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R. Shelby, David Smith, S. Schultz (2001)
Experimental Verification of a Negative Index of RefractionScience, 292
Roland Tarkanyan, D. Niarchos (2006)
Effective negative refractive index in ferromagnet-semiconductor superlattices.Optics express, 14 12
David Smith, S. Schultz, P. Markoš, C. Soukoulis (2001)
Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficientsPhysical Review B, 65
Yalin Lu (2007)
The Structural Engineering Strategy for Photonic Material Research and Device DevelopmentActive and Passive Electronic Components, 2007
Jing-Wei Li, F. Duewer, C. Gao, Hauyee Chang, X. Xiang, Yalin Lu (2000)
Electro-optic measurements of the ferroelectric-paraelectric boundary in Ba1−xSrxTiO3 materials chipsApplied Physics Letters, 76
(1983)
High-temperature infrared reflectivity spectroscopy by scanning interferometry
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 1 2 3 Yalin Lu, Gail J. Brown, and Kitt Reinhardt Laser and Optics Research Center (LORC), Department of Physics, U.S. Air Force Academy, CO 80840, USA AFRL/ RXPSO, Wright-Patterson Air Force Base, Building 651, 3005 Hobson Way, OH 45433, USA AFOSR/NE, Suite 326, 875 North Randolph Street, Arlington, VA 22203, USA Correspondence should be addressed to Yalin Lu, yalin.lu@usafa.edu 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 structural elements is usually greater than one tenth of the operation wavelength. In addition, certain polarization and Negative index materials (NIMs) have attracted extensive incident angle of an electromagnetic (EM) field must be attention in recent years since the first observation of maintained in order to realize such negative refraction. negative refraction in those artificially made metamaterials Considering the fact that an SRR in a metamaterial consisting of arrays of metallic rings/rods [1]. Majority of produces −εψ and −μψ,respectively[2], such a metamate- such NIMs use metallic split ring resonance (SRR), surface rial will be similar to a multilayer composed by alternating plasmonic resonance, or a combination of magnetic and −εψ and −μψ layers—the later will be much easier to realize as a natural material. It is also well known that metallic materials with naturally occurring negative perme- ability (μ) or negative permittivity (ε). Very unique prop- some natural materials have inherent −εψ or −μ,which erties of such metamaterials, including negative refraction, will be useful for multilayer NIM fabrications. For example, certain ferrites have −μ in microwave frequencies, and many have been previously demonstrated mainly for operation in microwave frequencies. A new trend of current NIM conducting materials have −ε below the plasma frequency. research is toward the optical frequency. For example, a Studies toward this direction have been performed, mostly lossless negative index slab material could act as a “superlens” by simulations, in stacked ferrite-dielectric waveguides, or a “perfect lens,” which could image object with a high ferrite-metal, ferromagnetic-superconductor, and ferrite- resolution far below the conventional optical diffraction semiconductor multilayers [3]. However, the use of conduc- limit, and are attractive to those applications including tive materials may excite surface waves at their interfaces, data storage, medical imaging, biophysics, and so forth. which in turn change their electromagnetic characters, and more seriously, result in a significant high-loss concern. In addition to those metamaterials, negative refraction has also been found in other material formats including planar Apparently, an NIM composing of nonconductive optical transmission lines, photonic crystals, and so forth. However, materials will be promising. all such NIMs use complicated artificial structures requiring Availability of the frequency tunability to an optical high-precision nanofabrication and can hardly be rigorously NIM will provide a much bigger freedom in exploring its considered as uniform materials, since the size of their potential applications as sensors, modulators, switches, and 2 Advances in OptoElectronics Dielectric resonance so forth. Variable electromagnetic response when changing a metamaterial’s structure is not a practical way of frequency Tuning tuning. External tuning via filling liquid crystals and pho- toconductive materials to metamaterials will work for some d Dielectric, −ε frequencies. It is normally slow and has concern on both reliability and stability of performances. − 1 This