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Purpose: The paper presents the implementation of the Transfer Matrix Method algorithm using Mathematica and the impact of the structure discretization steps number on the filters transmission. Tested materials were made with periodically varying refractive index. Design/methodology/approach: The properties of the filter transmission made of a materials having a periodically varying refractive index were analyzed. The study used a Transfer Matrix Method algorithm. The materials have a thickness of one micrometer. The refractive index of the analyzed material changed sinusoidally with a wavelength of 500nm. Sinusoid quantizing was performed each for 8, 16, 32, 50 and 60 layers. Findings: Maps show the nature of the transmission bands. Band structure of RHM materials (positive refractive index) is similar to the structure of the filter constructed of LHM material, characterized by a negative refractive index. Transmission band in a left-handed material has less width at half maximum. Thirty two layers discretization stabilizes the simulations of the tested materials filtration properties. Research limitations/implications: The paper had not been analyzed for materials with extinction coefficient different from zero. It would be worthwhile to conduct research for materials with variable refractive index of a different nature, for example a triangular or saw tooth shape. Practical implications: Analysis of the filter materials for a variety of photonic structures allows the prediction and design of materials with specified properties. These tests allow to design filters and mirrors for with very good applications parameters. Originality/value: The influence of the discretization level of continuous medium with periodically changing material properties on the transmission map stability was analyzed.
Wydawca
Rocznik
Tom
Strony
79--85
Opis fizyczny
Bibliogr. 33 poz., tab.
Twórcy
autor
- Institute of Physics, Technical University of Czestochowa, Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
autor
- Institute of Physics, Technical University of Czestochowa, Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
autor
- Institute of Physics, Technical University of Czestochowa, Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
autor
- Institute of Physics, Technical University of Czestochowa, Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
autor
- Institute of Materials Engineering, Technical University of Czestochowa, Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
Bibliografia
- [1] W. Steurer, D. Suter-Widmer, Journal of Physics D: Applied Physics 40/13 (2007) R229-R247.
- [2] J.E. Lugo, B. de la Mora, R. Doti, R. Nava, J. Tagueña, A. del Rio, J. Faubert, Multiband negative refraction in one-dimensional photonic crystals, Optics Express 17/5 (2009) 3042-3051.
- [3] H. Zhang, X. Chen, Y. Li, Y. Fu, N. Yuan, The Bragg gap vanishing phenomena in one-dimensional photonic crystals, Optics Express 17/10 (2009) 7800-7806.
- [4] X. Hu, Z. Liu, Q. Gong, A multichannel filter in a photonic crystal heterostructure containing single-negative materials, Journal Optics A: Pure and Applied Optics 9/10 (2007) 877-883.
- [5] F.F. de Medeiros, E.L. Albuquerque, M.S. Vasconcelos, Transmission spectra in photonic band-gap Fibonacci nanostructures, Surface Science 601/18 (2007) 4492-4496.
- [6] Y. Fang, S. He, Transparent structure consisting of metamaterial layers and matching layers, Physical Review A 78/2 (2008) 023813-1-023813-6.
- [7] E. Macia, The role of aperiodic order in science and technology, Reports on Progress in Physics 69/2 (2006) 397-441.
- [8] A. Bruno-Alfonso, E. Reyes-Gomez, S.B. Cavalcanti, L.E. Oliveira, Band edge states of the gap of Fibonacci photonic lattices, Physical Review A 78/3 (2008) 035801-1-035801-4.
- [9] M. de Dios-Leyva, J.C. Drake-Perez, Zero-width band gap associated with the n ̄=0 condition in photonic crystals containing left-handed materials, Physical Review E 79/3 (2009) 036608-1-036608-7.
- [10] M. de Dios-Leyva, O.E. Gonzales-Vasquez, Band structure and associated electromagnetic fields in one-dimensional photonic crystals with left-handed materials, Physical Review B 77/12 (2008) 125102-1-125102-8.
- [11] R. Srivastava, K.B. Thapa, S. Pati, S.P. Ojha, Negative refraction in 1D photonic crystals, Solid State Communications 147 (2008) 157-160.
