| The following overview paper is available: | A. Lakhtakia, M.W. McCall, W.S. Weiglhofer, J. Gerardin and J. Wang, 'On mediums with negative phase velocity: a brief overview,' Proc. SPIE 4806 (July 7-11, 2002). | Download Preprint physics/0205027 | Negative phase velocity in outer space: | T.G. Mackay and A. Lakhtakia, 'Negative refraction in outer space?,' Current Science, 86, 2004, 1593. | Download Preprint physics/0405103 | Negative refraction by vacuum: | A. Lakhtakia and T.G. Mackay, 'Negative refraction of light by vacuum,' August 2004. | Download Preprint physics/0408021 |
In a negative phase velocity medium, the phase velocity is directed opposite to the direction of energy flow (and attenuation).
Other names in use:
The emergence of a clear terminology is often a difficult process
with regards to scientific findings relating to novel effects,
something that is also apparent in the present instance. The first
label for the candidate materials is left-handed
materials. But chiral materials are important
subjects of electromagnetics research and the terms
left-handedness and right-handedness have been
applied to the molecular structure
of such materials for well over a century.
The continued use of the term left-handed materials
(LHMs) for achiral materials
will thus confuse crucial microstructural issues.
The term backward (BW) medium has been advanced
by some researchers. But every
wave propagates forward. Regardless of the
merits of any a priori definitions of
forward and backward directions for planewave propagation,
this term would be problematic
in the context of nonplanar interfaces.
Some researchers use the technical term double
negative (DNG) medium to indicate the
condition of the real parts of both
permittivity and permeability being negative. But double
negativity is not a necessary condition for
the phase velocity to be negative (in a passive material).
The term negative index medium (NIM) should also be avoided, because it is really the
phase velocity which is negatively directed.
The term
negative phase velocity (NPV) medium
is unambiguous
and is not in conflict with any physical scenario to which it is
applicable.
422. A. Lakhtakia, 'An electromagnetic trinity from "negative permittivity" and "negative permeability",' International Journal of Infrared and Millimeter Waves, 22, 2001, 1731 - 1734; correctly reprinted: 23, 2002, 813 - 818. [Nihility, vacuum, and anti-vacuum.]Updated on: May 26, 2012
429. A. Lakhtakia, 'Reversal of circular Bragg phenomenon in ferrocholesteric materials with negative real permittivities and permeabilities,' Advanced Materials, 14, 2002, 447 - 449. [NPV and structural chirality.]
431. A. Lakhtakia, 'Reversed circular dichroism of isotropic chiral mediums with negative real permeability and permittivity,' Microwave and Optical Technology Letters, 33, 2002, 96 - 97. [NPV and isotropic chirality.]
432. A. Lakhtakia, 'On perfect lenses and nihility,' International Journal of Infrared and Millimeter Waves, 23, 2002, 339 - 343. [The truth about perfect lenses.]
436. M.W. McCall, A. Lakhtakia & W.S. Weiglhofer, 'The negative index of refraction demystified,' European Journal of Physics, 23, 2002, 353 - 359. [Negative refractive index does not necessarily require both negative permittivity and negative permeability.]
437. J. Wang & A. Lakhtakia, 'On reflection from a half-space with negative real permittivity and permeability,' Microwave and Optical Technology Letters, 33, 2002, 465 - 467. [FDTD calculations of reflection coefficient.]
443. J. Gerardin & A. Lakhtakia, 'Negative index of refraction and distributed Bragg reflectors,' Microwave and Optical Technology Letters, 34, 2002, 409 - 411. [NPV and Bragg structures.]
444. J. Gerardin & A. Lakhtakia, 'Spectral response of Cantor multilayers made of materials with negative refractive index,' Physics Letters A, 301, 2002, 377 - 381. [NPV and fractal structures.]
. [Mini-review.]
