sophisticated functionality, including anisotropy and gradients.

[0040] In Figures 11-1 and11-2, a waveguide-based gradient index structure(e.g. having boundary conductors that include complementary E- and/or M-typeelements, as in Figures 7 and 10-1) is disposed as a feed structure for an array ofpatch antennas. In the exemplary embodiment of Figures 11-1 and 11-2, the feedstructure collimates waves from a single source that then drive an array of patchantennas. This type of antenna configuration is well known as the Rotman lensconfiguration. In this exemplary embodiment, the waveguide metamaterial provides aneffective gradient index lens within a planar waveguide, by which a plane wave can begenerated by a point source positioned on the focal plane of the gradient index lens,as illustrated by the “feeding points” in Figure 11-2. For the Rotman Lens antenna,one can place multiple feeding points on the focal plane of the gradient indexmetamaterial lens and connect antenna elements to the output ofthe waveguidestructure as shown in Figure 11-1. From well known optics theory, the phasedifference between each antenna will depend on the feed position ofthe source, sothat phased-array beam forming can be implemented. Figure 11-2 is a field map,showing the fields from a line source driving the gradient index planar waveguidemetamaterial at the focus, resulting in a collimated beam. While the exemplary feedstructure of Figures 11-1 and 11-2 depicts a Rotman-lens type configuration for whichthe antenna phase differences are substantially determined by the location ofthefeeding point, in other approaches the antenna phase differences are determined byfixing the feeding point and adjusting the electromagnetic properties (and therefore thephase propagation characteristics of) the gradient index lens (e.g. by deployingadjustable metamaterial elements, as discussed below), while other embodimentsmay combine both approaches (i.e. adjustment of both the feeding point position andthe lens parameters to cumulatively achieve the desired antenna phase differences). WO 2010/021736 PCT/US2009/004772 14 [0041] In some approaches, a waveguide structure having an input port orinput region for receiving electromagnetic energy may include an impedance matchinglayer (IML) positioned at the input port or input region, e.g. to improve the inputinsertion loss by reducing or substantially eliminating reflections at the input port or 5 input region. Alternatively or additionally, in some approaches a waveguide structurehaving an output port or output region for transmitting electromagnetic energy mayinclude an impedance matching layer (IML) positioned at the output port or outputregion, e.g. to improve the output insertion loss by reducing or substantiallyeliminating reflections at the output port or output region. An impedance matching 10 layer may have a wave impedance profile that provides a substantially continuousvariation of wave impedance, from an initial wave impedance at an external surface ofthe waveguide structure (e.g. where the waveguide structure abuts an adjacentmedium or device) to a final wave impedance at an interface between the IML and agradient index region (e.g. that provides a device function such as beam steering or 15 beam focusing). In some approaches the substantially continuous variation of waveimpedance corresponds to a substantially continuous variation of refractive index (e.g.where turning an arrangement of one species of element adjusts both an effectiverefractive and an effective wave impedance according to a fixed correspondence,such as depicted in Figure 8-2), while in other approaches the wave impedance may 20 be varied substantially independently of the refractive index (e.g. by deploying bothcomplementary E- and M-type elements and independently turning the arrangementsof the two species of elements to correspondingly independently tune the effectiverefractive index and the effective wave impedance).