manuscript intends to discuss one possible mech- Frequency ω anism potential able to realize negative refraction using all oxide-base materials in the format of multilayer. Such oxide- based negative index multilayers are expected to potentially d Magnetic, −μ have low optical losses, against to those existing designs using conductive materials, and are potentially frequency-tunable Tuning if the NIM’s composing materials are dielectrically tunable 2 by external fields including electric, optical, and microwave. Building block for the multilayer Magnetic resonance Tunable dielectrics are easily realizable in many piezoelectric Figure 1: Schematic of a negative permittivity and negative and piezomagnetic complex oxides. Therefore, the impact permeability double layer (the building block for multilayer, the of such NIMs to their potential applications such as super left side of the figure) and tuning of their resonance frequencies to lenses, optical cloaking, optoelectronics, and sensing can be concurrence-occur to the same frequency (inset at the right side). significant. 2. Oxide Multilayer NIMs for example, the dielectric response is primarily from the electronic polarization modes and the magnetic response The mechanism to build the oxide multilayer NIM to be from the magnetic dipoles. In the far-IR range, ionic polar- discussed is a resonance-tuned multilayer (RTM) composing ization modes, and antiferromagnetic resonances (AFMRs) of alternative dielectric and magnetic oxide layers having are mainly responsible for dielectric and magnetic responses, naturally occurring −εψ or −μ, respectively, and having respectively. Similarly, for those microwave frequencies, their resonance frequencies finely tuned to concurrence via electronic dipole reorientation (domain wall moving) and both structural and compositional engineering to both used ferromagnetic resonances (FMRs) are the main causes. materials. Other than the resonance frequency of the concern- The RTM mechanism considers the nonlattice-matched ing materials, both degree of damping and amplitude of multilayer case and the two alternative oxide layers as dielectric and magnetic responses will also play the key the multilayer have −μ or −ε, respectively. For example, rule. For example, in optical frequencies, direct magnetic the oxide multilayer can be represented as (A/B) ,and dipole response is orders of magnitude weaker than elec- “A” has an intrinsic dielectric resonance, and “B”rep- tronic dipole response. The above-discussed SCS mechanism resents a material with an intrinsic magnetic resonance. actually provides an indirect coupling of the magnetic dipole The RTM approach will be used to fine-tune the two response to a strong electronic dipole resonance via the resonance frequencies concurrence together, and realize the phonon resonance, yielding both negative permeability and negative refraction immediately after the merged resonance negative permittivity after the phonon resonance frequency. frequency. Fine-tuning to each oxide material can be realized The dielectric dispersion due to the electronic dipole by changing composition, structure, temperature, magnetic polarization can be fitted to the following empirical expres- field, and so forth. Schematic of the RTM NIM is shown sion: in Figure 1.In Figure 1, only two adjacent laminas (one dielectric and the other magnetic) having thickness of d 1 n ε (ω) − ε 1 ∞1 and d , respectively, are shown. They will be the building = g ,(1) ε − ε (1 + iωτ ) 0 ∞1 i i=1 block for further making into the multilayer structure. The insets on the right side schematically show the frequency where ε is the permittivity due to the ionic polarization, ε ∞1 0 spectra of both permittivity and permeability around the is the low-frequency permittivity, ω is the angular frequency, resonance frequencies. Arrows indicate the directions of and g is the distribution of relaxation time (τ ). On the other i i frequency tuning to make two resonance frequencies con- hand, the dielectric dispersion due to the ionic polarization currence. Figure 2 shows the schematic multilayer structure can be fitted to the following four-parameter semiquantum and the concurrence-occurred frequency spectra showing model [4]: the frequency region with both negative permittivity and negative permeability. n 2 ω − ω + iγ ω j LO j LO In order to achieve a concurrence of both dielectric and ε (ω) = ε ,(2) ∞2 ω − ω + iγ ω j TO magnetic resonances in dielectric and magnetic oxide mate- j TO j=1 rials, different origins of