455. A. Lakhtakia & J.A. Sherwin, 'Orthorhombic materials and perfect lenses,' International Journal of Infrared and Millimeter Waves, 24, 2003, 19 - 23. [More truth about perfect lenses.]
458. [NPV materials and GH shifts.]
466. A. Lakhtakia, 'Handedness reversal of circular Bragg phenomenon due to negative real permittivity and permeability,' Optics Express, 11, 2003, 716 - 722. [NPV and structural chirality.]
469. A. Lakhtakia & C.M. Krowne, 'Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),' Optik, 114, 2003, 305 - 307. [NPV, ENG and MNG.]
473. A. Lakhtakia & M.W. McCall, 'Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium,' Optik, 115, 2004, 28 - 30. [The truth about amphoteric refraction: positive refraction can masquerade as negative refraction.]
476. A. Lakhtakia, 'Conjugation symmetry in linear electromagnetism in extension of materials with negative real permittivity and permeability scalars,' Microwave and Optical Technology Letters, 40, 2004, 160 - 161. [NPV and underlying symmetries of the Maxwell postulates.]
483. T.G. Mackay & A. Lakhtakia, 'Plane waves with negative phase velocity in Faraday chiral mediums,' Physical Review E, 69, 2004, 026602. [Proper extension of NPV concept to anisotropic and bianisotropic materials.]
484. R.A. Depine & A. Lakhtakia, 'Perturbative approach for diffraction due to a periodically corrugated boundary between vacuum and a negative phase-velocity material,' Optics Communications, 233, 2004, 277 - 282. [Gratings made of NPV materials.]
486. A. Lakhtakia & T.G. Mackay, 'Infinite phase velocity as the boundary between negative and positive phase velocities,' Microwave and Optical Technology Letters, 41, 2004, 165 - 166. [NPV, PPV and IPV.]
487. R.A. Depine & A. Lakhtakia, 'A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,' Microwave and Optical Technology Letters, 41, 2004, 315 - 316. [Negative refractive index does not necessarily require negative permittivity and negative permeability.]
491. T.G. Mackay & A. Lakhtakia, 'Negative phase velocity in a uniformly moving, homogeneous, isotropic, dielectric-magnetic medium,' Journal of Physics A: Mathematical & General, 37, 2004, 5697 - 5711. [NPV and special theory of relativity.]
492. R.A. Depine & A. Lakhtakia, 'Plane-wave diffraction at the periodically corrugated boundary of vacuum and a negative-phase-velocity material,' Physical Review E, 69, 2004, 057602. [Gratings made of NPV materials.]
494. T.G. Mackay & A. Lakhtakia, 'Negative refraction in outer space?,' Current Science, 86, 2004, 1593. [NPV and special theory of relativity.]
495. A. Lakhtakia, 'Positive and negative Goos-Hänchen shifts and negative phase-velocity mediums (alias left-handed materials),' Archiv für Elektronik und Übertragungstechnik, 58, 2004, 229 - 231. [NPV materials and +/- GH shifts.]
498. A. Lakhtakia and T.G. Mackay, 'Towards gravitationally assisted negative refraction by vacuum,' Journal of Physics A: Mathematical & General, 37, 2004, L505 - L510; correction: 37, 2004, 12093; comment: 38, 2005, 2543 - 2544; reply: 38, 2005, 2545 - 2546. [NPV and general theory of relativity.]
507. R.A. Depine & A. Lakhtakia, 'Diffraction gratings of isotropic negative-phase velocity materials,' Optik, 116, 2005, 31 - 43. [Gratings made of NPV materials.]
511. A. Lakhtakia, T.G. Mackay & S. Setiawan, 'Global and local perspectives of gravitationally assisted negative-phase-velocity propagation of electromagnetic waves in vacuum,' Physics Letters A, 336, 2005, 89 - 96. [NPV and general theory of relativity.]
