Optical characterization of reduced graphene Based composite thin films: Left- Handed Materials (Metamaterials)
Negative index material is a type of metamaterial with negative refractive index; being an artificial material, its fabrication is quite difficult, scaling up the production to meet the commercial demand is a challenge and the strong energy dissipation by metals poses another difficulty. This study employed a low cost, scalable technique (Electrodeposition) to synthesis Al and Ca doped NiO-ZnO-rGO thin films on fluorine doped tin oxide (FTO) without any complexing agents. The thin films were optically characterized using double Spectrophotometer within 300-1000 nm wavelength. Results reveal low absorption for all films but high transmittance of max. 78 % for luminum doped thin films. The incorporation of Al3+ and Ca2+ indicate the optical band gap of NiO-ZnO-rGO shifted to low energy (2.0 eV) and high energy (2.20 eV) respectively. All the composite thin films have unique features; negative refractive indexes, negative imaginary dielectric constant, and negative optical conductivity. These optical results of the films show they are novel left handed materials suitable for wider applications such as telemedicine, internet of things, transmission lines, energy storage devices, bio sensing, wearable devices etc.
- Conference Article
- 10.1117/12.871948
- Aug 19, 2010
We investigate on the basis of a full three-dimensional spatio-temporal Maxwell-Bloch approach the possibility of complete loss compensation in non-bianisotropic negative refractive index (NRI) metamaterials. We show that a judicious incorporation of optically pumped gain materials, such as laser dyes, into a double-fishnet metamaterial can enable gain in the regime where the real part n<sup>′</sup> of the resulting effective refractive index (n = n<sup>′</sup> + in<sup>″</sup>) is negative. It is demonstrated that a frequency band exists for realistic opto-geometric and material (gain/loss) parameters where n<sup>′</sup> < 0 and simultaneously n<sup>″</sup> < 0 hold, resulting in a figure-of-merit that diverges at two distinct frequency points. Having ensured on the microscopic, meta-molecular level that realistic levels of losses and even gain are accessible in the considered optical frequency regime we explore the possibility of compensating propagation losses in a negative refractive index slow-light metamaterial heterostructure. The heterostructure is composed of a negative refractive index core-layer bounded symmetrically by two thin active cladding layers providing evanescent gain to the propagating slow light pulses. It is shown that backward-propagating light - having anti-parallel phase and group velocities and experiencing a negative effective refractive index - can be amplified inside this slow-light waveguide structure. Our results provide a direct and unambiguous proof that full compensation of losses and attainment of gain are possible on the microscopic as well as the macroscopic level in the regime where the non-bianisotropic refractive index is negative - including, in particular, the regime where the guided light propagates slowly.
- Research Article
5
- 10.1117/1.oe.54.3.037108
- Mar 24, 2015
- Optical Engineering
In recent years, considerable research has been carried out relative to the electromagnetic (EM) propagation and refraction characteristics in metamaterials with emphasis on the origins of negative refractive index. Negative refractive index may be introduced in metamaterials via different methods; one such is the con- dition whereby the Poynting vector of the EM wave is in opposition to the group velocity in the material. Alternatively, negative refractive index also occurs when the group and phase velocities in the medium are in opposition. The latter phenomenon has been extensively investigated in the literature, including recent work involving chiral metamaterials with material dispersion up to the first order. This paper examines the pos- sible emergence of negative refractive index in dispersive chiral metamaterials with material dispersion up to the second order. The motivation is to determine if using second- as opposed to first-order dispersion may lead to more practical negative index behavior. A spectral approach combined with a slowly time-varying phasor analy- sis is applied, leading to the analytic derivation of EM phase and group velocities, and the resulting phase and group velocities and the corresponding phase and group indices are evaluated by selecting somewhat arbitrary dispersive parameters. The results indicate the emergence of negative index (via negative phase indices along with positive group indices, as reported in the literature) or negative index material (NIM) behavior over infor- mation bandwidths in the low RF range. The second-order results are not significantly better than those for first-order results based on the theoretical analysis; however, greater parametric flexibility exists for the second-order system leading to the higher likelihood of achieving NIM over practical frequency bands. The velocities and indices computed using the Lorentzian and Condon models yield an NIM bandwidth around 200 − 400 Mrad∕sec, about 2 orders of magnitude higher than that for the parametric approach; more impor- tantly, NIM is found not to occur in the first order when using practical models. © 2015 Society of Photo-Optical
- Research Article
2183
- 10.1038/nature07247
- Aug 11, 2008
- Nature
Metamaterials are artificially engineered structures that have properties, such as a negative refractive index, not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies, but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals. Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide. Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction. Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded 'fishnet' structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices, compact resonators and highly directional sources.
