A metamaterial analog of electromagnetically induc

a r X i v :0801.1485v 2 [p h y s i c s .o p t i c s ] 10 J a n 2008

A metamaterial analog of electromagnetically induced transparency

N.Papasimakis,V.A.Fedotov,and N.I.Zheludev

Optoelectronics Research Centre,University of Southampton,SO171BJ,UK ∗

S.L.Prosvirnin

Institute of Radio Astronomy,National Academy of Sciences of Ukraine,Kharkov,61002,Ukraine

(Dated:February 2,2008)We present a new type of electromagnetic planar metamaterial that exhibit strong dispersion at a local minimum of losses and is believed to be the first metamaterial analog of electromagneti-cally induced transparency.We demonstrate that pulses propagating through such metamaterials experience considerable delay,whereas the thickness of the structure along the direction of wave propagation is much smaller than the wavelength,which allows successive stacking of multiple metamaterial slabs.This leads to a significant increase in the band of normal dispersion,as well as in transmission levels.

Changes in the velocity of light propagating through dispersive media have been the subject of extensive in-vestigations in the past [1].In fact,it was predicted [2]and later observed [3,4]that light pulses can propagate with apparent velocities greater or smaller than in vac-uum without strong distortion of shape and width due to pulse reshaping phenomena.Today,control over these effects is essential for the development of optical com-munication technologies leading to a number of different approaches [5,6,7,8,9,10,11,12,13,14,15,16],such as the quantum phenomenon of electromagnetically induced transparency (EIT)[17,18].In that case,an otherwise opaque atomic medium is rendered transparent in a nar-row spectral region within the absorption line through quantum interference of a pump and a probe laser beam [17].This sharp dispersion has important consequences such as dramatically reducing the group velocity [5]and enhancing non-linear interactions [19].Most of the pro-posed techniques,however,involve special experimental conditions,e.g.cryogenic temperatures,coherent pump-ing and high intensities.

Recently,the implementation of EIT-like behavior in classical systems has attracted a lot of attention [20,21,22,23,24,25,26,27,28],since in this case the operating frequency can be tuned simply by vary-ing the system geometry,while no pumping is necessary.In particular,interference between coupled classical res-onators can lead to the same effects as EIT,i.e.narrow transmission resonances within the single-resonator stop-band.Nevertheless,existing approaches involve spatial dispersion at the wavelength scale,introducing,there-fore,fundamental constraints on the minimum thickness of the medium.In this letter,we demonstrate a classical analogue of EIT in planar metamaterials,namely metal-dielectric slabs of vanishing thickness along the propaga-tion direction,periodically patterned on a subwavelength scale.The phenomenon arises as a result of engaging ”trapped-mode”resonances that are weekly coupled to the free space leading to low transmission losses and ex-ceptionally high quality factors.Such modes are nor-

mally forbidden,but can be excited in planar metamate-rials with special patterning [29].

FIG.1:The bilayered fish-scale metamaterial and its unit cell.The two fish-scale patterns (red)reside in the top and bottom face of the dielectric,respectively,and are displaced along the meandering stripes by a half unit cell in respect to one another.

The studied metamaterial is based on the continuous fish-scale copper pattern,which is known for its reso-nant properties [30].To illustrate the difference between a conventional planar frequency selective structure and the suggested EIT-like metamaterial,we manufactured two types of structures.In the reference structure,the metallic pattern is etched on one side of the dielectric slab,while in the EIT-like metamaterial the pattern re-sides on both sides of the PCB laminate,so that the pattern on one side of the dielectric slab is shifted along the meandering strips by half a translational cell with respect to the pattern on the other side (see Fig.1).As it will be shown,this inversion of the second layer combined with the separation of the two layers leads to

strong confinement of electromagnetic energy in the gap between the two layers and,consequently,to significantly different properties than those of the reference struc-ture.Both metamaterials were manufactured by etching 35µm thick copperfilms onfiberglass PCB substrates of1.5mm thickness.The size of the translational cell was15mm×15mm rendering the metamaterials non-diffracting at frequencies below20GHz

.

FIG.2:Transmission amplitude(blue)and phase change (red)of the single(a)and the bilayered(b)fish-scale meta-material.Frequency regions of resonant anomalous(a)and normal(b)dispersion are highlighted.In both cases the po-larization is along the vertical axis as shown in the inset to Fig. 1.The current configurations are marked by the blue and green arrows in the insets showing the samples.In the inset to Fig.2b,the mechanical analog of the bilayeredfish scale and its response are shown.Numerically simulated cur-rent and energy density at the resonant frequency(5.5GHz) are shown in(c)and(d),respectively.

The transmission properties of the metamaterials were measured in an anechoic chamber at normal incidence, in the frequency range of2to14GHz,using two broad-band horn antennas and a vector network analyzer.The measured spectra for the single-and double-layerfish scales are presented in Figs.2a and2b,respectively. In the reference case of the singlefish-scale structure,a wide stop band is visible,centered at6.5GHz and ac-companied,as the Kramers-Kronig relations dictate,by anomalous dispersion.On the contrary,when the bi-layered metamaterial is considered(Fig.2b),the spec-trum exhibits a narrow transmission resonance centered at around5.5GHz,in the middle of the stop band of the reference structure.The bandwidth of the transparency window is0.5GHz,while the transmission level exceeds 20%.Moreover,the quality factor of this resonance is significantly higher(>10)than what is typically en-countered in frequency selective surfaces.As a result, very sharp normal dispersion is also observed,which can lead,subsequently,to long pulse delays.