512. T.G. Mackay, A. Lakhtakia & S. Setiawan, 'Gravitation and electromagnetic wave propagation with negative phase velocity,' New Journal of Physics, 7, 2005, 75. [NPV and general theory of relativity.]
513. R.A. Depine, A. Lakhtakia & D.R. Smith, 'Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material,' Physics Letters A, 337, 2005, 155 - 160. [Gratings made of NPV materials.]
514. T.G. Mackay, S. Setiawan & A. Lakhtakia, 'Negative phase velocity of electromagnetic waves and the cosmological constant,' European Physical Journal C Direct, 41 (s01), 2005, 1 - 4. [NPV, general theory of relativity, and curvature.]
516. S. Setiawan, T.G. Mackay & A. Lakhtakia, 'A comparison of superradiance and negative phase velocity phenomenons in the ergosphere of a rotating black hole,' Physics Letters A, 341, 2005, 15 - 21; corrections: 361, 2007, 534. [NPV, general theory of relativity, and curvature.]
522. R.A. Depine & A. Lakhtakia, 'Diffraction by a grating made of a uniaxial dielectric-magnetic medium exhibiting negative refraction,' New Journal of Physics, 7, 2005, 158. [Gratings made of anisotropic NPV materials.]
523. T.G. Mackay & A. Lakhtakia, 'Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,' New Journal of Physics, 7, 2005, 165. [Anisotropic NPV materials.]
524. T.G. Mackay, A. Lakhtakia & Sandi Setiawan, 'Electromagnetic negative-phase-velocity propagation in the ergosphere of a rotating black hole,' New Journal of Physics, 7, 2005, 171. [NPV and black holes.]
531. T.G. Mackay, A. Lakhtakia & S. Setiawan, 'Electromagnetic waves with negative phase velocity in Schwarzschild-de Sitter spacetime,' Europhysics Letters, 71, 2005, 925 - 931. [NPV, black holes, radially expanding/contracting universes, and curvature.]
534. T.G. Mackay & A. Lakhtakia, 'Negative phase velocity in isotropic dielectric-magnetic media via homogenization,' Microwave and Optical Technology Letters, 47, 2005, 313 - 315. [Isotropic NPV materials as composite materials.]
537. A. Lakhtakia & T.G. Mackay, 'Fresnel coefficients for a permittivity-permeability phase space encompassing vacuum, anti-vacuum, and nihility,' Microwave and Optical Technology Letters, 48, 2006, 265 - 270. [Nihility.]
538. T.G. Mackay, A. Lakhtakia & R.A. Depine, 'Uniaxial dielectric media with hyperbolic dispersion relations,' Microwave and Optical Technology Letters, 48, 2006, 363 - 367. [Hyperbolic dispersion relations.]
539. R.A. Depine, M.E. Inchaussandague & A. Lakhtakia, 'Application of the differential method to uniaxial gratings with an infinite number of refraction channels: Scalar case,' Optics Communications, 258, 2006, 90 - 96. [Gratings made of NPV materials.]
546. R.A. Depine, M.E. Inchaussandague & A. Lakhtakia, 'Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction,' Journal of the Optical Society of America B, 23, 2006, 514 - 528. [Gratings made of NPV materials.]
547. T.G. Mackay & A. Lakhtakia, 'Gravity-induced negative refraction of electromagnetic waves,'Current Science, 90, 2006, 640 - 641. [NPV and general theory of relativity.]
548. R.A. Depine, M.E. Inchaussandague & A. Lakhtakia, 'Classification of dispersion equations for homogeneous dielectric-magnetic uniaxial materials,' Journal of the Optical Society of America A, 23, 2006, 949 - 955. [Anisotropic NPV materials.]
549. A. Lakhtakia & T.G. Mackay, 'Negative phase velocity in isotropic dielectric-magnetic media via homogenization: Part II,' Microwave and Optical Technology Letters, 48, 2006, 709 - 712. [Isotropic NPV materials as composite materials.]