- Research Article
- 10.4302/plp.2009.3.09
- Sep 30, 2009
- Photonics Letters of Poland
We study the properties of the photonic band structure (PBS) of infinite and binary Fibonacci superlattices (FS) containing metamaterial lossless layers. The transfer matrix method (TMM) and periodic boundary conditions are applied. The algebraic method of PBS calculations, based on the Bloch theorem, is described and used. The dispersion relations, for both type of light polarization, characterizing peculiarities of PBS are calculated numerically and presented. Fractal properties of a photonic band structure and the existence of so called zero-n gaps are established. Full Text: PDF References E. Macia,"The role of aperiodic order in science and technology", Rep. Prog. Phys. 69, 397 (2006) [CrossRef] W. Steurer, D. Suter-Widmer,"Photonic and phononic quasicrystals", J. Phys. D: Appl. Phys. 40, R229 (2007) [CrossRef] S. A. Ramakrishna, T. M. Grzegorczyk, "Physics and Applications of Negative Refractive Index Materials", SPIE Press and CRC Press 2009 J.E. Lugo et al,"Multiband negative refraction in one-dimensional photonic crystals", Optics Express, 17, 3042 (2009) [CrossRef] H. Zhang, X. Chen, Y. Li, Y. Fu, N. Yuan,"The Bragg gap vanishing phenomena in one-dimensional photonic crystals", Optics Express, 17, 7800 (2009) [CrossRef] M. de Dios-Leyva, J.C. Drake-Perez,"Zero-width band gap associated with the nŻ =0 condition in photonic crystals containing left-handed materials", Phys. Rev. E, 79, 036608 (2009) [CrossRef] M. de Dios-Leyva, O.E. Gonzales-Vasquez,"Band structure and associated electromagnetic fields in one-dimensional photonic crystals with left-handed materials", Phys. Rev. B, 77,125102 (2008) [CrossRef] R. Srivastava, K.B. Thapa, S. Pati, S.P. Ojha,"Negative refraction in 1D photonic crystals", Sol. State Comm., 147, 157 (2008) [CrossRef] Y. Fang, S. He,"Transparent structure consisting of metamaterial layers and matching layers", Phys. Rev. A, 78, 023813 (2008) [CrossRef] A. Bruno-Alfonso, E. Reyes-Gomez, S.B. Cavalcanti, L.E. Oliveira,"Band edge states of the ?n?=0 gap of Fibonacci photonic lattices", Phys. Rev. A, 78, 035801 (2008) [CrossRef] Eds. C. M. Krowne, Y. Zhang, "Physics of Negative Refraction and Negative Index Materials", Springer 2007 Y.-T Fang, J. Zhou, E.Y.B. Pun,"High-Q filters based on one-dimensional photonic crystals using epsilon-negative materials", Appl. Phys. B, 86, 587 (2007) [CrossRef] X. Hu, Z. Liu, Q. Gong,"A multichannel filter in a photonic crystal heterostructure containing single-negative materials", J. Opt. A: Pure Appl. Opt., 9, 877 (2007) [CrossRef] F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos,"Transmission spectra in photonic band-gap Fibonacci nanostructures", Surface Science, 601, 4492 (2007) [CrossRef] K. Tarnowski, W. Salejda, M. H. Tyc,"Propagation of polarized light through optical nanosuperlattices", Optica Applicata, 37, 387, 2007 M.H. Tyc, W. Salejda, A. Klauzer-Kruszyna, K. Tarnowski,"Photonic band structure of one-dimensional aperiodic superlattices composed of negative refraction metamaterials", SPIE Proceedings Series, 2007, 6581, 658112 [CrossRef] M.H. Tyc, W. Salejda, A. Klauzer-Kruszyna, K. Tarnowski,"Propagation of polarized light through superlattices composed of left- and right-handed materials", SPIE Proceedings Series, 2007, 6581, 658113 [CrossRef] P. Yeh, "Optical Waves in Layered Media", Wiley-Interscience 2005 H.X. Da, C. Xu, Z.Y. Li,"Omnidirectional reflection from one-dimensional quasi-periodic photonic crystal containing left-handed material", Phys. Lett. A, 345, 459 (2005) [CrossRef] W. Salejda, A. Klauzer-Kruszyna, M. H. Tyc, K. Tarnowski,"One-dimensional