Abstract
We investigate propagation behavior of electromagnetic waves in a slab uniaxial metamaterial waveguide with metal cladding and discuss the dispersion relation, group velocity and energy flux distribution of transverse electric guided modes in two kinds of uniaxial metamaterial waveguides with different orientations of optical axis in detail. The numerical results show that there exist anomalous dispersion properties such as backward modes existing in low-frequency range, and the group velocity can be negative or approach zero. If the orientation of optical axis is selected properly, each guided mode has two dispersion curves—one is normal dispersion and another belongs to anomalous dispersion and shows a transition from a backward mode to a forward one with the angular frequency increasing. In addition, the condition of the existence of cutoff frequency is clarified. These properties may have potential applications in optical information storage, optical communication, integrated optics and nanophotonic devices.
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References
V.G. Veselago, The electrodynamics of substances with simultaneously negative values of epsilon and miu. Sov. Phys. Usp 10, 509 (1968)
R. Shelby, D.R. Smith, S. Schultz, Experimental verification of a negative index of refraction. Science 292, 77 (2001)
L. Wu, S.L. He, H. Chen, On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials. Opt. Express 11, 1283 (2003)
D.R. Smith, W. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Shultz, Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184 (2000)
S.M. Zou, G.H. Wang, Magnetic coupling effect on nonlinear properties in negative index metamaterials with a kerr nonlinearity. Plasmonics 8, 1361 (2013)
M.W. Feise, P.J. Bevelacqua, J.B. Schneider, Effects of surface waves on the behavior of perfect lenses. Phys. Rev. B 66, 035113 (2002)
D.R. Smith, S. Schurig, Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Phys. Rev. Lett. 90, 077401 (2003)
V. Ginis, P. Tassin, C.M. Soukoulis, I. Veretennicoff, Enhancing optical gradient forces with metamaterials. Phys. Rev. Lett. 110, 057401 (2013)
Z. Shi, Q. Guo, Modal fields in a symmetric metal-clad planar uniaxial crystal waveguide. J. Lightwave Technol. 27, 3135 (2009)
G. Zheng, L. Ran, Light transmission along a slab waveguide with a core of anisotropic metamaterial. Optik 119, 591 (2008)
W. Yan, L. Shen, L. Ran, Surface modes at the interfaces between isotropic media and indefinite media. J. Opt. Soc. Am. A 24(2), 530 (2007)
V.A. Podolskiv, E.E. Narimanov, Strongly anisotropic waveguide as a nonmagnetic left-handed system. Phys. Rev. B 71, 201101 (2005)
I.V. Shadrivov, A.A. Sukhorukov, Y.S. Kivsar, Guided modes in negative-refractive-index waveguides. Phys. Rev. E 67, 057602 (2003)
Z.H. Wang, Z.Y. Xiao, S.P. Li, Guided modes in slab waveguides with a left-handed material cover or substrate. Opt. Commun. 281, 607 (2008)
P.A. Belov, C.R. Simovski, Subwavelength metallic waveguides loaded by uniaxial resonant scatterers. Phys. Rev. E 72, 036618 (2005)
T. Pan, G.-D. Xu, T.-C. Zang, L. Gao, Study of a slab waveguide loaded with dispersive anisotropic metamaterials. Appl. Phys. A 95, 367 (2009)
N.-H. Shen, Q. Wang, J. Chen, Y.-X. Fan, J. Ding, H.-T. Wang, Y. Tian, N.-B. Ming, Optically uniaxial left-handed materials. Phys. Rev. B 72, 153104 (2005)
J. Yao, X. Yang, X. Yina, G. Bartal, X. Zhang, Three-dimensional nanometer-scale optical cavities of indefinite medium. Proc. Nat. Acad. Sci. 108, 11327 (2011)
J. Gao, X. Yang, Anomalous optical coupling between two silicon wires of a slot waveguide inepsilon-near-zero metamaterials. Opt. Commun. 314, 18–22 (2014)
X.-F. Zhu, X.-Y. Zou, X.-W. Zhou, B. Liang, J.-C. Cheng, Concealing a passive sensing system with single-negative layers. Chin. Phys. Lett. 29, 014102 (2012)
J. Gao, L. Sun, H. Deng, C.J. Mathai, S. Gangopadhyay, X. Yang, Experimental realization of epsilon-near-zero metamaterial slabs with metal-dielectric multilayers. Appl. Phys. Lett. 103, 051111 (2013)
X. Yang, J. Yao, J. Rho, X. Yin, X. Zhang, Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nat. Photonics 6, 450 (2012)
X. Yang, A. Ishikawa, X. Yin, X. Zhang, Hybrid photonic-plasmonic crystal nanocavities. ACS Nano 5, 2831–2838 (2011)
X. Zhu, L. Feng, P. Zhang, X. Yin, X. Zhang, One-way invisible cloak using parity-time symmetric transformation optics. Opt. Lett. 38, 2821–2824 (2013)
J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A.M. Stacy, X. Zhang, Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930 (2008)
J.B. Pendry, A.J. Holden, W.J. Stewart, I. Youngs, Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773 (1996)
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This work was supported by the National Natural Science Foundation of China (Grant No. 61178003).
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Lei, Y., Wang, G. & Zhang, W. Anomalous dispersion and group velocity properties in subwavelength uniaxial metamaterial waveguide with metal cladding. Appl. Phys. A 117, 1437–1445 (2014). https://doi.org/10.1007/s00339-014-8571-4
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DOI: https://doi.org/10.1007/s00339-014-8571-4