DOI: 10.1126/science.1166949
, 366 (2009);
323Science世界第一大战
et al.R. Liu,Broadband Ground-Plane Cloak
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Broadband Ground-Plane Cloak
R.Liu,1*C.Ji,2*J.J.Mock,1J.Y.Chin,3T.J.Cui,3†D.R.Smith 1†
The possibility of cloaking an object from detection by electromagnetic waves has recently become a topic of considerable interest.The design of a cloak us transformation optics,in which a conformal coordinate transformation is applied to Maxwell ’s equations to obtain a spatially
distributed t of constitutive parameters that define the cloak.Here,we prent an experimental realization of a cloak design that conceals a perturbation on a flat conducting plane,under which an object can be hidden.To match the complex spatial distribution of the required constitutive parameters,we constructed a metamaterial consisting of thousands of elements,the geometry of each element determined by an automated design process.The ground-plane cloak can be realized with the u of nonresonant metamaterial elements,resulting in a structure having a broad
operational bandwidth (covering the range of 13to 16gigahertz in our experiment)and exhibiting extremely low loss.Our experimental results indicate that this type of cloak should scale well toward optical wavelengths.
T
ransformation optics is a method for the conceptual design of complex electro-magnetic media,offering opportunities for the control of electromagnetic waves (1,2).A wide variety of conventional devices can be designed by the transformation optical approach,including beam shifters (3),beam bends (4),beam splitters (3),focusing and collimating lens (5),and structures that concentrate electromagnetic waves (6,7).Whereas all of the devices have properties that are unique to the class of trans-formation optical structures,one of the most com-pelling and unprecedented concepts to emerge has been that of a medium that can conceal ob-jects from detection by electromagnetic waves.The prospect of electromagnetic cloaking has proven a tantalizing goal,with numerous con-cepts currently under investigation (1,2,8–14).In the transformation optical approach,one imagines warping space so as to control the trajectories of light in a desired manner.As an example of this approach,a cloak can be de-signed by performing a coordinate transforma-tion that squeezes the space from within a sphere to within a shell having the
same outer radius.Waves do not interact with or scatter from the core becau it is simply not part of the trans-formed space.The form invariance of Maxwell ’s equations implies that the coordinate transfor-mation can instead be applied to the permittivity and permeability tensors,yielding the prescrip-tion for a medium that will accomplish the de-sired functionality.The resulting medium is highly complex,being anisotropic and with spa-tial gradients in the components of the permittiv-ity and permeability tensors.
Such complicated gradient-index media are difficult to create with conventional materials but
are much easier to build with artificially struc-tured metamaterials,in which spatial variations of the material parameters can be achieved by modifying the geometry and placement of the constituent element.Even so,the large number of elements required in an arbitrary cloak medium can reprent a substantial computational burden resulting in long design cycles.To address this time-consuming design step,we have developed a systematic algorithm that is applied once the spatial distribution of the constitutive parameters has been determined by the transformation.Pre-viously,metamaterial structures requiring spatial gradients have been obtained by designing one unit cell at a time until a library of unique meta-material elements,who constitutive parameters span the range required by the transformation optical design,is generated.In contrast,the algorithm we u (15)requires only a c
ompara-tively small number of simulations of the meta-material element,relying on a regression scheme to generate the functional dependence of the con-stitutive parameters on the unit cell geometry.The reduced number of simulations vastly speeds the metamaterial cloak-design process and makes the design of complex media possible.