photonic quasicrystals: application to Bragg reflectors", SPIE Proceedings Series, 2005, 5950, 59501Q [CrossRef] W. Salejda, A. Klauzer-Kruszyna, M. H. Tyc, K. Tarnowski,"Electromagnetic wave propagation through aperiodic superlattices composed of left- and right-handed materials", SPIE Proceedings Series, 2005, 5955, 595514 [CrossRef] J. Li, D. Zhao, Z. Liu,"Zero n - photonic band gap in a quasiperiodic stacking of positive and negative refractive index materials", Phys. Lett. A, 332, 461 (2004) [CrossRef] A. Klauzer- Kruszyna, W. Salejda, M.H. Tyc,"Polarized Light Transmission through Generalized Fibonacci Multilayers. I. Dynamical maps approach", Optik, 115, 257 (2004) A. Klauzer- Kruszyna, W. Salejda, M.H. Tyc,"Polarized Light Transmission through Generalized Fibonacci Multilayers. II. Numerical Results", Optik, 115, 267 (2004) M. Kohomoto, B. Sutherland, K. Iguchi,"Localization of optics: Quasiperiodic media", Phys. Rev. Lett., 58, 2436 (1987) [CrossRef] J. Li, L. Zhou, C.T. Chan, P. Shang,"Photonic Band Gap from a Stack of Positive and Negative Index Materials", Phys. Rev. Lett., 90, 083901 (2003) [CrossRef]
- Research Article
43
- 10.1016/j.electacta.2004.02.066
- Aug 7, 2004
- Electrochimica Acta
Fabrication and characterization of SnO 2–RuO 2 composite anode thin film for lithium ion batteries
- Research Article
- 10.1149/ma2016-02/20/1588
- Sep 1, 2016
- Electrochemical Society Meeting Abstracts
Si thin films are attracted as materials for ultra-large-scale solar cell systems at relatively low cost. Electrodeposition is expected as one fabrication method of Si thin films due to its advantages such as relatively simplicity process, precision control of nanostructure and continuous deposition in large area. Si thin films have been electrodeposited in non-aqueous solvents owing to their large electrochemical windows which allows for the study of Si electrodeposition [1-3]. Among various non-aqueous solvents, organic solvents and ionic liquids, which can be used under low temperature, have been used as electrolytes for the electrodeposition of Si thin films in our laboratory. We have previously succeeded to electrodeposit Si thin films in organic solvents and ionic liquids [4-6]. However, there is a problem for applications to solar cells that some impurities (mainly carbon and oxygen) are incorporated in thin films. We have reported the carbon content can be reduced by annealing treatment [7]. On the other hand, the decrease of oxygen content is still required. Thus, we evaluate the composition of Si thin films electrodeposited in an organic solvent and an ionic liquid without oxygen atoms in order to analysis the effect of bath conditions on the composition of thin films (especially, where the oxygen incorporated in Si thin films comes from). Si thin films were electrodeposited with 3 electrode cell (W.E. : Au, R.E. : Ag/Ag+, C.E. : Pt) in acetonitrile, 0.3 M tetrabutylammonium chloride and 0.5 M SiCl4 was used as an organic solvent, and 1-butyl-3-methylimidazolium hexafluorophosphate and 0.5 M SiCl4 as an ionic liquid. The composition of Si thin films were evaluated by X-ray photoelectron spectroscopy. As a result, the oxygen content in Si thin films were decreased by using the solvents without oxygen atoms in both organic solvent and ionic liquid cases. This results suggest that the reason the oxygen inclusion is derived from the incorporation of solvents themselves in films during electrodeposition, and propose us the way to obtain films with low impurities. In addition, the rotating disk electrode was used in the organic solvent case in order