[0042] While exemplary embodiments provide spatial arrangements of 25 complementary metamaterial elements having varied geometrical parameters (suchas a length, thickness, curvature radius, or unit cell dimension) and correspondinglyvaried individual electromagnetic responses (e.g. as depicted in Figure 8-2), in otherembodiments other physical parameters of the complementary metamaterial elementsare varied (alternatively or additionally to varying the geometrical parameters) to 30 provide the varied individual electromagnetic responses. For example, embodimentsmay include complementary metamaterial elements (such as CSRRs or CELCs) thatare the complements of original metamaterial elements that include capacitive gaps, WO 2010/021736 PCT/US2009/004772 15 and the complementary metamaterial elements may be parameterized by variedcapacitances of the capacitive gaps of the original metamaterial elements.Equivalently, noting that from Babinet’s theorem a capacitance in an element (e.g, inthe form of a planar interdigitated capacitor having a varied number of digits and/orvaried digit length) becomes an inductance in the complement thereof (e.g. in the formof a meander line inductor having a varied number of turns and/or varied turn length),the complementary elements may be parameterized by varied inductances of thecomplementary metamaterial elements. Alternatively or additionally, embodimentsmay include complementary metamaterial elements (such as CSRRs or CELCs) thatare the complements of original metamaterial elements that include inductive circuits,and the complementary metamaterial elements may be parameterized by variedinductances of the inductive circuits of the original metamaterial elements.Equivalently, noting that from Babinet’s theorem an inductance in an element (e.g. inthe form of a meander line inductor having a varied number of turns and/or varied turnlength) becomes a capacitance in the complement thereof (e.g. in the form of anplanar interdigitated capacitor having a varied number of digits and/or varied digitlength), the complementary elements may be parameterized by varied capacitancesof the complementary metamaterial elements. Moreover, a substantially planarmetamaterial element may have its capacitance and/or inductance augmented by theattachment of a lumped capacitor or inductor. In some approaches, the variedphysical parameters (such as geometrical parameters, capacitances, inductances) aredetermined according to a regression analysis relating electromagnetic responses tothe varied physical parameters (c.f. the regression curves in Figure 8-2) [0043] In some embodiments the complementary metamaterial elements areadjustable elements, having adjustable physical parameters corresponding toadjustable individual electromagnetic responses of the elements. For example,embodiments may include complementary elements (such as CSRRs) havingadjustable capacitances (e.g. by adding varactor diodes between the internal andexternal metallic regions of the CSRRs, as in A. Velez and J. Bonarche, “Varactor-loaded complementary split ring resonators (VLCSRR) and their application to tunablemetamaterial transmission lines,” IEEE Microw. Wireless Compon. Lett. 18, 28(2008)). In another approach, for waveguide embodiments having an upper and a WO 2010/021736 PCT/US2009/004772 16 lower conductor (e.g. a strip and a ground plane) with an intervening dielectricsubstrate, complementary metamaterial elements embedded in the upper and/orlower conductor may be adjustable by providing a dielectric substrate having anonlinear dielectric response (e.g. a ferroelectric material) and applying a bias voltage5 between the two conductors. In yet another approach, a photosensitive material (e.g. a semiconductor material such as GaAs or n-type silicon) may be positioned adjacentto a complementary metamaterial element, and the electromagnetic response of theelement may be adjustable by selectively applying optical energy to the photosensitivematerial (e.g. to cause photodoping). In yet another approach, a magnetic layer (e.g. 10 of a ferrimagnetic or ferromagnetic material) may be positioned adjacent to acomplementary metamaterial element, and the electromagnetic response of theelement may be adjustable by applying a bias magnetic field (e.g. as described in J.

Gollub et al, "Hybrid resonant phenomenon in a metamaterial structure with integratedresonant magnetic material," arXiv:0810.4871 (2008)). While exemplary 15 embodiments herein may employ a regression analysis relating electromagneticresponses to geometrical parameters (cf. the regression curve in Figure 8-2),embodiments with adjustable elements may employ a regression analysis relatingelectromagnetic responses to adjustable physical parameters that substantiallycorrelate with the electromagnetic responses. 20 [0044] In some embodiments with adjustable elements having adjustable physical parameters, the adjustable physical parameters may be adjustable inresponse to one or more external inputs, such as voltage inputs (e.g. bias voltages foractive elements), current inputs (e.g. direct injection of charge carriers into activeelements), optical inputs (e.g. illumination of a photoactive material), or field inputs 25 (e.g. bias electric/magnetic fields for approaches that include ferroelectrlcs/ferromagnets). Accordingly, some embodiments provide methods thatinclude determining respective values of adjustable physical parameters (e.g. by aregression analysis), then providing one or more control inputs corresponding to thedetermined respective values. Other embodiments provide adaptive or adjustable 30 systems that incorporate a control unit having circuitry configured to determinerespective values of adjustable physical parameters (e.g. by a regression analysis) WO 2010/021736 PCT/US2009/004772 17 and/or provide one or more control inputs corresponding to determined respectivevalues.

[0045] While some embodiments employ a regression analysis relatingelectromagnetic responses to physical parameters (including adjustable physicalparameters), for embodiments wherein the respective adjustable physical parametersare determined by one or more control inputs, a regression analysis may directlyrelate the electromagnetic responses to the control inputs. For example, where theadjustable physical parameter is an adjustable capacitance of a varactor diode asdetermined from an applied bias voltage, a regression analysis may relateelectromagnetic responses to the adjustable capacitance, or a regression analysismay relate electromagnetic responses to the applied bias voltage.

