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NegativeRefractionUsingFrequency-Tuned ...
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Hindawi Publishing Corporation Advances in OptoElectronics Volume 2008, Article ID 948614, 4 pages doi:10.1155/2008/948614 Research Article Negative Refraction Using Frequency-Tuned Oxide Multilayer Structure Yalin Lu, 1 Gail J. Brown, 2 and Kitt Reinhardt 3 1 Laser and Optics Research Center (LORC), Department of Physics, U.S. Air Force Academy, CO 80840, USA 2 AFRL/ RXPSO, Wright-Patterson Air Force Base, Building 651, 3005 Hobson Way, OH 45433, USA 3 AFOSR/NE, Suite 326, 875 North Randolph Street, Arlington, VA 22203, USA Correspondence should be addressed to Yalin Lu, [email protected] Received 14 May 2008; Accepted 31 August 2008 Recommended by Hiroshi Murata An oxide-based multilayer structure was proposed to realize negative refraction. The multilayer composes of alternative layers having negative permittivity and negative permeability, respectively. In order to realize negative refraction, their dielectric and magnetic resonances of layers will be tuned to the frequency as close as possibly via changing their temperature, composition, structure, and so forth. Such oxide-based NIMs are attractive for their potential applications as optical super lenses, imagers, optical cloaking, sensors, and so forth, those are required with low-loss, low-cost, and good fabrication flexibility. Copyright © 2008 Yalin Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Negative index materials (NIMs) have attracted extensive attention in recent years since the first observation of negative refraction in those artificially made metamaterials consisting of arrays of metallic rings/rods [1]. Majority of such NIMs use metallic split ring resonance (SRR), surface plasmonic resonance, or a combination of magnetic and metallic materials with naturally occurring negative perme- ability (μ) or negative permittivity (ε). Very unique prop- erties of such metamaterials, including negative refraction, have been previously demonstrated mainly for operation in microwave frequencies. A new trend of current NIM research is toward the optical frequency. For example, a lossless negative index slab material could act as a “superlens” or a “perfect lens,” which could image object with a high resolution far below the conventional optical diffraction limit, and are attractive to those applications including data storage, medical imaging, biophysics, and so forth. In addition to those metamaterials, negative refraction has also been found in other material formats including planar transmission lines, photonic crystals, and so forth. However, all such NIMs use complicated artificial structures requiring high-precision nanofabrication and can hardly be rigorously considered as uniform materials, since the size of their structural elements is usually greater than one tenth of the operation wavelength. In addition, certain polarization and incident angle of an electromagnetic (EM) field must be maintained in order to realize such negative refraction. Considering the fact that an SRR in a metamaterial produces −εψ and −μψ , respectively [2], such a metamate- rial will be similar to a multilayer composed by alternating −εψ and −μψ layers—the later will be much easier to realize as a natural material. It is also well known that some natural materials have inherent −εψ or −μ, which will be useful for multilayer NIM fabrications. For example, certain ferrites have −μ in microwave frequencies, and many conducting materials have −ε below the plasma frequency. Studies toward this direction have been performed, mostly by simulations, in stacked ferrite-dielectric waveguides, ferrite-metal, ferromagnetic-superconductor, and ferrite- semiconductor multilayers [3]. However, the use of conduc- tive materials may excite surface waves at their interfaces, which in turn change their electromagnetic characters, and more seriously, result in a significant high-loss concern. Apparently, an NIM composing of nonconductive optical materials will be promising. Availability of the frequency tunability to an optical NIM will provide a much bigger freedom in exploring its potential applications as sensors, modulators, switches, and
Transcript of NegativeRefractionUsingFrequency-Tuned ...
Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2008, Article ID 948614, 4 pagesdoi:10.1155/2008/948614
Research Article
Negative Refraction Using Frequency-TunedOxide Multilayer Structure
Yalin Lu,1 Gail J. Brown,2 and Kitt Reinhardt3
1 Laser and Optics Research Center (LORC), Department of Physics, U.S. Air Force Academy, CO 80840, USA2 AFRL/ RXPSO, Wright-Patterson Air Force Base, Building 651, 3005 Hobson Way, OH 45433, USA3 AFOSR/NE, Suite 326, 875 North Randolph Street, Arlington, VA 22203, USA
Correspondence should be addressed to Yalin Lu, [email protected]
Received 14 May 2008; Accepted 31 August 2008
Recommended by Hiroshi Murata
An oxide-based multilayer structure was proposed to realize negative refraction. The multilayer composes of alternative layershaving negative permittivity and negative permeability, respectively. In order to realize negative refraction, their dielectric andmagnetic resonances of layers will be tuned to the frequency as close as possibly via changing their temperature, composition,structure, and so forth. Such oxide-based NIMs are attractive for their potential applications as optical super lenses, imagers,optical cloaking, sensors, and so forth, those are required with low-loss, low-cost, and good fabrication flexibility.
Copyright © 2008 Yalin Lu et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
Negative index materials (NIMs) have attracted extensiveattention in recent years since the first observation ofnegative refraction in those artificially made metamaterialsconsisting of arrays of metallic rings/rods [1]. Majority ofsuch NIMs use metallic split ring resonance (SRR), surfaceplasmonic resonance, or a combination of magnetic andmetallic materials with naturally occurring negative perme-ability (μ) or negative permittivity (ε). Very unique prop-erties of such metamaterials, including negative refraction,have been previously demonstrated mainly for operationin microwave frequencies. A new trend of current NIMresearch is toward the optical frequency. For example, alossless negative index slab material could act as a “superlens”or a “perfect lens,” which could image object with a highresolution far below the conventional optical diffractionlimit, and are attractive to those applications includingdata storage, medical imaging, biophysics, and so forth.In addition to those metamaterials, negative refraction hasalso been found in other material formats including planartransmission lines, photonic crystals, and so forth. However,all such NIMs use complicated artificial structures requiringhigh-precision nanofabrication and can hardly be rigorouslyconsidered as uniform materials, since the size of their
structural elements is usually greater than one tenth of theoperation wavelength. In addition, certain polarization andincident angle of an electromagnetic (EM) field must bemaintained in order to realize such negative refraction.
Considering the fact that an SRR in a metamaterialproduces −εψ and −μψ, respectively [2], such a metamate-rial will be similar to a multilayer composed by alternating−εψ and −μψ layers—the later will be much easier torealize as a natural material. It is also well known thatsome natural materials have inherent −εψ or −μ, whichwill be useful for multilayer NIM fabrications. For example,certain ferrites have −μ in microwave frequencies, and manyconducting materials have −ε below the plasma frequency.Studies toward this direction have been performed, mostlyby simulations, in stacked ferrite-dielectric waveguides,ferrite-metal, ferromagnetic-superconductor, and ferrite-semiconductor multilayers [3]. However, the use of conduc-tive materials may excite surface waves at their interfaces,which in turn change their electromagnetic characters, andmore seriously, result in a significant high-loss concern.Apparently, an NIM composing of nonconductive opticalmaterials will be promising.
Availability of the frequency tunability to an opticalNIM will provide a much bigger freedom in exploring itspotential applications as sensors, modulators, switches, and
2 Advances in OptoElectronics
so forth. Variable electromagnetic response when changing ametamaterial’s structure is not a practical way of frequencytuning. External tuning via filling liquid crystals and pho-toconductive materials to metamaterials will work for somefrequencies. It is normally slow and has concern on bothreliability and stability of performances.
This manuscript intends to discuss one possible mech-anism potential able to realize negative refraction using alloxide-base materials in the format of multilayer. Such oxide-based negative index multilayers are expected to potentiallyhave low optical losses, against to those existing designs usingconductive materials, and are potentially frequency-tunableif the NIM’s composing materials are dielectrically tunableby external fields including electric, optical, and microwave.Tunable dielectrics are easily realizable in many piezoelectricand piezomagnetic complex oxides. Therefore, the impactof such NIMs to their potential applications such as superlenses, optical cloaking, optoelectronics, and sensing can besignificant.
2. Oxide Multilayer NIMs
The mechanism to build the oxide multilayer NIM to bediscussed is a resonance-tuned multilayer (RTM) composingof alternative dielectric and magnetic oxide layers havingnaturally occurring −εψ or −μ, respectively, and havingtheir resonance frequencies finely tuned to concurrence viaboth structural and compositional engineering to both usedmaterials.