to promote the convection. The usage of this rotating disk electrode showed the decrease of impurities in Si thin films. Therefore, it is indicated that the stable supply of SiCl4 to the electrode surface is important factor to obtain films with low impurities. This study reveals that bath condition significantly affects to the composition of Si thin films, and could help us to fabricate films for applications to solar cells. This study was financially supported in part by the Japan Science and Technology Agency (JST) CREST program, and Y. T. acknowledges the Leading Graduate Program in Science and Engineering, Waseda University, from MEXT, Japan. [1] S. Zein El Abedin, N. Borrissenko, F. Endres, Electrochem. Comm., 6 (2004) 510. [2] T. Munisamy, A. J. Bard, Electrochim. Acta, 55 (2010) 3797. [3] M. Bechelany, J. Elias, P. Brodard, J. Michler, L. Philippe, Thin Solid Films 520 (2012) 1895. [4] Y. Nishimura and Y. Fukunaka, Electrochim. Acta, 53 (2007) 111. [5] T. Homma, J. Komadina, Y. Nakano, T. Ouchi, T. Akiyoshi, Y. Ishibashi, Y. Nishimura, T. Nishida, and Y. Fukunaka, Electrochem. Soc. Trans., 41 (2012) 9. [6] J. Komadina, T. Akiyoshi, Y. Ishibashi, Y. Fukunaka, T. Homma, Electrochim. Acta, 100 (2013) 236. [7] Y. Tsuyuki, A. Pham, J. Komadina, Y. Fukunaka, T. Homma, Electrochim. Acta, 183 (2015) 49.
- Research Article
8
- 10.1016/s1003-6326(06)60188-x
- Jun 1, 2006
- Transactions of Nonferrous Metals Society of China
Photoluminescence properties of ZnSe/SiO 2 composite thin films prepared by sol-gel method
- Book Chapter
2
- 10.5772/6850
- Jan 1, 2010
The emergence of artificially designed subwavelength electromagnetic materials, known as metamaterials, catches an increasing interest of researchers. Metamaterials are artificially structured materials featuring properties that do not or may normally take place and can not be acquired in nature (Engheta & Ziolkowski, 2006). In recent years greater attention has been paid to the metamaterials with negative index of refraction which have quite uncommon electromagnetic properties. The new type of materials with the negative index of refraction were theoretically predicted in 1968 by Veselago (Veselago, 1967). In these materials both the permittivity and the permeability take on simultaneously negative values at certain frequencies. In materials with the negative refractive index the direction of the Pointing vector is antiparallel to the one of the phase velocity, as contrasted to the case of plane wave propagation in conventional media. The complex refractive index of a medium is defined as the ratio between the speed of an electromagnetic wave in medium and that in vacuum and can thus be expressed as μe = 2 n , where μ is relative magnetic permeability and e relative dielectric permittivity. If we change simultaneously the signs of e and μ, the ratio μe = 2 n will not change. If both e and μ are positive, this means that μ e = n , if e and μ are negative in a given wavelength range, this means that μ e − = n . In negative index metamaterials the Poynting vector ] [EH S= and vectors E and H form the left-hand triple, which leads to opposite directions of the group and phase velocity of plane waves propagating in the material. Consequently, metamaterials with simultaneously negative permittivity and permeability are named as left-handed metamaterials, backward-wave media, double negative materials, Smith, Shelby et al. were the first to demonstrate by means of experiment the existence of metamaterials with simultaneously negative permittivity and permeability at microwave frequencies (Smith et al., 2000), (Shelby et al., 2001). After the