[0046] While some embodiments provide substantially narrow-band responsesto electromagnetic radiation (e.g. for frequencies in a vicinity of one or moreresonance frequencies of the complementary metamaterial elements), otherembodiments provide substantially broad-band responses to electromagnetic radiation(e.g. for frequencies substantially less than, substantially greater than, or otherwisesubstantially different than one or more resonance frequencies of the complementarymetamaterial elements). For example, embodiments may deploy the Babinetcomplements of broadband metamaterial elements such as those described in R. Liuet al, “Broadband gradient index optics based on non-resonant metamaterials,"unpublished; see attached Appendix) and/or in R. Liu et al, "Broadband ground-planecloak," Science 323, 366 (2009)).

[0047] While the preceding exemplary embodiments are planar embodimentsthat are substantially two-dimensional, other embodiments may deploycomplementary metamaterial elements in substantially non-planar configurations,and/or in substantially three-dimensional configurations. For example, embodimentsmay provide a substantially three-dimensional stack of layers, each layer having aconducting surface with embedded complementary metamaterial elements.Alternatively or additionally, the complementary metamaterial elements may beembedded in conducting surfaces that are substantially non-planar (e.g. cylinders,spheres, etc.). For example, an apparatus may include a curved conducting surface WO 2010/021736 PCT/US2009/004772 18 (or a plurality thereof) that embeds complementary metamaterial elements, and thecurved conducting surface may have a radius of curvature that is substantially largerthan a typical length scale of the complementary metamaterial elements butcomparable to or substantially smaller than a wavelength corresponding to an 5 operating frequency of the apparatus.

[0048] While the technology herein has been described in connection withexemplary illustrative non-limiting implementations, the invention is not to be limited bythe disclosure. The invention is intended to be defined by the claims and to cover allcorresponding and equivalent arrangements whether or not specifically disclosed 10 herein.

[0049] All documents and other information sources cited above are herebyincorporated in their entirety by reference. 211356/2 19 [0050] R. Uu et al. have described broadband gradient index optics based on non-resonant metamaterials as set out hereunder.

Broadband Gradient Index Optics Based on Non-Resonant Metamaterials R. Liu1. Q. Cheng1, Λ Y. Cihm\ J. J. Mock’, T. J. Cui1, D. R. Smith' 'Center for Melantuteriais and integrated Piasmonics and Departntettt of Electrical and Computer Engineering, Duke University. Dox9(1291, Durham, NC 27708 }The Stale Key Laboratory of Millimeter ii-'avex. Department of Radio Engineering, Southeast University, Nanjing 2! 0096, P. II. China(27 Novcinbcr'200S)

Abstract

Unfixing non-resonant rnetamaterial elements, we demonstrate that complex gradient index optics canbe constructed exhibiting low material losses and large frequency bandwidth. Although the range ofstructures Is limited to those having only electric response, with an electric permittivity always equal toor greater than unity, there are still numerous melamaterial design possibilities enabled by leveragingthe non-resonant elements. For example, a gradient, impedance matching layer can be added thatdrastically reduces the return loss of the optical elements, making them essentially reflection less andlossless. In microwave experiments, we demonstrate the broadband design concepts with a gradientindex lens and a beam-steering element, both of which are confirmed to operate over the entire X-band(roughly 8-12 GHz) frequency spectrum.

Because the electromagnetic response of mctainaterialelements can be precisely controlled, they can be viewed asthe fundamental building blocks for a wide range of complex,electromagnetic media. To date, mctamatcrials havecommonly been formed from resonant conducting circuits,whose dimensions and spacing are much less than thewavelength of operation. By engineering the large dipolarresponse of these resonant elements, an unprecedented rangeof effective material response cun be realized, includingartificial magnetism and large positive and negative values ofthe effective permittivity and permeability tensor elements.

