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In this work, a zero index magnetic metamaterial (ZIMM) is designed based on the two-dimensional array of ferrite rods periodically arranged in the air. By calculating the photonic band structures within the framework of multiple scattering theory and retrieving the effective electric permittivity εeff and effective magnetic permeability μeff, the structure parameters can be optimized and then the effectively matched zero index with εeff = μeff = 0 is achieved. Within this matched ZIMM, electromagnetic (EM) wave can propagate without any phase delay, resulting in the manipulation of phase pattern in space. By simulating the electric field patterns of a Gaussian beam incident on ZIMM slabs with different thickness, zero phase delay inside the slab can be observed. By designing various outgoing interfaces a plane EM wavefront can be transformed into a cylindrical one, or even into a more general wavefront. In addition, the focusing and beam splitting effects are demonstrated as well. Besides, since the permeability of magnetic materials can be controlled by an external magnetic field or a temperature, the EM features of ZIMM can be flexibly tuned, enabling a promising prospect in designing EM devices and potential applications.
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Keywords:
- zero index metamaterial /
- Mie scattering theory /
- multiple scattering theory /
- effective-medium theory
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[2] Gómez R J, Janke C, Bolivar P, Kurz H 2005 Opt. Express 13 847
[3] Spitzer W G, Kleinman D, Walsh D 1959 Phys. Rev. 113 127
[4] Veselago V C 1968 Sov. Phys. Usp. 10 509
[5] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[6] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[7] He Q, Sun S L, Xiao S Y, Li X, Song Z Y, Sun W J, Zhou L 2014 Chin. Phys. B 23 047808
[8] Monticone F, Alù A 2014 Chin. Phys. B 23 047809
[9] Edwards B, Alù A, Young M, Silveirinha M, Engheta N 2008 Phys. Rev. Lett. 100 033903
[10] Liu R P, Cheng Q, Hand T, Mock J J, Cui T J, Cummer S A, Smith D R 2008 Phys. Rev. Lett. 100 023903
[11] Jin Y, Zhang P, He S L 2010 Phys. Rev. B 81 085117
[12] Jin Y, He S L 2010 Opt. Express 18 16587
[13] Silveirinha M, Engheta N 2007 Phys. Rev. B 75 075119
[14] Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nat. Mater. 10 582
[15] Cheng Q, Jiang W X, Cui T J 2011 Appl. Phys. Lett. 99 131913
[16] Cheng Q, Jiang W X, Cui T J 2012 Phys. Rev. Lett. 108 213903
[17] Silveirinha M G, Engheta N 2006 Phys. Rev. Lett. 97 157403
[18] Cheng Q, Liu R P, Huang D, Cui T J, Smith D R 2007 Appl. Phys. Lett. 91 234105
[19] Silveirinha M G, Engheta N 2007 Phys. Rev. B 76 245109
[20] Enoch S, Tayeb G, Sabouroux P, Guerin N, Vincent P 2002 Phys. Rev. Lett. 89 213902
[21] Yuan Y, Shen L F, Ran L X, Jiang T, Huangfu J T, Kong J A 2008 Phys. Rev. A 77 053821
[22] Ma Y G, Wang P, Chen X, Ong C K 2009 Appl. Phys. Lett. 94 044107
[23] Edwards B, Alù, Silveirinha M G, Engheta N 2009 J. Appl. Phys. 105 044905
[24] Luo J, Xu P, Chen H Y, Hou B, Gao L, Lai Y 2012 Appl. Phys. Lett. 100 221903
[25] Hao J, Yan W, Qiu M 2010 Appl. Phys. Lett. 96 101109
[26] Nguyen V C, Chen L, Halterman K 2010 Phys. Rev. Lett. 105 233908
[27] Wang N, Chen H J, Lu W L, Liu S Y, Lin Z F 2013 Opt. Express 21 23712
[28] Alù A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410
[29] Su Y Y, Gong B Y, Zhao X P 2012 Acta Phys. Sin. 61 084102 (in Chinese) [苏妍妍, 龚伯仪, 赵晓鹏 2012 物理学报 61 084102]
[30] Yang H, Wang C H, Guo X R 2014 Acta Phys. Sin. 63 014103 (in Chinese) [杨怀, 王春华, 郭小蓉 2014 物理学报 63 014103]
[31] Liu S Y, Du J J, Lin Z F, Wu R X, Chui S T 2008 Phys. Rev. B 78 155101
[32] Bi K, Dong G Y, Fu X J, Zhou J 2012 Appl. Phys. Lett. 103 131915
[33] Liu S Y, Chen W K, Du J J, Lin Z F, Chui S T, Chan C T 2008 Phys. Rev. Lett. 101 157407