dielectric and magnetic responses have to be considered for different frequencies ranging from where ε is the permittivity due to the electronic polar- ∞2 the UV/visible, far-infrared (including the major terahertz ization, n is the number of optical phonon mode, γ is band), to microwave. For the UV to visible spectrum, the damping factor, and TO and LO represent transverse Advances in OptoElectronics 3 In a magnetic material having a uniaxial anisotropy and −μ the magnetic field is applied parallel to the easy axis, the AFMR frequency ω at low temperature (below Neel ´ −ε AFMR Concurrence-occurred temperature) is given by −μ resonance frequencies 2πω AFMR −ε = 2H H ± H,(H< H ), E A SF (5) −μ 2πω AFMR = H − 2H H ,(H> H ), E A SF −ε γ Frequency-tuned Frequency where γ(≡ gμ /) is the magnetomechanical ratio, H is the B E multilayer exchange field, H is the anisotropy field, and H is the spin- A SF ε(ω) flop field. When H is applied perpendicular to the easy axis, μ(ω) then the ω is given by AFMR Figure 2: Schematic of the frequency-tuned multilayer structure (left) and the concurrence-occurred resonances on both permit- 2πω AFMR = H +2H H . (6) E A tivity and permeability (right). After the concurrence-occurred resonance frequency, both negative permittivity and negative permeability will occur, which indicates negative optical refraction. For FMR, a simple expression about the ω is Kittel’s FMR equation and longitudinal optical phonon modes, respectively. The ω FMR = (H + H )4πM,(7) A,eff E s relationship between the ε and IR reflectivity R(ω)can be given by where H is the effective anisotropy field, and 4πM the A,eff s ε (ω) − 1 saturation magnetization. For both AFMR and FMR cases R(ω) = . (3) ε (ω)+1 and when for qualitative analyses, it can be simplified to ω ∝ H H . A E Equations (1), (2), and (3) permit a direct identification Depending on the material selection for such multilayer, of the dielectric spectra and resonance frequencies via the above equations provide the way to measure their the experimental IR reflectivity measurement on a specific resonance frequencies via a variety of approaches including dielectric material system. Contribution from domain wall optical reflection, time-domain terahertz (THz) transmis- relaxation is usually masked by electronic and ionic relax- sion, magnetic analysis, and so forth. The above equations ations, unless the temperature is close to the material’s also theoretically provide the direction to realize the efficient Curie temperature or phase transition temperature. It has frequency tuning in order to achieve concurrence of both been usually reported at above 100 kHz frequencies, will be dielectric and magnetic resonance frequencies. minor to those optical frequencies of our current discussion interest. Magnetic resonances can be identified from recording 3. Frequency Tuning the complex permeability spectra on those magnetic oxide Tuning both dielectric and magnetic resonance frequencies materials of interests. Accordingly, the complex permeability mayfollowafewdifferent ways. In certain ferroelectric can be expressed as a superposition of two contributions, ∼ ∼ materials, optical mode of the lattice (phonon) is depen- χ χ μ(ω) = 1+ (ω)+ (ω), namely, the domain wall compo- dw rot dent on both temperature (T) and the material’s Curie ∼ ∼ χ χ nent (ω) and the magnetic moment rotation (ω): temperature (T ), roughly following an empirical relation: dw rot ω ∝ (T − T ) as an example. As an example, Figure 3 χ ω dw dw shows the dependence of relative dielectric constant on the (ω) = , dw ω − ω + j (β/m )ω dw dw composition. The dielectric maximum occurs at x ∼0.7[at Ba (4) where the ferroelectric-paraelectric boundary (FPB) occurs], (ω + jαω)χ ω rot rot rot = , rot and it Curie temperature changes from 415 K (x ∼1) to Ba (ω + jαω) − ω rot about 40 K (x ∼0) almost linearly [5]. Similarly, tuning Ba where χ and χ are static (or low frequency) susceptibili- by changing both temperature and material composition dw rot ties for domain wall (DW) and magnetic moment rotation is also applicable to some magnetic oxide materials. Inset (ROT) motions, ω and ω are resonance frequencies in Figure 2 show a general frequency tuning schematic via dw rot of DW and ROT components, β and α are corresponding changing the temperature, in order to reach a concurrence damping factors, m is the effective mass of wall, and ω is at the same frequency for both dielectric and magnetic dw the frequency of the driving ac magnetic field. Description resonances. Apparently, tuning