Leveraging the flexibility inherent in these resonantelements, meiatrialerials have been used to implementstructures that would have been otherwise difficult orimpossible to achieve using conventional materials. Negativeindex materials, for example, sparked a surge of interest inmctamaterials, since negative refractive index is not amaterial property available in nature. Still, as remarkable asnegative index media are. they represented only thebeginning of the possibilities available with artificiallystructured media. Inhomogeneous media, ‘in which thematerial properties vary in a controlled manner throughoutspace, also can be used to develop optical components, andare an extremely good match for implementation bymctamaterials. indeed, gradient index optical elements havealready been demonstrated at microwave frequencies Innumerous experiments, Moreover, since mctamaterials allowunprecedented freedom to control the constitutive tensorelements independently, point-by-point throughout a regionof space, metamalerials* can be used as the technology torealize structures designed by the method of trans formationoptics [!}. The “invisibility" cloak, demonstrated atmicrowave frequencies in 2006, is an example of ametamaterials [2],

Although metarnaterials have proven successful i?i therealization of unusual electromagnetic response, thestructures demonstrated are often of only marginal utility inpractical applications due to the large losses that are Inherentto the resonant elements most typically used. The situationcan be illustrated using the curves presented in fig. I. in which the effective constitutive parameters are shown inFig.l (a) and (b) for the metamateriai unit cell in the inset,According to the effective medium theory described InRcf,[3j, the retrieved curves are significantly affected byspatial dispersion effect. To remove the spatial dispersionfactor, wc can apply rhe formulas in the theorem |‘3'J andachieve (hat μ = /71^(/2/2)/(^/2) in which, Θ a copJspt and p is the periodicity of the unit cell.

Fig, I (c) shows a· with frequency and the regular Dritde-Lorentz resonant form after removing the spatial dispersionfactor.

<img img-format="tif" img-content="drawing" file="IL211356AD00021.tif" id="idf0001" />

fig, L («) Retrieved permitticity fur a mcfainaicriol composed ofthe repeated unit ceil shown in the inset: (b) retrieved permeability 211356/2 20 for a metomalcrial composed ol"the repealed nilii ceil shown In theinset, (c) Thu disloriinns and :snifouls in ilu- relricved parameim arcdue to spatial dispersion. which can be removed 10 find the Dnuie-Lorenlz like resonance shown in lhe lower figure.

Note that lhe unit cell possesses a resonance in lhepermittivity at a frequency near 42 GHz. in addition to theresonance in the permittivity, there is also structure in themagnetic permeability. These artifacts are phenomenarelated to sparial dispersion—an elTeet due to the finite sizeof the unit cell with respect to the wavelengths. Aspreviously painted our, the effects of sparial dispersion aresimply described analytically, and can thus be removed toreveal a relatively uncomplicated Dm de-Lorentz typeoscillator characterized by only a few parameters. Theobserved resonance takes lhe form __=£τ^Η£ιϊ. οιar-ας +/Tro &lt;y* - ή?,, 4'ίΓω . where is the plasma frequency, ωϋ is the resonancefrequency and Γ is a damping (actor. The frequency whereε (m) ~ 0 occurs at /fl = /fl ψ flt.

As can be seen from cither Eq. 2 or Eig, 1. the effectivepermittivity can achieve very large values, either positive ornegative, near the resonance. Yet, these values are inherentlyaccompanied by both dispersion and relatively large losses,especially for frequencies very close to the resonancefrequency. Thus, ah hough a very wide and interesting rangeof constitutive parameters can be accessed by working withmctamaterial elements near the resonance, rhe advantage ofthese values is somewhat tempered by the inherent loss anddispersion. The strategy in utilizing meiainiitenals in thisregime is to reduce rhe losses of lhe «nil ceil as much aspossible. Because the skin depth of a metal,..

If we examine the response of the electric metamaterialshown in Fig, I at very low frequencies, we find, in lhe zerofrequency limit. • -&gt; 0) = I + —~ ~ ¢3)

The equation is reminiscent of the Lyddanc-Sachs-Tellerrelation that describes the contribution of the polaritonresonance to the dielectric constant al zero frequency [4|. Arfrequencies far away from the resonance, we see that thepermittivity approaches a constant that differs from unity bythe square of the ratio of the plasma to the resonancefrequencies. Although lhe values of the permittivity arenecessarily positive and greater than unity, lhe permittivity isboth dispersionless and lossless—a considerable advantage.Note that this property does not extend io magneticmetamaterial media, such as split ring resonators, which aregenerally characterized by effective permeability of rhe form

Fw' r (4) - (fl v i\~ca which approaches unity in the low frequency limit. Becauseartificial magnetic effects arc based on induction rather thanpolarization, artificial magnetic response must vanish at zerofrequency,