553. A. Lakhtakia, 'Scattering by a nihility sphere,' Microwave and Optical Technology Letters, 48, 2006, 895 - 896. [Nihility.]
563. T.G. Mackay & A. Lakhtakia, 'Correlation length and negative phase velocity in isotropic dielectric-magnetic materials,' Journal of Applied Physics, 100, 2006, 063533. [Isotropic NPV materials as composite materials.]
568. A. Lakhtakia & J.B. Geddes, 'Scattering by a nihility cylinder,' AEÜ International Journal of Electronics and Communications, 61, 2007, 62 - 65. [Nihility.]
569. A. Lakhtakia & T.G. Mackay, 'Meet the metamaterials,' OSA Optics & Photonics News, 18 (1), January 2007, 32 - 39. [Simple introduction to metamaterials.]
571. T.G. Mackay & A. Lakhtakia, 'Concealment by uniform motion,' Journal of the European Optical Society - Rapid Publications, 2, 2007, 07003. [NPV and special theory of relativity.]
581. T.G. Mackay & A. Lakhtakia, 'Counterposition and negative refraction due to uniform motion,' Microwave and Optical Technology Letters, 49, 2007, 874 - 876. [NPV and special theory of relativity.]
584. T.G. Mackay & A. Lakhtakia, 'Simultaneous negative- and positive-phase-velocity propagation in an isotropic chiral medium,' Microwave and Optical Technology Letters, 49, 2007, 1245 - 1246. [Isotropic chiral NPV materials.]
588. T.G. Mackay & A. Lakhtakia, 'Lorentz covariance of the canonical perfect lens,' Physics Letters A, 366, 2007, 179 - 183. [Perfect lens.]
596. T.G. Mackay & A. Lakhtakia, 'Negative- and positive-phase-velocity propagation in an isotropic chiral medium moving at constant velocity,' Microwave and Optical Technology Letters, 49, 2007, 2640 - 2643. [Isotropic chiral medium.]
598. J.B. Geddes III, T.G. Mackay & A. Lakhtakia, 'On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy,' Optics Communications, 280, 2007, 120 - 125. [Perfect lens.]
601. A. Lakhtakia, J.B. Geddes III & T.G. Mackay, 'When does the choice of the refractive index of a linear, homogeneous, isotropic, active, dielectric medium matter?,' Optics Express, 15, 2007, 17709 - 17714. [Active dielectric medium.]
604. T.G. Mackay & A. Lakhtakia, "Response to 'On negative refraction in classical vacuum'," Journal of Modern Optics, 55, 2008, 323 - 328. [NPV and general theory of relativity.]
606. T.G. Mackay & A. Lakhtakia, 'Electromagnetic fields in linear bianisotropic mediums,' Progress in Optics, 51, 2008, 121 - 209. [Basic theory.]
607. M.E. Inchaussandague, A. Lakhtakia & R.A. Depine, 'On metallic gratings coated conformally with isotropic negative-phase-velocity materials,' Physics Letters A, 372, 2008, 2522 - 2526. [NPV gratings.]
619. T.G. Mackay & A. Lakhtakia, 'Negative reflection in a Faraday chiral medium,' Microwave and Optical Technology Letters, 50, 2008, 1368 - 1371. [Negative reflection.]
623. A. Lakhtakia, 'Radiation pressure efficiencies of spheres made of isotropic, achiral, passive, homogeneous, negative-phase-velocity materials,' Electromagnetics, 28, 2008, 346 - 353. [NPV spheres.]
627. J. Han, A. Lakhtakia & C.W. Qiu, 'Terahertz metamaterials with semiconductor split-ring resonators for magnetostatic tunability,' Optics Express, 16, 2008, 14390 - 14390. [Tunable split-ring resonators.]
634. T.G. Mackay & A. Lakhtakia, 'Positive-, negative-, and orthogonal-phase-velocity propagation of electromagnetic plane waves in a simply moving medium -- reformulation and reappraisal,' Optik, 120, 2009, 45 - 48.
