Zero Refractive Index Properties of Two-Dimensional Photonic Crystals with Dirac Cones
-
Abstract
The zero refractive index properties of two-dimensional photonic crystals (PCs) are studied theoretically. Three necessary conditions for PCs to mimic the zero index materials (ZIMs) are obtained. In addition, through a comparative study of the properties for two representative PC structures with different types of Dirac cones, we find that the PC with a Dirac-like cone which meets the three necessary conditions does not behave as a ZIM in some cases. Further analysis shows that its non-zero index properties originate from the flat dispersion band. These findings clarify the fundamental physical issue of which type of Dirac cone PC can mimic a real ZIM. -
-
References
[1] Nguyen V C, Chen L and Halterman K 2010 Phys. Rev. Lett. 105 233908 doi: 10.1103/PhysRevLett.105.233908[2] Enoch S, Tayeb G, Sabouroux P, Guerin N and Vincent P 2002 Phys. Rev. Lett. 89 213902 doi: 10.1103/PhysRevLett.89.213902[3] Silveirinha M and Engheta N 2006 Phys. Rev. Lett. 97 157403 doi: 10.1103/PhysRevLett.97.157403[4] Hao J M, Yan W and Qiu M 2010 Appl. Phys. Lett. 96 101109 doi: 10.1063/1.3359428[5] Zhai T R, Shi J W, Chen S J and Liu D H 2011 Appl. Phys. Express 4 074301 doi: 10.1143/APEX.4.074301[6] Zhai T R, Shi J W, Chen S J, Liu D H and Zhang X D 2011 Opt. Lett. 36 2689 doi: 10.1364/OL.36.002689[7] Fu Y, Xu L, Hang Z H and Chen H 2014 Appl. Phys. Lett. 104 193509 doi: 10.1063/1.4878400[8] Zhu W R, Rukhlenko I D and Premaratne M 2012 Phys. Rev. Lett. 108 213903 doi: 10.1103/PhysRevLett.108.213903[9] Wang N, Chen H J, Lu W L, Liu S Y and Lin Z F 2013 Opt. Express 21 23712 doi: 10.1364/OE.21.023712[10] Yu X N, Chen H J, Lin H X, Zhou J L, Yu J J, Qian C X and Liu S Y 2014 Opt. Lett. 39 4643 doi: 10.1364/OL.39.004643[11] Lin H X, Yu X N and Liu S Y 2015 Acta Phys. Sin. 64 034203 doi: 10.7498/aps.64.034203[12] Kinsey N, Devault C, Kim J, Ferrera M, Shalaev V M and Boltasseva A 2015 Optica 2 616 doi: 10.1364/OPTICA.2.000616[13] Ou J Y, So J K, Adamo G, Sulaev A and Wang L 2014 Nat. Commun. 5 5139 doi: 10.1038/ncomms6139[14] Huang X, Lai Y, Hang Z H, Zheng H and Chan C T 2011 Nat. Mater. 10 582 doi: 10.1038/nmat3030[15] Moitra P, Yang Y, Anderson Z, Kravchenko I I, Briggs D P and Valentine J 2013 Nat. Photon. 7 791 doi: 10.1038/nphoton.2013.214[16] Li Y, Kita S, Muñoz P, Reshef O and Vulis D I 2015 Nat. Photon. 9 738 doi: 10.1038/nphoton.2015.198[17] Mei J, Wu Y, Chan C T and Zhang Z Q 2012 Phys. Rev. B 86 035141 doi: 10.1103/PhysRevB.86.035141[18] Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H and Chen Y F 2015 Sci. Rep. 4 4613 doi: 10.1038/srep04613[19] Ashraf M W and Faryad M 2016 J. Opt. Soc. Am. B 33 1008 doi: 10.1364/JOSAB.33.001008[20] Fang K, Zhang Y, Li F, Jiang H and Li Y 2012 Opt. Lett. 37 4654 doi: 10.1364/OL.37.004654[21] Dong J W, Chang M L, Huang X Q, Hang Z H, Zhong Z C, Chen W J, Huang Z Y and Chan C T 2015 Phys. Rev. Lett. 114 163901 doi: 10.1103/PhysRevLett.114.163901[22] Boriskina S V 2015 Nat. Photon. 9 422 doi: 10.1038/nphoton.2015.107[23] D'Aguanno G, Mattiucci N, Conti C and Bloemer M J 2013 Phys. Rev. B 87 085135 doi: 10.1103/PhysRevB.87.085135[24] Li Y and Mei J 2015 Opt. Express 23 12089 doi: 10.1364/OE.23.012089[25] Sepkhanov R A, Bazaliy Y B and Beenakker C W J 2007 Phys. Rev. A 75 063813 doi: 10.1103/PhysRevA.75.063813[26] Gao H, Ouyang M, Wang Y, Shen Y, Zhou J and Liu D H 2007 Optik 118 452 doi: 10.1016/j.ijleo.2006.04.017