The specification of a ground-plane cloak can be determined in the manner described in (16).If waves are restricted to a single plane of inci-dence,with the polarization of the waves being transver electric (electric field perpendicular to the plane of incidence or parallel to the ground plane),then the cloak parameters need only be determined across a two-dimensional (2D)plane.The domain of the problem is thus a 2D space,filled with a uniform dielectric with refractive in-dex value n b and bounded by a conducting sheet.A family of coordinate transformations that will map a given nonplanar conducting surface to a planar surface can be found;however,such trans-formations generally lead to an anisotropic me-dium with values of n x and n y that vary as a function of the spatial coordinate.Yet,given the restricted geometry,it is possible to find a coor-dinate map that minimizes the anisotropy in the permeability components.Defining an anisotro-py factor as a =max(n x /n y ,n y /n x ),transformations
can be found for which a is near unity so that the isotropic refractive index value varies throughout th
e space.If n b in the original space is sufficiently greater than unity,then the values for the refrac-tive index of the cloaking structure are also greater than unity.Under the conditions,nonresonant metamaterial elements can be ud,and the cloak can exhibit a broad frequency bandwidth (15).In our particular design,we followed the optimization technique (16)for the transforma-tion region,in which a quasi-conformal coor-dinate map is generated by minimizing the Modified-Liao functional (17,18)with slipping boundary conditions.The Jacobian matrix L that relates the physical and virtual systems is then computed numerically,from which the index
distribution n 2¼1ffiffiffiffiffiffiffiffiffij L T L j
p of the cloak is found (here,T is the transpo of the Jacobian matrix).In our final design,a =1.04,which is treated as negligible (that is,we assume n x =n y ).
A photograph of the fabricated sample,a color map indicating the transformed space,and the associated refractive index distribution are prented in Fig.1.We assume that the entire cloak is embedded in a background material with refractive index n b =1.331.Under the assump-tions,the transformation leads to refractive index values for the ground-plane cloak that range from n =1.08to 1.67(values that can be achieved with the u of nonresonant metamaterial elements).On the right a
nd left side of the sample in Fig.1B,the refractive index distribution is uniform (n b =1.331),taking the value of the background mate-rial.Becau the cloak is designed to be em-bedded in a higher dielectric region,we add an impedance matching layer (IML)that surrounds the entire structure,for which the index changes gradually and linearly from that of air to that of the background index (15).This step is taken to minimize reflection from the cloak surface when illuminated by a microwave beam within the scattering chamber,which exists in an n =1.0(air)environment.The procedure for designing the IML layer is described in (15).Becau of the index gradient coupled with the cloak,we expect no amplitude scattering and only a slight offt of the wave reflected from the ground-plane struc-ture due to the refractive index change.The effect should be similar to obrving a mirror through a layer of glass;objects on the top of the mirror,within the cloaked region,remain hidden from detection (visualized by ray tracing in Fig.1D).It is important to note that this type of cloaking phenomena is distinct from current scattering sup-pression technologies becau it both eliminates backscattering and restores the reflected beam.To implement the cloak defined by the index distribution prented in Fig.1C and the asso-ciated background material and IML in Fig.1B,the continuous theoretical constitutive param-eter distribution must be approximated by a discrete number of metamaterial elements.In our design,the entire sample region is divided into 2-by-2–mm squares,requiring more than 10,000elements,about 6000of which are unique.
1
清朝铜币Center for Metamaterials and Integrated Plasmonics,Department of Electrical and Computer Engineering,Duke University,Durham,NC 27708,USA.2Department of Statistical Science,Duke University,Durham,NC 27708,USA.3State Key Laboratory of Millimeter Waves,Southeast University,Nanjing 210096,China.
*The authors contributed equally to this work.
†To whom correspondence should be addresd.E-mail:tjcui@u.edu (T.J.C.);drsmith@duke.edu (D.R.S.)
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The elements chon to achieve the design are all variations of the structure shown in Fig.2.By changing the dimension a ,we are able to span the required index range of n =1.08to 1.67.After a
刘涵颂
well-established retrieval process,modified to include the effects of the finite unit cell size rela-tive to the wavelength (19,20),the effective per-mittivity and permeability for a given element
can be found via numerical simulation.A regres-sion curve can then be made that relates the refractive index associated with a given element to the length a .Once a t of elements has
been
Fig.1.The transformation optical design for the ground-plane cloak.The metamaterial cloak region is embedded in a uniform higher index background with gradients introduced at the edges to form impedance matching regions.(A )Photograph of the fabricated metamaterial sample.(B )Metamaterial refractive index distribution.The coordinate transformation region is shown within the box outlined in black.The surrounding material is the higher index embedding region and the IMLs.(C )Expanded view of the transformation optical region in which the mesh lines indicate the quasi-conformal mapping (lateral dimensions of the unit cells are ~3.5times smaller).(D )Ray tracing of a beam incidents illuminating on (i)the ground,(ii)the perturbation,and (iii)the perturbation covered by a ground-plane cloak.The gray area and dashed lines in (iii)indicate the transformation region,embedded background material,and IML.
