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In a zero index material, the phase velocity of light is much greater than the speed of light in vacuum and can even approach to infinity. Thus, the phase of light throughout a piece of zero-index material is essentially a constant. The zero index material has recently been used in many areas due to its extraordinary optical properties, including beam collimation, cloaking and phase matching in nonlinear optics. However, most of zero index materials usually have narrow operating bandwidths and the operating frequencies are not tunable. In this work, the model of tunable near-zero index photonic crystal is established by using colloidal magnetic fluid. Magnetic fluid, as a kind of easy-made mature nanoscale magnetic material, has proved to be an excellent candidate for fabricating self-assembled photonic crystal, especially the band-tunable photonic crystal with fast and reversible response to external magnetic field. The band structure can be calculated using the plane wave expansion method. For TE mode, it can be seen that a triply-degenerate point (normalized frequency f=0.734) at point under external magnetic field H=147 Oe, forms a Dirac-like point in the band structure, which is called an accidental-degeneracy-induced Dirac-like point. The effective permittivity eff and permeability eff are calculated using an expanded effective medium theory based on the Mie scattering theory. The calculated results show that both eff and eff are equal to zero at Dirac-like point, which means that the effective index neff is zero and the effective impedance Zeff is 1. The lattice structure of such a self-assembled photonic crystal will change with the external magnetic field, leading to the disappearance of Dirac-like point. However, when 143.6 OeH 152.4 Oe (1 Oe=79.5775 A/m), |neff | can keep less than 0.05 under the condition of Zeff = 1. Correspondingly, the operating frequency will change from 0.75 to 0.716. The model is verified by the numerical simulations (COMSOL Multiphysics) and the theoretical results agree well with the numerical ones.
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Keywords:
- zero index /
- Dirac-like point /
- photonic crystal /
- magnetic fluids
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[10] Alu A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410
[11] Hao J, Yan W, Qiu M 2010 Appl. Phys. Lett. 96 101109
[12] Suchowski H, O'Brien K, Wong Z J, Salandrino A, Yin X, Zhang X 2013 Science 342 1223
[13] Ge J, Yin Y 2008 Adv. Mater. 20 3485
[14] Kim H, Ge J, Kim J, Choi S E, Lee H, Park W, Yin Y, Kwon S 2009 Nat. Photon. 3 534
[15] Horng H E, Hong C Y, Yang S Y, Yang H C 2003 Appl. Phys. Lett. 82 2434
[16] Yang S Y, Chieh J J, Horng H E, Hong C Y, Yang H C 2004 Appl. Phys. Lett. 84 5204
[17] Wen W, Zhang L, Sheng P 2000 Phys. Rev. Lett. 85 5464
[18] Buchenau U, Mller I 1972 Solid. State. Commun. 11 1291
[19] Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[20] Geng T, Wang Y, Wang X, Dong X M 2015 Acta Phys. Sin. 64 154210 (in Chinese) [耿滔, 王岩, 王新, 董祥美 2015 64 154210]
[21] Leger J R, Swanson G J 1990 Opt. Lett. 15 288
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[1] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[2] Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102
[3] Chen J, Wang Y, Jia B, Geng T, Li X, Feng L, Qian W, Liang B, Zhang X, Gu M, Zhuang S 2011 Nat. Photon. 5 239
[4] Huang X, Lai L, Hang Z H, Zheng H, Chan Z T 2011 Nat. Mater. 10 582
[5] Kocaman S, Aras M S, Hsieh P, McMillan J F, Biris C G, Panoiu N C, Yu M B, Kwong D L, Stein A, Wong C W 2011 Nat. Photon. 5 499
[6] Liu R, Cheng Q, Hand T, Mock J J, Cui T J, Cummer S A, Smith D R 2008 Phys. Rev. Lett. 100 023903
[7] Mocella V, Cabrini S, Chang A S P, Dardano P, Moretti L, Rendina I, Olynick D, Harteneck B, Dhuey S 2009 Phys. Rev. Lett. 102 133902
[8] Zhao H, Shen Y F, Zhang Z J 2014 Acta Phys. Sin. 63 174204 (in Chinese) [赵浩, 沈义峰, 张中杰 2014 63 174204]
[9] Lin H X, Yu X N, Liu S Y 2015 Acta Phys. Sin. 64 034203 (in Chinese) [林海笑, 俞昕宁, 刘士阳 2015 64 034203]
[10] Alu A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410
[11] Hao J, Yan W, Qiu M 2010 Appl. Phys. Lett. 96 101109
[12] Suchowski H, O'Brien K, Wong Z J, Salandrino A, Yin X, Zhang X 2013 Science 342 1223
[13] Ge J, Yin Y 2008 Adv. Mater. 20 3485
[14] Kim H, Ge J, Kim J, Choi S E, Lee H, Park W, Yin Y, Kwon S 2009 Nat. Photon. 3 534
[15] Horng H E, Hong C Y, Yang S Y, Yang H C 2003 Appl. Phys. Lett. 82 2434
[16] Yang S Y, Chieh J J, Horng H E, Hong C Y, Yang H C 2004 Appl. Phys. Lett. 84 5204
[17] Wen W, Zhang L, Sheng P 2000 Phys. Rev. Lett. 85 5464
[18] Buchenau U, Mller I 1972 Solid. State. Commun. 11 1291
[19] Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[20] Geng T, Wang Y, Wang X, Dong X M 2015 Acta Phys. Sin. 64 154210 (in Chinese) [耿滔, 王岩, 王新, 董祥美 2015 64 154210]
[21] Leger J R, Swanson G J 1990 Opt. Lett. 15 288
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