- [12] Y.-T. Fang, J. Zhou, E.Y.B. Pun, High-Q filters based on one-dimensional photonic crystals using epsilon-negative materials, Applied Physics B 86/4 (2007) 587-591.
- [13] S.A. Ramakrishna, T.M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials, SPIE Press and CRC Press, 2009.
- [14] C.M. Krowne, Y. Zhang (Eds.), Physics of Negative Refraction and Negative Index Materials, Springer, 2007.
- [15] H.X. Da, C. Xu, Z.Y. Li, Omnidirectional reflection from one-dimensional quasi-periodic photonic crystal containing left-handed material, Physics Letters A 345 (2005) 459-468.
- [16] J. Li, D. Zhao, Z. Liu, Zero-ṅ photonic band gap in a quasiperiodic stacking of positive and negative refractive index materials, Physics Letters A 332 (2004) 461-468.
- [17] M. Kohomoto, B. Sutherland, K. Iguchi, Localization of optics: Quasiperiodic media, Physical Review Letters 58/23 (1987) 2436-2838.
- [18] A. Klauzer-Kruszyna, W. Salejda, M.H. Tyc, Polarized Light Transmission through Generalized Fibonacci Multilayers. I. Dynamical maps approach, Optik – International Journal for Light and Electron Optics 115/6 (2004) 257-266.
- [19] A. Klauzer-Kruszyna, W. Salejda, M.H. Tyc, Polarized Light Transmission through Generalized Fibonacci Multilayers. II. Numerical Results, Optik – International Journal for Light and Electron Optics 115/6 (2004) 267-276.
- [20] A. Klauzer-Kruszyna, Propagation of polarized light in selected aperiodic superstructures, PhD Thesis, Wrocław, 2005 (in Polish).
- [21] P. Yeh, Optical Waves in Layered Media, John Wiley & Sons, New York, 1988.
- [22] K. Iguchi, Optical property of a quasi-periodic multilayer, Materials Science and Engineering: B 15/3 (1992) L13–L17.
- [23] W. Gellermann, M. Kohmoto, B. Sutherland, P.C. Taylor, Localization of Light Waves in Fibonacci Dieletric Multilayers, Physical Review Letters 72/5 (1994) 633-636.
- [24] V.G. Veselago, Elektrodinamika veshchestv s odnovremeno otricatelnymi znacheniami ε i μ, Usp. Fiz. Nauk 92 (1968) 517-529.
- [25] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite Medium with Negative Permeability and Permittivity, Physical Review Letters 84/18 (2000) 4184-4187.
- [26] E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, C.M. Soukoulis, Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens, Physical Review Letters 91/20 (2003) 207401-1-207401-4.
- [27] E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, C.M. Soukoulis, Electromagnetic waves: Negative refraction by photonic crystals, Nature 423 (2003) 604-605.
- [28] R.A. Shelby, D.R. Smith, S. Schultz, Experimental Verification of a Negative Index of Refraction, Science 292 (2001) 77-79.
- [29] J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Transactions on Microwave Theory and Techniques 47/11 (1999) 2075-2084.
- [30] A. Houck, J.B. Brock, I.I. Chuang, Experimental Observations of a Left-Handed Material That Obeys Snell’s Law, Physical Review Letters 90/13 (2003) 137401-1-137401-4.
- [31] C.G. Parazzoli, R.B. Greegor, K. Li, B.E.C. Koltenbah, M. Tanielian, Experimental Verification and Simulation of Negative Index of Refraction Using Snell’s Law, Physical Review Letters 90/10 (2003) 107401-1-107401-4.
- [32] J.Q. Shen, Z.Ch. Ruan, S. He, Influence of signal light on the transient optical properties of a four-level EIT medium, Physics Letters A 330/6 (2004) 487-495.
- [33] M.O. Oktel, Ö.E. Müstecaplioglu, Electromagnetically induced left-handedness in a dense gas of three level atoms, Physical Review A 70/5 (2004) 053806-1-053806-7.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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