The RTM mechanism considers the nonlattice-matchedmultilayer case and the two alternative oxide layers asthe multilayer have −μ or −ε, respectively. For example,the oxide multilayer can be represented as (A/B)m, and“A” has an intrinsic dielectric resonance, and “B” rep-resents a material with an intrinsic magnetic resonance.The RTM approach will be used to fine-tune the tworesonance frequencies concurrence together, and realize thenegative refraction immediately after the merged resonancefrequency. Fine-tuning to each oxide material can be realizedby changing composition, structure, temperature, magneticfield, and so forth. Schematic of the RTM NIM is shownin Figure 1. In Figure 1, only two adjacent laminas (onedielectric and the other magnetic) having thickness of d1
and d2, respectively, are shown. They will be the buildingblock for further making into the multilayer structure. Theinsets on the right side schematically show the frequencyspectra of both permittivity and permeability around theresonance frequencies. Arrows indicate the directions offrequency tuning to make two resonance frequencies con-currence. Figure 2 shows the schematic multilayer structureand the concurrence-occurred frequency spectra showingthe frequency region with both negative permittivity andnegative permeability.
In order to achieve a concurrence of both dielectric andmagnetic resonances in dielectric and magnetic oxide mate-rials, different origins of dielectric and magnetic responseshave to be considered for different frequencies ranging fromthe UV/visible, far-infrared (including the major terahertzband), to microwave. For the UV to visible spectrum,
d1
d2
Dielectric, −ε
Magnetic, −μ
Building block for the multilayer Magnetic resonance
Dielectric resonance
Frequency ω
Tuning
Tuning
ω2
ω1
+ε
0
−+μ
0
−
Figure 1: Schematic of a negative permittivity and negativepermeability double layer (the building block for multilayer, theleft side of the figure) and tuning of their resonance frequencies toconcurrence-occur to the same frequency (inset at the right side).
for example, the dielectric response is primarily from theelectronic polarization modes and the magnetic responsefrom the magnetic dipoles. In the far-IR range, ionic polar-ization modes, and antiferromagnetic resonances (AFMRs)are mainly responsible for dielectric and magnetic responses,respectively. Similarly, for those microwave frequencies,electronic dipole reorientation (domain wall moving) andferromagnetic resonances (FMRs) are the main causes.
Other than the resonance frequency of the concern-ing materials, both degree of damping and amplitude ofdielectric and magnetic responses will also play the keyrule. For example, in optical frequencies, direct magneticdipole response is orders of magnitude weaker than elec-tronic dipole response. The above-discussed SCS mechanismactually provides an indirect coupling of the magnetic dipoleresponse to a strong electronic dipole resonance via thephonon resonance, yielding both negative permeability andnegative permittivity after the phonon resonance frequency.
The dielectric dispersion due to the electronic dipolepolarization can be fitted to the following empirical expres-sion:
ε∗(ω)− ε∞1
ε0 − ε∞1=
n∑
i=1
gi
[1
(1 + iωτi)
], (1)
where ε∞1 is the permittivity due to the ionic polarization, ε0
is the low-frequency permittivity, ω is the angular frequency,and gi is the distribution of relaxation time (τi). On the otherhand, the dielectric dispersion due to the ionic polarizationcan be fitted to the following four-parameter semiquantummodel [4]:
ε∗(ω) = ε∞2
n∏
j=1
ω2jLO − ω2 + iγ jLOω
ω2jTO − ω2 + iγ jTOω
, (2)
where ε∞2 is the permittivity due to the electronic polar-ization, n is the number of optical phonon mode, γ isthe damping factor, and TO and LO represent transverse
Advances in OptoElectronics 3
−μ
−ε
−μ
−ε
−μ
−ε
ε(ω
)/ε 0
,μ(ω
)/μ
0
Concurrence-occurredresonance frequencies
Frequency-tunedmultilayer
Frequency
ε(ω)μ(ω)
Figure 2: Schematic of the frequency-tuned multilayer structure(left) and the concurrence-occurred resonances on both permit-tivity and permeability (right). After the concurrence-occurredresonance frequency, both negative permittivity and negativepermeability will occur, which indicates negative optical refraction.
