Spatial dispersion and negative refraction of light

Negative refraction occurs at interfaces as a natural consequence of the negative group velocity of waves in one of the interfacing media. The historical origin of this understanding of the phenomenon is briefly discussed. We consider several physical systems that may exhibit normal electromagnetic waves (polaritons) with negative group velocity at optical frequencies. These systems are analyzed in a unified way provided by the spatial dispersion framework. The framework utilizes the notion of the generalized dielectric tensor eij(ω, k) representing the electromagnetic response of the medium to perturbations of frequency ω and wave vector k. Polaritons with negative group velocity can exist in media (whether in natural or in artificial meta-materials) with a sufficiently strong spatial dispersion. Our examples include both gyrotropic and nongyrotropic systems, and bulk and surface polariton waves. We also discuss the relation between the spatial dispersion approach and the more familiar, but more restricted, description involving the dielectric permittivity e(ω) and the magnetic permeability μ(ω) .

[1]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[2]  V. Veselago The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[3]  Plane waves with negative phase velocity in isotropic chiral mediums , 2004, physics/0412131.

[4]  Donald B. Melrose,et al.  Electromagnetic processes in dispersive media : a treatment based on the dielectric tensor , 1991 .

[5]  J. Mugnier,et al.  Strong coupling between surface plasmons and excitons in an organic semiconductor. , 2004, Physical review letters.

[6]  Bruce A. Garett Molecular Light Scattering and Optical Activity, 2nd ed , 2005 .

[7]  Reflection of light at structured chiral interfaces. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  U. Chettiar,et al.  Negative index of refraction in optical metamaterials. , 2005, Optics letters.

[9]  Anvar A. Zakhidov,et al.  Negative refraction in gyrotropic media , 2006 .

[10]  Optical bulk and surface waves with negative refraction , 2004 .

[11]  A. Geim,et al.  Nanofabricated media with negative permeability at visible frequencies , 2005, Nature.

[12]  V. Veselago,et al.  Электродинамика веществ с одновременно отрицательными значениями ε и μ , 1967 .

[13]  M. Laue Die Fortpflanzung der Strahlung in dispergiernden und absorbierenden Medien , 1905 .

[14]  R. Baughman,et al.  Linear and nonlinear wave propagation in negative refraction metamaterials , 2003 .

[15]  隆夫 国府田,et al.  V. M. Agranovich and D. L. Mills 編: Surface Polaritons, Electromagnetic Waves at Surfaces and Interfaces, North-Holland, Amsterdam and New York, 1982, xvi+717ページ, 24.5×17cm, 38,350円 (Modern Problems in Condensed Matter Sciences, Vol. 1). , 1983 .

[16]  Daniel W. van der Weide,et al.  Wave propagation in nonlinear left-handed transmission line media , 2005 .

[17]  K. McDonald Negative Group Velocity , 2000, physics/0008013.

[18]  A. P. Vinogradov METHODOLOGICAL NOTES: On the form of constitutive equations in electrodynamics , 2002 .

[19]  Sailing He,et al.  Focusing by a slab of chiral medium. , 2005, Optics express.

[20]  G. Zhizhin,et al.  The surface polariton splitting due to thin surface film LO vibrations , 1975 .

[21]  R. Shelby,et al.  Experimental Verification of a Negative Index of Refraction , 2001, Science.

[22]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[23]  Y. Kivshar,et al.  Nonlinear properties of left-handed metamaterials. , 2003, Physical review letters.

[24]  Ari Sihvola,et al.  Waves and Energy in Chiral Nihility , 2002 .

[25]  John B. Pendry,et al.  Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials , 2004 .

[26]  D. Forester,et al.  Negative refraction and focusing of circularly polarized waves in optically active media. , 2005, Physical review letters.

[27]  M. Lapine,et al.  Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  T. A. Leskova,et al.  Diffraction methods in the spectroscopy of thin films in the vicinity of resonances , 1988 .

[29]  G. Dresselhaus,et al.  Linear Wave-Vector Shifts in the Raman Spectrum of α-Quartz and Infrared Optical Activity , 1969 .

[30]  Yuri S. Kivshar,et al.  Second-harmonic generation in nonlinear left-handed metamaterials , 2006 .

[31]  J. Pendry A Chiral Route to Negative Refraction , 2004, Science.

[32]  Horace Lamb,et al.  On Group - Velocity , 1904 .

[33]  T. López-Rios,et al.  Splitting of the Al surface plasmon dispersion curves by Ag surface layers , 1978 .

[34]  V. Agranovich Meetings and Conferences: the Problem of the Defects in the Process of Excition Luminescence of Molecular Crystals , 1960 .

[35]  A. Brillante,et al.  Exciton–surface plasmon coupling: An experimental investigation , 1982 .