Fig.2.The design of the nonresonant ele-ments and the relation between the unit cell ge-ometry and the effective index.The dimensions of the metamaterial unit cells are l =2mm,w 1=0.3mm,w 2=0.2mm,and a varying from 0to 1.7
mm.
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numerically simulated,all subquent tasks in the cloak design —from the generation of the regres-si
on curve to the final layout of the elements in a mask for lithographic processing —are performed using a single Matlab program.The metamaterial elements we employ actually exhibit some de-gree of frequency dispersion in their constitutive parameters caud by their finite dimension with respect to the wavelength,as described in the supporting online material.In particular,the in-plane permeability and out-of-plane permittivity vary as a function of frequency such that the index stays approximately constant but the wave imped-ance varies considerably.Becau the cell-to-cell change in impedance is minor,there is no reflec-tion and no discernable disturbance in the cloak properties over the entire frequency range measured.As with previous metamaterial designs imple-mented for microwave experiments,the final ground-plane cloak is fabricated on copper-clad printed circuit board with FR4substrate (the substrate thickness is 0.2026mm,with a dielec-tric constant of 3.85+i 0.02).The completed sample is 500by 106mm with a height of 10mm.
The center region,250by 96mm,corresponds to the transformed cloaking region,whereas the rest of the sample is ud for dielectric embedding and impedance matching.The cloak transforma-tion is specifically designed to compensate a per-turbation introduced on the conducting surface that follows the curve y =12cos 2[(x –125)p /125](units in millimeters).
To verify the predicted behavior of the ground-plane cloak design,we make u of a pha-nsitive,
near-field microwave scanning system to map the electric field distribution inside a pla-nar waveguide.The planar waveguide restricts the wave polarization to transver electric.The details of the apparatus have been described pre-viously (21).A large area field map of the scat-tering region,including the collimated incident and scattered beams,is shown in Fig.3.The waves are launched into the chamber from a standard X-band coax-to-waveguide coupler and pass through a dielectric lens that produces a nearly collimated microwave beam.The beam is arbitrarily chon to be incident on the ground plane at an angle of 40°with respect to the nor-mal.A flat ground plane produces a near perfect reflection of the incident beam in Fig.3A,where-as the prence of the perturbation produces con-siderable scattering,as shown in Fig.3B (note the prence of the strongly scattered condary beam).By covering the space surrounding the perturbation with the metamaterial cloaking struc-ture,however,the reflected beam is restored,as if the ground plane were flat in Fig.3C.The beam is slightly bent as it enters the cloaking region becau of the refractive index change of the embedding material but is bent back upon exit-ing.The gradient-index IML introduced into the design minimizes reflections at the boundaries of the cloaking region.
As the ground-plane cloak makes u of nonresonant elements,it is expected to exhibit a large frequency range of operation.The cloaking behavior was confirmed in our measurements from the ra
nge 13to 16GHz,though we expect the bandwidth to actually stretch to very low frequencies (<1GHz)that cannot be verified experimentally becau of limitations of the mea-surement apparatus and the beam-forming lens.We illustrate the broad bandwidth of the cloak with the field maps taken at 13GHz in Fig.3D,15GHz in Fig.3E,and 16GHz in Fig.3F,which show similar cloaking behavior to the map taken at 14GHz in Fig.3C.The collimated beam at 16GHz has begun to deteriorate becau of multi-mode propagation in our 2D measurement cham-ber,which is also obrved in the flat ground-plane control experiment at that frequency.However,on the basis of the predicted respon of the broadband unit cells,we expect this cloak to func-tion up to ~18GHz.
To further visualize the performance of the ground-plane cloak,we illuminated the sample from the side (90°from the surface normal)with a narrow collimated beam.As the ground-plane cloaked perturbation should also be cloaked with the respect to an obrver located on the ground,the wave,which should follow the metric as de-fined by the quasi-transformation map in Fig.1,can be expected to detour around the perturbation and then return back to its original propagation direction.The field map for this ca is shown in Fig.4B,which corresponds with the predicted transformation extremely well (a low-resolution reprentation of the transformation grid is over-laid on the experimental data).For comparison,Fig.4A shows a map of the field strongly scattered from the perturbation in the abnce of the cloak.