[34] Liu S Y, Lu W L, Lin Z F, Chui S T 2011 Phys. Rev. B 84 045425
[35] Poo Y, Wu R X, Liu S Y, Yang Y, Lin Z F, Chui S T 2012 Appl. Phys. Lett. 101 081912
[36] Yu J J, Chen H J, Wu Y B, Liu S Y 2012 EPL 100 47007
[37] Shen M, Ruan L X, Wang X L, Shi J L, Wang Q 2011 Phys. Rev. A 83 045804
[38] Yannopapas V, Vanakaras A 2011 Phys. Rev. B 84 045128
[39] Litchinitser N M, Maimistov A I, Gabitov I R, Sagdeev R Z, Shalaev V M 2008 Opt. Lett. 33 2350
[40] Ding Y S, Chan C T, Wang R P 2013 Sci. Rep. 3 2954
[41] Pozar D M 2005 Microwave Engineering (3rd Ed.) (New York: Wiley)
[42] Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[43] Jin J F, Liu S Y, Lin Z F, Chui S T 2011 Phys. Rev. B 84 115101
-
[1] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
[2] Gómez R J, Janke C, Bolivar P, Kurz H 2005 Opt. Express 13 847
[3] Spitzer W G, Kleinman D, Walsh D 1959 Phys. Rev. 113 127
[4] Veselago V C 1968 Sov. Phys. Usp. 10 509
[5] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[6] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[7] He Q, Sun S L, Xiao S Y, Li X, Song Z Y, Sun W J, Zhou L 2014 Chin. Phys. B 23 047808
[8] Monticone F, Alù A 2014 Chin. Phys. B 23 047809
[9] Edwards B, Alù A, Young M, Silveirinha M, Engheta N 2008 Phys. Rev. Lett. 100 033903
[10] Liu R P, Cheng Q, Hand T, Mock J J, Cui T J, Cummer S A, Smith D R 2008 Phys. Rev. Lett. 100 023903
[11] Jin Y, Zhang P, He S L 2010 Phys. Rev. B 81 085117
[12] Jin Y, He S L 2010 Opt. Express 18 16587
[13] Silveirinha M, Engheta N 2007 Phys. Rev. B 75 075119
[14] Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nat. Mater. 10 582
[15] Cheng Q, Jiang W X, Cui T J 2011 Appl. Phys. Lett. 99 131913
[16] Cheng Q, Jiang W X, Cui T J 2012 Phys. Rev. Lett. 108 213903
[17] Silveirinha M G, Engheta N 2006 Phys. Rev. Lett. 97 157403
[18] Cheng Q, Liu R P, Huang D, Cui T J, Smith D R 2007 Appl. Phys. Lett. 91 234105
[19] Silveirinha M G, Engheta N 2007 Phys. Rev. B 76 245109
[20] Enoch S, Tayeb G, Sabouroux P, Guerin N, Vincent P 2002 Phys. Rev. Lett. 89 213902
[21] Yuan Y, Shen L F, Ran L X, Jiang T, Huangfu J T, Kong J A 2008 Phys. Rev. A 77 053821
[22] Ma Y G, Wang P, Chen X, Ong C K 2009 Appl. Phys. Lett. 94 044107
[23] Edwards B, Alù, Silveirinha M G, Engheta N 2009 J. Appl. Phys. 105 044905
[24] Luo J, Xu P, Chen H Y, Hou B, Gao L, Lai Y 2012 Appl. Phys. Lett. 100 221903
[25] Hao J, Yan W, Qiu M 2010 Appl. Phys. Lett. 96 101109
[26] Nguyen V C, Chen L, Halterman K 2010 Phys. Rev. Lett. 105 233908
[27] Wang N, Chen H J, Lu W L, Liu S Y, Lin Z F 2013 Opt. Express 21 23712
[28] Alù A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410
[29] Su Y Y, Gong B Y, Zhao X P 2012 Acta Phys. Sin. 61 084102 (in Chinese) [苏妍妍, 龚伯仪, 赵晓鹏 2012 物理学报 61 084102]
[30] Yang H, Wang C H, Guo X R 2014 Acta Phys. Sin. 63 014103 (in Chinese) [杨怀, 王春华, 郭小蓉 2014 物理学报 63 014103]
[31] Liu S Y, Du J J, Lin Z F, Wu R X, Chui S T 2008 Phys. Rev. B 78 155101
[32] Bi K, Dong G Y, Fu X J, Zhou J 2012 Appl. Phys. Lett. 103 131915
[33] Liu S Y, Chen W K, Du J J, Lin Z F, Chui S T, Chan C T 2008 Phys. Rev. Lett. 101 157407
[34] Liu S Y, Lu W L, Lin Z F, Chui S T 2011 Phys. Rev. B 84 045425
[35] Poo Y, Wu R X, Liu S Y, Yang Y, Lin Z F, Chui S T 2012 Appl. Phys. Lett. 101 081912
[36] Yu J J, Chen H J, Wu Y B, Liu S Y 2012 EPL 100 47007
[37] Shen M, Ruan L X, Wang X L, Shi J L, Wang Q 2011 Phys. Rev. A 83 045804
[38] Yannopapas V, Vanakaras A 2011 Phys. Rev. B 84 045128
[39] Litchinitser N M, Maimistov A I, Gabitov I R, Sagdeev R Z, Shalaev V M 2008 Opt. Lett. 33 2350
[40] Ding Y S, Chan C T, Wang R P 2013 Sci. Rep. 3 2954
[41] Pozar D M 2005 Microwave Engineering (3rd Ed.) (New York: Wiley)
[42] Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[43] Jin J F, Liu S Y, Lin Z F, Chui S T 2011 Phys. Rev. B 84 115101
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