and longitudinal optical phonon modes, respectively. Therelationship between the ε∗ and IR reflectivity R(ω) can begiven by
R(ω) =∣∣∣∣∣
(√ε∗(ω)− 1
)(√ε∗(ω) + 1
)∣∣∣∣∣. (3)
Equations (1), (2), and (3) permit a direct identificationof the dielectric spectra and resonance frequencies viathe experimental IR reflectivity measurement on a specificdielectric material system. Contribution from domain wallrelaxation is usually masked by electronic and ionic relax-ations, unless the temperature is close to the material’sCurie temperature or phase transition temperature. It hasbeen usually reported at above 100 kHz frequencies, will beminor to those optical frequencies of our current discussioninterest.
Magnetic resonances can be identified from recordingthe complex permeability spectra on those magnetic oxidematerials of interests. Accordingly, the complex permeabilitycan be expressed as a superposition of two contributions,
μ(ω) = 1+∼χdw(ω)+
∼χrot(ω), namely, the domain wall compo-
nent∼χdw(ω) and the magnetic moment rotation
∼χrot(ω):
∼χdw(ω) = χdwω
2dw
ω2dw − ω2 + j(β/mdw)ω
,
∼χrot =
(ωrot + jαω)χrotωrot
(ωrot + jαω)2 − ω2,
(4)
where χdw and χrot are static (or low frequency) susceptibili-ties for domain wall (DW) and magnetic moment rotation(ROT) motions, ωdw and ωrot are resonance frequenciesof DW and ROT components, β and α are correspondingdamping factors, mdw is the effective mass of wall, and ω isthe frequency of the driving ac magnetic field. Descriptionof magnetic moment motions will be highly dependent onmaterials. For simplicity, we consider both AFMR and FMRcases which will be similar in theory.
In a magnetic material having a uniaxial anisotropy andthe magnetic field is applied parallel to the easy axis, theAFMR frequency ωAFMR at low temperature (below Neeltemperature) is given by
2πωAFMR
γ=√
2HEHA ±H , (H < HSF),
2πωAFMR
γ=√H2 − 2HEHA, (H > HSF),
(5)
where γ(≡ gμB/�) is the magnetomechanical ratio, HE is theexchange field,HA is the anisotropy field, andHSF is the spin-flop field. When H is applied perpendicular to the easy axis,then the ωAFMR is given by
2πωAFMR
γ=√H2 + 2HEHA. (6)
For FMR, a simple expression about the ωFMR is Kittel’sequation
ωFMR
γ=√
(HA,eff +HE)4πMs, (7)
where HA,eff is the effective anisotropy field, and 4πMs thesaturation magnetization. For both AFMR and FMR casesand when for qualitative analyses, it can be simplified to ω ∝√HAHE.
Depending on the material selection for such multilayer,the above equations provide the way to measure theirresonance frequencies via a variety of approaches includingoptical reflection, time-domain terahertz (THz) transmis-sion, magnetic analysis, and so forth. The above equationsalso theoretically provide the direction to realize the efficientfrequency tuning in order to achieve concurrence of bothdielectric and magnetic resonance frequencies.
3. Frequency Tuning
Tuning both dielectric and magnetic resonance frequenciesmay follow a few different ways. In certain ferroelectricmaterials, optical mode of the lattice (phonon) is depen-dent on both temperature (T) and the material’s Curietemperature (Tc), roughly following an empirical relation:ω2 ∝ (T − Tc) as an example. As an example, Figure 3shows the dependence of relative dielectric constant on thecomposition. The dielectric maximum occurs at xBa∼0.7 [atwhere the ferroelectric-paraelectric boundary (FPB) occurs],and it Curie temperature changes from 415 K (xBa∼1) toabout 40 K (xBa∼0) almost linearly [5]. Similarly, tuningby changing both temperature and material compositionis also applicable to some magnetic oxide materials. Insetin Figure 2 show a general frequency tuning schematic viachanging the temperature, in order to reach a concurrenceat the same frequency for both dielectric and magneticresonances. Apparently, tuning their compositions to reacha room temperature operation of the NIMs will be themost attractive, simply because of the practicability forapplications.
