References

1. Metamaterial Photonic Crystals: What is Real?P.Y. Chen1, A.A. Asatryan2, C.G. Poulton2, K.B. Dossou2, M.J. Steele3, L.C. Botten2, R.C McPhedran1, C.M. de Sterke11 School of Physics, University of Sydney, NSW, 2006 2School of Mathematical Sciences, University of Technology Sydney, NSW, 20073 Department of Physics & CUDOS, Macquarie University, 2109parche@physics.usyd.edu.au Abstract ─ We examine the bandstructures of 2D photonic crystals incorporating both positive and negative refractive index materials. In the absence of both dispersion and loss, metamaterial inclusions yield bands that tend to cluster around the high symmetry reciprocal lattice points and hence do not span the entire Brillouin zone. Incorporating metamaterials with causal dispersion relations (satisfying the Kramers-Kronig relations) destroys these unique band topologies, unless the dispersion relation is specially engineered to be flat over a large frequency range. Such dispersion relations include loss is an almighty pain in the butt. • Dispersionless and Lossless • Bands do not span entire Brillouin zone • Bands cluster around high symmetry points • Leads to extra large bandgaps and island states • Turing points correspond to zero energy modes • Positive energy not satisfied by dispersion relation • Bandstructure may be explained by reconnection phenomona • Causal Dispersion • Must satisfy postive energy • Drude lossless dispersion relation destroys interesting effects • Based on a series of Lorentz oscillators, dispersion can be engineered Dispersion with Loss Small amounts of loss cause cusping Depends on complex k or complex omega Possibly depends on direction of complex k Epsilon and mu chosen to be the same References [1] L.C. Botten et al., Photonic band structure calculations using scattering matrices, Phys. Rev. E, 64 (4), 046603, (2001). [2] L.C. Botten et al., Scattering and propogation through grating stacks for photonic crystals, J. Opt. Soc. Am. A, 17 (12), 2165-76, (2000). [3] J. Li et al., Photonic Band Gap from a Stack of Positive and Negative Index Materials, Phys. Rev. Lett.,90 (8), 083901 (2003). [4] A.D. Boardman and K. Marinov, Electromagnetic energy in a dispersive metamaterial, Phy. Rev. B, 73 (16), 165110 (2006). [5] H. van derLem et al., J. Opt. Soc. Am. B, 20 (6), 1334-41 (2003). [6] K.J. Webb and L. Thylén, Perfect-lens-material condition from adjacent absorptive and gain resonances, Opt. Lett., 33 (7), 747-9, (2008) [7] R.C. McPhedran et al., Density of states functions for photonic crystals, Phys. Rev. E, 69 (1), 016609, (2004)