their compositions to reach of magnetic moment motions will be highly dependent on a room temperature operation of the NIMs will be the materials. For simplicity, we consider both AFMR and FMR most attractive, simply because of the practicability for cases which will be similar in theory. applications. ε(ω)/ε , μ(ω)/μ 0 0 4 Advances in OptoElectronics to the easy axis of the magnetic material. The multilayer Dielectric structure itself to be discussed in this theory actually provides the great easiness to reach such frequency tuning for the Magnetic magnetic part inside the multilayer. Structural parameters 300 that can be varied when designing include the layer thickness, Temperature periodic duty cycle, and magnetic orientation, and so forth. An efficient way to optimize material compositions and structural parameters may follow the combinatorial strategy 100 [6]. Effort toward efficient material selection, simulation for frequency tuning, and the multilayer fabrication is ongoing and will be published separately. 0 0 0.20.40.60.8 BaTiO SrTiO 3 3 Composition 4. Conclusion Figure 3: Dependence of the dielectric constant and Curie tem- One possible physical mechanism toward realizing negative perature of (Ba,Sr)TiO on its composition. Inset shows a possible refraction in a fully oxide-based multilayer was theoretically frequency tuning by changing the temperature for reaching the discussed. Inside the multilayer structure, such negative concurrence of both dielectric and magnetic resonance frequencies. refraction may be achieved by tuning their resonances to the same frequency via changing temperature, layer composition, structural parameter, and so forth. Such oxide- based NIMs are attractive for their potential applications as optical super lenses, imagers, sensors, and so forth, that are potential with low-loss, cost-effectiveness, and good fabrication flexibility. References [1] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, vol. 292, no. 5514, pp. 77–79, 2001. Measuring μ [2] D.R.Smith,S.Schultz,P.Markos, ˇ and C. M. Soukoulis, “Determination of effective permittivity and permeability of Figure 4: Schematic of the multilayer structure alignment required metamaterials from reflection and transmission coefficients,” for possibly tuning the FMR resonance frequency via changing Physical Review B, vol. 65, no. 19, Article ID 195104, 5 pages, the structural parameters—width, period, duty cycle, and the orientation angle. [3] R. H. Tarkanyan and D. G. Niarchos, “Effective negative refractive index in ferromagnet-semiconductor superlattices,” Optics Express, vol. 14, no. 12, pp. 5433–5444, 2006. [4] F. Gervais, “High-temperature infrared reflectivity spec- An alternative way of possibly tuning the magnetic troscopy by scanning interferometry,” in Infrared and Millimeter resonance frequency is by changing the magnetic layer’s Waves, K. J. Button, Ed., vol. 8, pp. 279–339, Academic Press, alignment inside the multilayer structure. Figure 4 shows the New York, NY, USA, 1983. schematic of such a structure in which the FMR frequency [5] J. Li, F. Duewer, C. Gao, H. Chang, X.-D. Xiang, and Y. Lu, will be tuned by changing either the orientation angle “Electro-optic measurements of the ferroelectric-paraelectric θ or the layer thickness, following the rewritten Kittel’s Sr TiO materials chips,” Applied Physics boundary in Ba 1−x x 3 formula involving both uniaxial anisotropy field (H )and Letters, vol. 76, no. 6, pp. 769–771, 2000. the additional shape anisotropy field (H ) into the total [6] Y. Lu, “The structural engineering strategy for photonic k,eff effective anisotropy field (H ) material research and device development,” Active and Passive A,eff Electronic Components, vol. 2007, Article ID 17692, 7 pages, H = H + H cosθ, A,eff u k,eff (8) 2πω AFMR = 4πM H . s A,eff In Figure 4, the main picture shows the parallel strait structure to be made in the magnetic layer inside the superlattice, via selective etching the as-fabricated magnetic layer or mask-shielding growth, and so forth. The inset shows that when one measures the permeability horizontally, the result will be actually tunable by changing the strait’s size (both period and width) or by changing the angle respective Relative dielectric constant (ε) Easy axis Resonance frequency Curie temperature (k) International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014
Advances in OptoElectronics – Hindawi Publishing Corporation
Published: Oct 30, 2008
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