The agreement between the measured field patterns for the ground-plane cloak and the theo-ry (16)provides convincing evidence that meta-materials can indeed be ud to construct such complex electromagnetic media.Although this cloak is not able to hide objects from detection that do not lie under the conducting curtain formed by the perturbation of the ground plane,its broadband and low-loss properties are com-pelling and offer a path toward realization of some forms of cloaking at frequencies
approach-
Fig.3.Measured field mapping (E-field)of the ground,perturbation,and ground-plane cloaked perturbation.The rays display the wave propagation direction,and the dashed line indicates the normal of the ground in the ca of free space and that of the ground-plane cloak in the ca of the transformed space.(A )Collimated beam incident on the ground plane at 14GHz.(B )Collimated beam incident on the perturbation at 14GHz (control).(C )Collimated beam incident on the ground-plane cloaked perturbation at 14GHz.(D )Collimated beam incident on the ground-plane cloaked perturbation at 13GHz.(E )Collimated beam incident on the ground-plane cloaked perturbation at 15GHz (F )Collimated beam incident on the ground-plane cloaked perturbation at 16
GHz.
Fig.4.2D field mapping (E-field)of the perturbation and ground-plane cloaked perturbation,illuminated
by the waves from the left side (A )perturbation and (B )ground-plane cloaked perturbation.The grid pattern indicates the quasi-conformal mapping of the transformation optics material parameters.
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ing the optical.By merging the nascent technique of transformation optics with traditional gradient-index optics,we have shown that more functional hybrid structures can be developed that enable us to access previously unen electromagnetic be-havior while mitigating some of the inherent limitations.Though transformation optical de-signs are highly complex,metamaterial imple-mentations can be rapidly and efficiently achieved using the algorithms and approach described in this report.
References and Notes
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3.3.M.Rahm,S.A.Cummer,D.Schurig,J.B.Pendry,D.R.Smith,Phys.Rev.Lett.100,063903(2008).
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9.A.Hendi,J.Henn,U.Leonhardt,Phys.Rev.Lett.97,073902(2006).
10.D.Schurig et al .,Science 314,977(2006);published
你阿妈大减价online 18October 2006(10.1126/science.1133628).11.W.Cai,U.K.Chettiar,A.V.Kildishev,V.M.Shalaev,
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99,063903(2007).
13.A.Alu,N.Engheta,Phys.Rev.Lett.100,113901(2008).14.W.X.Jiang et al .,Phys.Rev.E Stat.Nonlin.Soft Matter
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15.See the supporting material on Science Online.
16.J.Li,J.B.Pendry,Phys.Rev.Lett.101,203901(2008).17.J.F.Thompson,B.K.Soni,N.P.Weatherill,Handbook of
Grid Generation (CRC Press,Boca Raton,FL,1999).18.P.Knupp,S.Steinberg,Fundamentals of Grid Generation
(CRC Press,Boca Raton,FL,1994).
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Phys.Rev.E Stat.Nonlin.Soft Matter Phys.71,036617(2005).
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21.B.J.Justice et al .,Opt.Express 14,8694(2006).22.This work was supported by a gift from Raytheon
毛蟹的做法Missile Systems (Tucson),and the rapid design approach was supported by a Multiple University Rearch Initiative supported by the Air Force Office of Scientific Rearch,contract no.FA9550-06-1-0279.T.J.C.
acknowledges the support from InnovateHan Technology,National Science Foundation of China (60871016and 60671015),National Basic Rearch Program (973)of China (2004CB719802),Natural Science Foundation of Jiangsu Province (BK2008031),and the 111Project (
111-2-05).We thank C.Harrison,N.Kundtz,and J.Allen for assistance for the experimental apparatus;A.Degiron for careful reading of the manuscript;Q.Cheng for the nonresonant element metamaterials technique development;and H.Schmitt,D.Barker (Raytheon Missile Systems),and M.West for helpful discussions.