experimental demonstration of such materials, the properties and possible applications of various metamaterials with negative index of refraction gained a rapidly increasing interest. Now the negative refractive index metamaterials are demonstrated for near infrared and optical range (Falcone et al. 2004), (Iyer & Eleftheriades, 2002), (Caloz & Itoh, 2002). In metamaterials with negative refractive index many interesting phenomena that do not appear in natural media can be Source: Wave Propagation in Materials for Modern Applications, Book edited by: Andrey Petrin, ISBN 978-953-7619-65-7, pp. 526, January 2010, INTECH, Croatia, downloaded from SCIYO.COM
- Research Article
8
- 10.4028/www.scientific.net/amr.415-417.1942
- Dec 1, 2011
- Advanced Materials Research
A novel TiO2/Cu composite photocatalyst thin film was successfully fabricated by 2-step Mechanical Coating Technique (2-step MCT). The composite photocatalyst thin film was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), among others. The formation process of Cu thin film and TiO2/Cu composite photocatalyst thin film were also examined. The results revealed that the formation of Cu thin film can fall into the following stages: nucleation, growth of nuclei and connection, formation and thickening of continuous thin film, and the exfoliation of thin film. In addition, TiO2/Cu composite thin film had a composite microstructure of TiO2islands coated on Cu thin film. Furthermore, the photocatalytic activity of TiO2/Cu composite photocatalyst thin film was evaluated by measuring the degradation rate of methylene blue (MB). Enhancement on the photocatalytic activity of TiO2was confirmed. The improvement of the photocatalytic activity of TiO2/Cu composite photocatalyst thin film should result from the increase of the charge separation efficiency and the mass increase of TiO2in the composite thin film.
- Conference Article
- 10.1117/12.2237699
- Nov 9, 2016
Optical coatings have been referred as thin films that create interference effect to change optical properties of substrates. The most common applications of optical thin films are anti-reflection coatings, high reflective coatings, beamsplitter coatings, and bandpass filter coatings. In the recent development of metamaterials, the optical coatings also play a critical role in design, fabrication and measurement. In fabrication, glancing angle deposition has been applied to grow slanted metal nanorod arrays. The associated longitudinal plasmon and transverse plasmon modes under linear polarized illuminations are induced and generate anisotropic refractive index and extinction coefficient. Strong birefringence of a silver nanorod array reveals positive and negative real refractive indices exist for two orthogonal linear polarization states. Recently, negative index materials and hyperbolic metamaterials are realized as multilayers comprising subwavelength-scale metal and dielectric films alternatively. From the view of optical coatings, the design of optical edge filters can be applied to arrange the metal-dielectric multilayer as a symmetrical film sack to perform equivalent complex admittance and refractive index. On the other hand, the traditional admittance diagram used in design of antireflection and bandpass filters can be applied to induce the transmission of a negative index multilayer. The admittance loci of metal films are designed to be huge contours in the admittance diagram to reduce the energy loss in metal films. Five-layered symmetrical film stack and seven-layered symmetrical film stack are shown here to present as new bandpass filters with negative real refractive indices.