639. A. Lakhtakia, T.G. Mackay & J.B. Geddes III, 'On the inapplicability of a negative-phase-velocity condition as a negative-refraction condition for active materials,' Microwave and Optical Technology Letters, 51, 2009, 1230; comment: 52, 2010, 247; reply: 52, 2010, 1681.
643. Y.-J. Jen, A. Lakhtakia, C.-W. Yu & C.-T. Lin, 'Vapor-deposited thin films with negative real refractive index in the visible regime,' Optics Express, 17, 2009, 7784 - 7789.
653. T.G. Mackay & A. Lakhtakia, 'Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,' Physical Review B, 79, 2009, 235121.
661. T.G. Mackay & A. Lakhtakia, 'Counterposition and negative phase velocity in uniformly moving dissipative materials,' Journal of Physics A: Mathematical and Theoretical, 42, 2009, 415401.
663. Y.-J. Jen, A. Lakhtakia, C.-W. Yu & C.-T. Lin, 'Negative refraction in an uniaxial absorbent dielectric material,' European Journal of Physics, 30, 2009, 1381 - 1390.
666. T.G. Mackay & A. Lakhtakia, 'Negative refraction and positive refraction are not Lorentz covariant,' Physics Letters A, 374, 2009, 101 - 105.
667. Á. Gómez, M.L. Martinez Ricci, R.A. Depine & A. Lakhtakia, 'Photonic band gap materials comprising positive-phase-velocity and negative-phase-velocity layers in waveguides,' Journal of Modern Optics, 56, 2009, 1688 - 1697.
672. T.G. Mackay & A. Lakhtakia (Invited Paper), 'Negatively refracting chiral metamaterials: a review,' SPIE Reviews, 1, 2009, 018003.
675. B.M. Ross, T.G. Mackay & A. Lakhtakia, 'On negative-phase-velocity propagation in the ergosphere of a charged rotating black hole,' Optik, 121, 2010, 401 - 407.
689. Y.-J. Jun, A. Lakhtakia, C.-W. Yu & Y.-H. Wang, 'Negative real parts of the equivalent permittivity, permeability, and refractive index of sculptured-nanorod arrays of silver,' Journal of the Vacuum Society of America A, 28, 2010, 1078 - 1083.
712. Q.A. Naqvi, T.G. Mackay & A. Lakhtakia, 'Optical refraction in silver: counterposition, negative phase velocity and orthogonal phase velocity,' European Journal of Physics, 32, 2011, 883 - 893 [doi:10.1088/0143-0807/32/4/004].
725. Y.-J. Jen, A. Lakhtakia, C.-W. Yu, J.-J. Jhou, W.-H. Wang, M.-J. Lin, H.-M. Wu & H.-S. Liao, 'Silver/silicon dioxide/silver sandwich films in the blue-to-red spectral regime with negative-real refractive index,' Applied Physics Letters, 99, 2011, 181117 [doi:10.1063/1.3658624].
729. T.G. Mackay & A. Lakhtakia, ''Response to 'On the orthogonality of the phase velocity and its feasibility for plane waves'," Optik, 123, 2012, 280 - 281 [doi:10.1016/j.ijleo.2010.10.054].
732. X. Zhang, J. Gu, W. Cao, J. Han, A. Lakhtakia & W. Zhang, 'Bilayer-fish-scale ultrabroad terahertz bandpass filter,' Optics Letters, 37, 2012, 906 - 908 [doi:10.1364/OL.37.000906].
736. Q. Li, X. Zhang, W. Cao, A. Lakhtakia, J.F. O'Hara, J. Han & W. Zhang, 'An approach for mechanically tunable, dynamic terahertz bandstop filters,' Applied Physics A, 107, 2012, 285 - 291 [doi 10.1007/s00339-012-6861-2].