Supporting Online Material
www.sciencemag/cgi/content/full/323/5912/366/DC1SOM Text Figs.S1to S6Movies S1to S5
8October 2008;accepted 5December 200810.1126/science.1166949
Coherent Intrachain Energy
黄晓明个人资料简介Migration in a Conjugated Polymer at Room Temperature
Elisabetta Collini and Gregory D.Scholes *
The intermediate coupling regime for electronic energy transfer is of particular interest
becau excitation moves in space,as in a classical hopping mechanism,but quantum pha informa
tion is conrved.We conducted an ultrafast polarization experiment specifically designed to obrve quantum coherent dynamics in this regime.Conjugated polymer samples with different chain conformations were examined as model multichromophoric systems.The data,recorded at room temperature,reveal coherent intrachain (but not interchain)electronic energy transfer.Our results suggest that quantum transport effects occur at room temperature when chemical donor-acceptor bonds help to correlate dephasing perturbations.N
umerous systems,such as natural photo-synthetic proteins and artificial polymers,organize light-absorbing molecules (chro-mophores)to channel photon energy to create elec-tronic or chemical gradients.The excitation energy from the absorbed light is either transferred through space or shared quantum mechanically among v-eral chromophores (1).The interplay among the classical and quantum limits of electronic energy transfer (EET)dynamics is dictated by the way the chromophores communicate with each other via long-range Coulombic interactions,as well as by the strength of perturbations from the bath of fluc-tuating nuclear motions in the molecular archi-tecture and surrounding external medium (2–6).An elusive intermediate EET regime is of par-ticular interest becau the excitation moves in space —which is a deterministic,classical attribute —
yet a preferred path can be adopted through wave function delocalization and associated interfer-en
ce effects,which introduce quantum character-istics to the dynamics (7).Together the attributes may in principle allow pha information to be transferred through space,with the electronic Ham-iltonian of the entire system thereby steering EET.By learning how to obrve the intermediate coupl-ing ca and thereafter to understand its properties,we could learn how to control excitation waves in a complex,multichromophoric system.Here,we prent the results of an ultrafast spectroscopy ex-periment specifically designed to probe quantum coherent EET in the intermediate coupling ca.Rapid decoherence —the loss of memory of the initial electronic transition frequency distribu-tion in an enmble,caud by random fluctua-tions due to interaction of the system with its surroundings —is the primary reason for the scarcity of reports of coherent EET in complex condend-pha systems.In the following,|0〉designates the ground state,|d 〉is the donor,and |a 〉is the acceptor.According to theory,the evolution of
the acceptor probability density in EET can be written as a product of forward (|d 〉to |a 〉)and rever propagations of the system [e.g.,(2)],which allows us to describe how the competition between electronic interaction and decoherence determines the EET dynamics.In the strong coupl-ing ca,the electronic coupling period dominates over decoherence;therefore,forward and rever donor-acceptor paths tend to be almost identical.Pha is prerved over each path,and a kind of st
anding wave connects the two states so that their evolution is intimately entangled in a quan-tum state.In the weak coupling ca,the fluctua-tions of the electronic transition frequency of a chromophore occur faster than the characteristic time of the donor-acceptor coupling.Owing to the tremendous number of different possible tra-jectories of transition energy fluctuations that can occur,the forward and rever donor-acceptor propagations differ,so that decoherence domi-nates and the excitation is localized on the donor or acceptor at any one time —but not on both simultaneously —and the EET dynamics follow classical rate laws.
The rate of EET is often measured by tran-sient absorption spectroscopy,where an ultrafast lar pul photoexcites the donor chromophores and a probe pul monitors the probability that the excitation has been transferred to an acceptor as a function of pump-probe delay time T .When the donor and acceptor chromophores have sim-ilar excitation energies,they cannot be spectrally distinguished,so we instead record anisotropy as a function of T .This technique has been exten-sively exploited to study EET in various kinds of multichromophoric systems (8–10).The anisot-ropy decay is caud by any process that changes the orientation of the chromophores probed rel-ative to tho initially photoexcited.For instance,electronic excitation could pass between two g-ments that are oriented at an angle in space.Alter-natively,an excited chromophore could physically
Department of Chemistry,Institute for Optical Sciences,and Center for Quantum Information and Quantum Control,Uni-versity of Toronto,Toronto,Ontario M5S 3H6,Canada.*To whom correspondence should be addresd.E-mail:gscholes@chem.utoronto.ca
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