The behavior of the double layerfish-scale is a result of ”trapped mode”excitation that is weakly coupled to free space radiation and originates from the special pattern-ing of the metamaterial.More concisely,as our numer-ical simulations show,the currents in the twofish-scale layers oscillate with opposite phases(Fig.2c),leading to concentration of electromagnetic energy in the region be-tween the overlapping segments(Fig.2d).In the far-field zone,the waves emitted by these resonant,antisymmet-ric currents interfere destructively,hence ensuring the high q-factor of the resonance by dramatically reducing scattering,the principal mechanism of losses in metama-terials at this frequency range.Furthermore,since the studied metamaterials exhibit no diffraction losses in the measured spectral range,the observed losses at the trans-mission peak can be attributed mainly to energy dissipa-tion in the dielectric(that may be reduced with a higher quality substrate),and secondarily to the weak scatter-ing that occurs at the non-overlapping curved segments of eachfish-scale layer.

The response of the bilayeredfish-scale metamaterial is a direct classical analog of EIT,as the weak coupling of the counter-propagating currents to free space in the metamaterial is reminiscent of the weak probability for photon absorption in EIT[17].The main difference lies in the fact that,in the present case,the transparent state is a result of classicalfield interference,rather than quan-tum interference of atomic excitation pathways.More-over,in the EIT-like metamaterial system no external pumping is required.In fact,similarly to how an EIT sys-tem may be modeled by a set of interacting classical har-monic oscillators[20],the response of the bilayered meta-material may also be explained by appealing to coupled classical oscillators:the currents on the twofish-scale lay-ers can be represented by two oscillating masses on elas-tic springs coupled through much softer springs to a third lighter mass,which accounts for the far-field interference of the two layers(see inset to Fig.2b).In this analogy, the small mass is subject to friction,which represents the scattering losses of the metamaterial,while the two large mass oscillators are lossless.The system is excited by3

an external force acting on both large mass oscillators, representing the incident electromagnetic wave.When the oscillators are identical,the mechanical system sup-ports only symmetric modes leading to high-amplitude oscillations of the small mass and consequently to high dissipation.However,the situation can change by intro-ducing a small asymmetry,for example by allowing dif-ferent stiffness in the springs coupling the large masses to the smaller one(see inset to Fig.2).This allows for the antisymmetric mode to be excited,where the two large masses oscillate with large amplitudes and opposite phases,while the small mass remains still.All the energy pumped by the external force is being stored in the os-cillations of the large masses and the dissipative losses in the system are thus minimized.In the metamaterial case,the excitation of the”trapped mode”is achieved by the relative displacement of the two layers along the propagation direction,which leads to a phase difference in their excitation by the incident electromagnetic wave. In fact,the response of both the metamaterial and the oscillator system are very similar exhibiting high qual-ity factor resonances,as shown in the inset to Fig.2b. However,in thefirst case,the resonance is broadened by additional(dissipative and radiative)losses resulting in a weaker transmission

peak.

FIG.3:Reconstructed response of the bilayeredfish scale (red)to a2.5ns microwave Gaussian pulse(blue)with center frequency at the maximum of the transmission window.The transmitted pulse is delayed by40%of the pulse width,when compared to a pulse propagating through free space(grey). The EIT-like nature of the meta-material response can be further illustrated by considering propagating elec-tromagnetic pulses,rather than monochromatic plane waves.Indeed the ability to delay pulses substantially with only small attenuation and minimal distorsion is a most characteristic and useful property of EIT media.To this end,we reconstruct the response of the metamaterial by applying the inverse Fourier transform to the convolu-tion of the transmission spectrum with the pulse power spectrum.In particular,we consider Gaussian-shaped pulses with2.5ns width at half maximum.The center frequency of the pulse is near the peak of the transmis-sion band,while its spectral width is roughly equal to that of the pass band.As a result of the strong nor-mal dispersion,a microwave pulse propagating through the bilayeredfish-scale array will be delayed by∼1ns, which is greater than1/3of the incident pulse width (see Fig.3).At the same time,the pulse retains its Gaussian shape with the exception of a weak broadening, since most of its spectral power lies in regions where the phase derivative is approximately constant.Achieving this level of pulse delay is remarkable when one consid-ers the thickness(λ/35)of the structure.Moreover,the transmission is reasonably high,exceeding∼15%(may be improved by using substrates with lower losses),and enables the successive stacking of metamaterial slabs,at the expense,however,of pulse intensity.

Indeed,we demonstrated that thefish-scale design can be cascaded by stacking multiple layers in such a way, that each slab is inverted with respect to the adjacent ones(see insets to Fig.4),while the distance between successivefish-scale patterns is defined by the thickness of the dielectric substrates(1.5mm).The experimental results for three and fourfish-scale layers are shown in Figs.4a and4b,respectively.In both cases,stacking of multiple slabs results in an increase of maximum trans-mitted intensity and width of the frequency region,where normal dispersion occurs.More concisely,with each ad-ditional layer,a new transmission peak appears shifted at lower frequencies with respect to the bilayered case. At the same time,the sharp normal phase dispersion ex-tends over a wide frequency band exceeding1.5GHz and2.5GHz for three and four layers,respectively.This allows to address the frequent requirement of practical applications for high bandwidth,whereas the thickness of the resulting metamaterial remains much smaller than the wavelength(at leastλ/10in the present case).

In conclusion,we propose a new type of type of pla-nar meta-material,which shows behavior analogous to that of EIT media,enabling thus long optical delays in very thin,sub-wavelength structures.This approach al-lows successive stacking of metamaterial layers,in order to increase transmission and bandwidth.These proper-ties make such metamaterials particularly appealing as broadband,ultra-compact delay lines operating at a pre-scribed wavelengths.

The authors would like to acknowledge thefinancial support of the Engineering and Physical Sciences Re-search Council,UK.

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∗Electronic address:N.Papasimakis@soton.ac.uk4

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