4 Advances in OptoElectronicsR
elat
ive
diel
ectr
icco
nst
ant
(ε)
0
100
200
300
400
500
Composition
BaTiO3 0.2 0.4 0.6 0.8 SrTiO3
Cu
rie
tem
per
atu
re(k
)
0
100
200
300
400
Temperature
Res
onan
cefr
equ
ency
Dielectric
Magnetic
Figure 3: Dependence of the dielectric constant and Curie tem-perature of (Ba,Sr)TiO3 on its composition. Inset shows a possiblefrequency tuning by changing the temperature for reaching theconcurrence of both dielectric and magnetic resonance frequencies.
Measuring μ
Eas
yax
is
θ
Figure 4: Schematic of the multilayer structure alignment requiredfor possibly tuning the FMR resonance frequency via changingthe structural parameters—width, period, duty cycle, and theorientation angle.
An alternative way of possibly tuning the magneticresonance frequency is by changing the magnetic layer’salignment inside the multilayer structure. Figure 4 shows theschematic of such a structure in which the FMR frequencywill be tuned by changing either the orientation angleθ or the layer thickness, following the rewritten Kittel’sformula involving both uniaxial anisotropy field (Hu) andthe additional shape anisotropy field (Hk,eff) into the totaleffective anisotropy field (HA,eff)
HA,eff = Hu +Hk,eff cosθ,
2πωAFMR
γ=√
4πMsHA,eff.(8)
In Figure 4, the main picture shows the parallel straitstructure to be made in the magnetic layer inside thesuperlattice, via selective etching the as-fabricated magneticlayer or mask-shielding growth, and so forth. The inset showsthat when one measures the permeability horizontally, theresult will be actually tunable by changing the strait’s size(both period and width) or by changing the angle respective
to the easy axis of the magnetic material. The multilayerstructure itself to be discussed in this theory actually providesthe great easiness to reach such frequency tuning for themagnetic part inside the multilayer. Structural parametersthat can be varied when designing include the layer thickness,periodic duty cycle, and magnetic orientation, and so forth.An efficient way to optimize material compositions andstructural parameters may follow the combinatorial strategy[6]. Effort toward efficient material selection, simulation forfrequency tuning, and the multilayer fabrication is ongoingand will be published separately.
4. Conclusion
One possible physical mechanism toward realizing negativerefraction in a fully oxide-based multilayer was theoreticallydiscussed. Inside the multilayer structure, such negativerefraction may be achieved by tuning their resonancesto the same frequency via changing temperature, layercomposition, structural parameter, and so forth. Such oxide-based NIMs are attractive for their potential applicationsas optical super lenses, imagers, sensors, and so forth, thatare potential with low-loss, cost-effectiveness, and goodfabrication flexibility.
References
[1] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimentalverification of a negative index of refraction,” Science, vol. 292,no. 5514, pp. 77–79, 2001.
[2] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis,“Determination of effective permittivity and permeability ofmetamaterials from reflection and transmission coefficients,”Physical Review B, vol. 65, no. 19, Article ID 195104, 5 pages,2002.
[3] R. H. Tarkanyan and D. G. Niarchos, “Effective negativerefractive index in ferromagnet-semiconductor superlattices,”Optics Express, vol. 14, no. 12, pp. 5433–5444, 2006.
[4] F. Gervais, “High-temperature infrared reflectivity spec-troscopy by scanning interferometry,” in Infrared and MillimeterWaves, K. J. Button, Ed., vol. 8, pp. 279–339, Academic Press,New York, NY, USA, 1983.
[5] J. Li, F. Duewer, C. Gao, H. Chang, X.-D. Xiang, and Y. Lu,“Electro-optic measurements of the ferroelectric-paraelectricboundary in Ba1−xSrxTiO3 materials chips,” Applied PhysicsLetters, vol. 76, no. 6, pp. 769–771, 2000.
[6] Y. Lu, “The structural engineering strategy for photonicmaterial research and device development,” Active and PassiveElectronic Components, vol. 2007, Article ID 17692, 7 pages,2007.
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