The effective constitutive parameters of melamatcirals arenot only complicated by spatial dispersion but also possess anmfifiile number of higher order resonances that shouldproperly be represented as a sum over oscillators. It is thusexpected that the simple analytical formulas presented aboveare only approximate. Still, we can investignie the generaltrend of the iow frequency permittivity as a function of lhehigh-frequency resonance properties of the unit cell. Byadjusting the dimension of the square closed ring in the unitcell, we can compare lhe retrieved zero-frequencypermittivity with that predicted by Eq. 2, The si mu lai tons arecarried out using HFSS (Ansoft), a commercialelectromagnetic, finite-element, solver that can determine theexact field disiributions and scattering (S-) parameters for anarbitrary metamalerial structure. The permittivity andpermeability can be retrieved from the S-parameters by awell-established algorithm, Tabic I demonstrates thecomparison between such simulated extraction andtheoretical prediction. We should notice tharas the unit cell iscombined with a dielectric substrate. Eq. (3) has been,.ϊ j modified imo £-(^^.0) = ^(1 + 521.) = ^/55.. in which.ffl " efl

So “ 1.9, The additional fitting parameter can represent thepractical situation of the affect from substrate dielectricconstant and the contribution to DC permittivity from highorder resonances. Though I here is significant disagreementbetween the predicted and retrieved values of permittivity,the values are of similar order and show clearly a similar(rend: the high frequency resonance properties are stronglycorrelated to the zero frequency polarizability. By modifyingthe high-frequency resonance properties of the element, thezero- and low-frequency permittivity can be adjusted toarbitrary values. fit fr predicted Sactupi 1.70 · . 44.0. ' , • .59,0 . - 3,416: 3.425 1.55 54,0 64.0 2.670 2,720 1.40 . .64,0··. . . -71.0-. . 2,-338" 2.31,5 1,20 77.4 79.2 1.989 • 1,885

Table t. The predicted and actual zero-frequency permittivityvalues ax a function of the unit cell dimension, a.

Because Lhe closed ring design shown in Fig, 2 caneasily be tuned to provide a ranee of dielectric values, wcutilize it us lhe base element to illustrate more complexgradient-index structures. Though its primary response iselectric, the closed ring also possesses a wcakf diamagneticresponse that is induced when the incident magnetic field liesalong (he ring axis. The closed ring medium there fore isebantcienzed by a magnetic permeability that differs fromunity, and which must be taken into account for a lulldescription of the material properties. The presence of bothelectric and magnetic dipolar responses is generally useful in 211356/2 21 designing complex media, having been demonstrated in lhemetamaterial cioak. By changing the dimensions of the ring,it is possible to control rhe coniribuiion of the magnetic response.

The pennirtivity can be accurately controlled bychanging the geometry of the closed ring. The electricresponse of rhe closed ring structure is identical io the '‘cut-wire" structure previously studied, where it has been shownthat the plasma and resonance frequencies are simply relatedto circuit parameters according to » .1 and ; * ·™·&gt;

Here. L is the inductance associated with the arms of theclosed ring and C is the capacitance associated with the gapbetween adjacent closed rings. For a fixed unit ceil size, theinductance can be tuned either by changing the thickness, &gt;i\of the conducting rings or their length, a. The capacitancecan be controlled primarily by changing the overall size ofthe ring.

<img img-format="tif" img-content="drawing" file="IL211356AD00022.tif" id="idf0002" />

Fig. 2. {Color online? Retrieval results for the closed ring medium.In nil cases the ruditts of curvature of lhe corners is (}.6 mm, endwMJ.2 mm. (n) 'Fhe eximcted permittivity with &lt;?“l.4 mm. (h) Theextracted index and Impedance for severtil vuiues of u. The lowfrequency region is shown, te) The relationship between diedimension a and the extracted refrticiivc index and wavy impedance.

Changing the resonance properties in turn changes thelow frequency, permittivity value, as illustrated by thesimulation results presented in Fig. 2. The closed ringstructure sitown in Fig. 2(a) is assumed to be deposited onFR4 substrate, whose permittivity is 3.85Ή0.02 and thicknessis 0,2026 mm. The unit cell dimension is 2inm( and thethickness of the deposited metal layer (assumed to be copper)is 0.018 mm. For this structure, a resonance occurs near 25GHz with the permittivity nearly constant over a largefrequency region (roughly zero to 15 GHz). Simulations ofthree different unit ceil with ring dimensions of o “ 0.7 mm,1.4 mm and 1,625 mm were also simulated to illustrate theeffect on the material parameters. In Fig, 2b, it is observedthat the index value becomes larger as the ring dimension isincreased, reflecting the larger polarizability of the largerrings.