- Book Chapter
- 10.1117/3.832717.ch2
- Dec 29, 2009
The art and science of optics is centered upon our ability to control the refractive index of materials, thereby directing the flow of light. From the stained-glass windows of Gothic cathedrals to modern LCD projectors, from Galileo's telescope to terabit optical communication systems, devices made possible by skillful manipulation of the refractive index have resulted in countless technological and cultural breakthroughs. For centuries, the refractive index has been regarded as a strictly positive quantity â such was the universal experience. Recent advances in fabrication and processing techniques, however, have enabled the creation of materials with a negative refractive index. This development opens many new chapters in the fields of optical physics and device engineering. Negative index greatly expands the parameter space accessible for manipulating light, opening the way for devices with unprecedented capabilities â for example, imaging systems with subwavelength resolution and ultrasmall waveguides. The novel systems made possible by negative index materials (NIMs) may bring about revolutionary technological changes. In the present chapter we describe a method to achieve negative refraction via materials with a hyperbolic dispersion relation. Both natural materials and metamaterials can exhibit this property. We show that in addition to providing a simple path to nonmagnetic negative refraction, the hyperbolic dispersion relation enables novel devices for waveguiding and subwavelength imaging. The present-day interest in NIMs started in the early 2000s. The origins of the subject, however, date back many decades. Indeed, as a general wave propagation phenomenon, negative refraction has been known since the early 20th century. It was noted, in particular, that negative refraction naturally occurs at the interface with a medium characterized by negative phase velocity. No such materials were known in the electromagnetic domain, and so the early discussions involved only mechanical oscillations. The first detailed treatment of negative refraction in electromagnetism was provided by Veselago in 1968. He showed that to attain negative phase velocity for electromagnetic (EM) waves, the material response must be of the form Iµ < 0, I¼ < 0. When this condition is satisfied, the E, H, and k vectors form a left-handed triplet. As a result, the wave vector k and the Poynting vector S are oriented in opposite directions; the system has negative phase velocity, which is the condition for negative refraction. Indeed, negative phase velocity serves as a definition of negative index materials. While mechanical and radio frequency devices exhibiting such effective negative indices were known at the time of Veselago's writing, bulk materials with negative phase velocity were not found in nature and were not readily attainable.
- Conference Article
2
- 10.1117/12.518133
- Jul 6, 2004
Due to the recent experimental validations of left-handed metamaterials, negative refractive index has now become recognized as a new parameter space for the electromagnetic response of materials. Because materials with negative index behave quite differently than materials with positive index, many familiar electromagnetic phenomena must be reconsidered. Having established now the scientific basis of negative index, the effort of the community is turning toward the practical realization of both the predicted scientific phenomena and associated applications. In both of these pursuits, the ability to design, characterize and fabricate negative index materials is critical; we can consider the current status of negative refraction in some sense a materials issue, as our ability to demonstrate the predicted phenomena is linked to the quality of metamaterials we can produce. In this paper we consider several issues associated with the design and simulation of negative index metamaterials. Keywords: Negative index, left-handed materials, metamaterials
- Research Article
31
- 10.1016/j.crhy.2009.04.002
- Jun 1, 2009
- Comptes Rendus. Physique
Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces
- Research Article
188
- 10.1103/physrevb.82.094306
- Sep 16, 2010
- Physical Review B
A one-dimensional acoustic negative refractive index metamaterial based on the transmission line approach is presented. This structure implements the dual transmission line concept extensively investigated in microwave engineering. It consists of an acoustic waveguide periodically loaded with membranes realizing the function of series ?capacitances? and transversally connected open channels realizing shunt ?inductances.? Transmission line based metamaterials can exhibit a negative refractive index without relying on resonance phenomena, which results in a bandwidth of operation much broader than that observed in resonant devices. In the present case, the negative refractive index band extends over almost one octave, from 0.6 to 1 kHz. The developed structure also exhibits a seamless transition between the negative and positive refractive index bands with a zero index at the transition frequency of 1 kHz. At this frequency, the unit cell is only one tenth of the wavelength. Simple acoustic circuit models are introduced, which allow efficient designs both in terms of dispersion and impedance, while accurately describing all the physical phenomena. Using this approach, a good matching at the structure terminations is achieved. Full-wave simulations, made for a 10-cell-long structure, confirm the good performances in terms of dispersion diagram, Bloch impedance, and reflection and transmission coefficients.
- Conference Article
- 10.1115/mnhmt2012-75033
- Mar 3, 2012
A tunable metamaterial is proposed by combining a thermochromic oxide with a fishnet structure. The reflection and transmission coefficients are calculated by finite-difference time-domain (FDTD) method. Then the effective electromagnetic parameters of the metamaterial are retrieved on the basis of these data. The results reveal that an effective negative refractive index is obtained by this proposed structure. Furthermore, the wavelength region with negative refractive index can be self-regulated by simply tuning the temperature, which is of importance to extend the applications of negative refractive index materials. The effects of structural sizes on the negative refractive index are discussed in detail. The size-dependence indicates that wavelength region with negative refractive index can be designed to locate at the desired position by dexterously tailoring the structural parameters.
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