The refractive index remains, fbr the most part, relativelyflat as a function of frequency for frequencies well below theresonance. The index does exhibit a slight monotonicIncrease as a function of frequency, however, which is due tothe higher frequency resonance. The impedance changes alsoexhibits some amount of frequency dispersion, due to theeffects of spatial dispersion on the permittivity andpermeability. The losses in this structure arc found to benegligible, as a result of being faraway from the resonancefrequency. This result is especially striking, because thesubstrate is not one optimized for RF circuits—in fact, theFR4 circuit board substrate assumed here is generallyconsidered quite lossy.

As can be seen from the simulation results in Fig, 2,meta materia I structures based on the closed ring elementshould be nearly non-dtspersive and low-loss, provided theresonances of the elements are sufficiently above the desiredrange of operating frequencies. To illustrate the point, wemake use of the closed ring element to realize two gradientindex devices: a gradient index lens and a beam steering lens.The use of resonant metanmtcrials to implement positive andnegative gradient index structures was introduced in (5) andsubsequently applied in various contexts. The designapproach is first to determine the desired continuous indexprofile to accomplish the desired function (e.g., focusing orsteering) and then to stepwise approximate the index profileusing a discrete number of metamaterial elements. Theelements can be designed by performing numericalsimulations for a large number of variations of thegeometrical parameters of the unit cell (I,¢., a, w, etc.): onceenough simulations have been run so that a reasonableinterpolation can be formed of the permittivity as a functionof the geometrical parameters, the metamaterial gradientindex structure can be laid out and fabricated. This basicapproach has been followed in [6],

Two gradient index samples were designed to test thebandwidth of the non-resonant metamarerials. The colormaps in Fig, 3 show the index distribution corresponding tolhe beam steering layer (Fig. 3a) and the beam focusing lens(Fig. 3b). Although the gradient index distributions providethe desired function of either focusing or steering a beam,there remains a substantial mismatch between thepredominantly high index structure and tree-space. Thismismatch was managed in prior demonstrations by adjusting 211356/2 22 the properties of each metamateria} element such that thepermittivity and permeability were essentially equal. Thisflexibility in design is an inherent advantage of resonantmctamaterials, where the permeability response can beengineered on a nearly equal footing with rhe electricresponse. By contrast, that flexibility is nm available fordesigns involving non-rcsonanl elements, so wc have insteadmade use of a gradient index impedance matching layer(JML) to provide a match from free-space to the lens, as wellas a march from the exit of the lens backio free space. Γήΐίο’χ:'ί.41' -&gt;.ΰΊ

Im^kIWm· Match tj&gt;yftr "(IML.j'Beam Steeling Layer , .·: ‘ β V

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iMpiThtekniieftW

Steering Layer Thickneisfp'cm r' ' .. T·1;'

Color Baror inoox t.76

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1,1G (4) patron vt Onr»4lro*&lt;raiin4 rectr«(n$r

Fig. 3. Refractive Index distributions for the designed gradient indexstructures, (a) Λ beam·steering clement based on π linear indexgradient tb) Λ beam focusing Sens, based on n higher order'polynomial index gradient Note the presence in both designs of tinimpedance ntlrtehirtg layer (IML), provided to improve lhe insertionloss of the structures.

<img img-format="tif" img-content="drawing" file="IL211356AD00026.tif" id="idf0006" />

Fig. 4. Fabricated sample, in which, the metnmnleriiil structuresvary with space coordinate.

The beam steering layer is a shtb with a linear indexgradient In the direction transverse, to rhe direction of wavepropagation. The index values range from n 1.16 to n =1.66, consistent with the range available from our designedset of closed ring meiarnaterial elements. To improve theinsertion loss and to minimize reflection, the IML is placedon both sides of Lhc sample (’input and output). The indexvalues of the IML gradually change from unity (air) to n ~L4I, the index value at the center of the beam steering slab.This index value was chosen because most of the energy ofthe collimated beam passes through (he center of the sample.Ta implement the actual beam steering sample, we made useof the dosed ring unit cell shown in Fig. 2 and designed anarray of unit cells having the distribution shown in fig. 3a.

The beam focusing lens is a planar slab with the indexdistribution as represented in Fig. 3b. The index distributionhas the functional form of

Re(n) == 4 x 10"r‘ |.rf ~ 5 χ I (Γ1 |x|* - 6x Hr4 |.v|+! .75 . (5) in which .r is the distance away from the center of the lens.Once again, an IML was used to match the sample to freespace. In this case, the index profile in the IML was rampedlinearly from n ~ L15 to n = 1.75, the latter value selected tomatch the index at the center of the lens. The same unit celldesign was utilized for the beam focusing lens as for thebeam steering lens.

To confirm ihc properties of the gradient indexstructures, we fabricated the two designed samples usingcopper dad FR4 printed circuit board substrate, shown inFig. 4, Following a procedure previously described; sheets ofthe samples were fabricated by standard optical lithography,then cut into I cm tail strips that could be assembled togetherto form the gradient index slabs, To measure the sample, weplaced them into a 2D mapping apparatus, which has beendescribed in detailss and mapped the near field distribution[7],

<img img-format="tif" img-content="drawing" file="IL211356AD00027.tif" id="idf0007" />

9.99 GHz 11.72 GHz

Fig. 5, Field mapping measurements αΓίΙια beam steering lens. Thelens has a linear gradient that causes die incoming beam to bedeflected by an angle of 16.2 degrees. The cficci is bruadhniul, axcan he seen from the identical maps taken at four differentfrequencies ihrit span the X-hand range of lhe experimentalapparatus.

J 211356/2 23

<img img-format="tif" img-content="drawing" file="IL211356AD00028.tif" id="idf0008" />

10GHz 11GHz

Fig. 6, Field mapping, measurements of the beam focusing lens. Thelens has n symmL'irie profile about liw center (given in the lexil liwicauses the incoming beam io'be focused let a point. Once again, thefunction is broadband, as cun be seen from the idertliwd maps fake.fiat four differcnl frequencies thru span Ihe X-bantl range of theexperimental apparatus.

Fig.5 shows the beam steering of the ultra-broadbandmctamaterial design, in which, a large broadband is covered.The actual bandwidth starts from DC and goes up toapproximately 14GHz, From Fig.3, it is obvious that-beamsteering occurs at all the four different frequencies from738GHz to I L72GHz with an identical steering angle of16.2 degree. The energy loss through propagation isextremely low and can barely be observed. Fig.6 shows themapping result of the beam focusing sample. Broadbandproperty is demonstrated again at four different frequencieswith an exact same focal distance of 35mm and low loss.

In summary, we proposed ultra-broadbandmetamtitertals, based on which complex inhomogeneousmateria! can be realized and accurately controlled. Theconfiguration of ultra-broadband metamaterials and the design approach are validated by experiments. Due to its lowloss, design able properties and easy access to inhomogeneousmalerial parameters, the ultra-broadband metamatcrials willfind wide-applications in the future.

Acknowledgments

This work was supported by the Air Force Office ofScientific Research through a Multiple University. Researchinitiative, Contract No. FA95 50-06-1-0279. TJC, QC andJVC acknowledge support from the National Basic ResearchProgram (973) of China under Grant No, 2004CB719802, theIII Project under Grant No. IJ J -2-05, InnovaleHanTechnology Ltd. and the National Science Foundation ofChina under Grant Nos. 60671015 and 60496317,

References fl] J. B. Pendry, D, Schurig, D. R. Smith Science 312, 1780(2006) [2] D. Schurig, J. J. Mock, B. J, Justice, S. A, Cummer, J. B.Pendry, A. F. Starr and D. R. Smith, Science 314, 977-980(2006). [3] R. Liu, T. J. Cut, D, Huang, B. Zhao, D. R. Smith.Physical Review Ex 76, 026606 (2007) [4] C. Kittel, Solid Stale Physics (John Wiley &lt;&amp;amp; Sons, NewYork, 1986), 6'h ed„ p275 |5| D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, Λ. F. StarrPhysical Review Letters , 93 , J 37405 (2004) [6] T, Driscoll, et. al. Applied Physics Leiters 88, 081101(2006) [7] B. J. Justice, J, J. Mock, L, Guo, A, Degiron. D. Schurig,D, R. Smith. Optics Express 14, 8694 (2006).