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25:
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224:. While this restriction is not practically significant, the criterion has been generalized into a covariant form. Veselago NPV media are also called "left-handed (meta)materials", as the components of plane waves passing through (electric field, magnetic field, and wave vector) follow the left-hand rule instead of the
480:. However, in NPV materials, the negative square root is chosen to mimic the fact that the wave vector and phase velocity are also reversed. The refractive index is a derived quantity that describes how the wavevector is related to the optical frequency and propagation direction of the light; thus, the sign of
265:
and wave vector of a propagating light field, and instead directly consider the response of the materials. Assuming the material is achiral, one can consider what values of permittivity (ε) and permeability (μ) result in negative phase velocity (NPV). Since both ε and μ are generally complex, their
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Mackay, Tom G.; Lakhtakia, Akhlesh (2009-06-12). "Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials".
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270:) material to display negative refraction. In these materials, the criterion for negative phase velocity is derived by Depine and Lakhtakia to be
1023:
R. A. Depine and A. Lakhtakia (2004). "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity".
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that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a
129:(i.e., a positive refractive index), and the other has the more exotic negative phase velocity (a negative refractive index).
161:, and energy to velocity. "Phase velocity" is used conventionally, as phase velocity has the same sign as the wave vector.
1401:
Zhang, S.; Park, Y.-S.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. (2009). "Negative
Refractive Index in Chiral Metamaterials".
945:
Veselago, Viktor G (1968-04-30). "The electrodynamics of substances with simultaneously negative values of ε and μ".
634:
61:
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Tretyakov, S.; Nefedov, I.; Shivola, A.; Maslovski, S.; Simovski, C. (2003). "Waves and Energy in Chiral
Nihility".
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do not need to be negative. A negative refractive index due to chirality was predicted by Pendry and
Tretyakov
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394:
NPV occurrence does not necessarily imply negative refraction (negative refractive index). Typically, the
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391:
are the real valued parts of ε and μ, respectively. For active materials, the criterion is different.
1341:
Plum, E.; Zhou, J.; Dong, J.; Fedotov, V. A.; Koschny, T.; Soukoulis, C. M.; Zheludev, N. I. (2009).
228:. The terms "left-handed" and "right-handed" are generally avoided as they are also used to refer to
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P. Kinsler and M. W. McCall (2008). "Criteria for negative refraction in active and passive media".
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Negative refraction occurs at interfaces between materials at which one has an ordinary positive
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The consequence of negative refraction is light rays are refracted on the same side of the
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A comparison of refraction in a left-handed metamaterial to that in a normal material
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M. W. McCall (2008). "A Covariant Theory of
Negative Phase Velocity Propagation".
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on entering the material, as indicated in the diagram, and by a general form of
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Video representing negative refraction of light at uniform planar interface.
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J. Skaar (2006). "On resolving the refractive index and the wave vector".
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Proceedings of
International Conference on Antenna Theory and Techniques
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Light wave refraction with opposite properties to those usually observed
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Negative phase velocity (NPV) is a property of light propagation in a
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122:. Such materials are sometimes called "double negative" materials.
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A typical criterion used to determine
Veselago's NPV is that the
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which has been designed to achieve a negative value for electric
600:{\displaystyle n=\pm {\sqrt {\epsilon _{r}\mu _{r}}}\pm \kappa }
1235:
Pendry, J. B. (2004). "A Chiral Route to
Negative Refraction".
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imaginary parts do not have to be negative for a passive (i.e.
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of the
Poynting vector and wave vector is negative (i.e., that
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730:, and first observed simultaneously and independently by Plum
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341:{\displaystyle \epsilon _{r}|\mu |+\mu _{r}|\epsilon |<0,}
141:. There are different definitions of NPV; the most common is
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213:{\displaystyle \scriptstyle {\vec {P}}\cdot {\vec {k}}<0}
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A negative refractive index occurs for one polarization if
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where by convention the positive square root is chosen for
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1289:Journal of Electromagnetic Waves and Applications
930:: CS1 maint: DOI inactive as of September 2024 (
261:One can choose to avoid directly considering the
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500:must be chosen to match the physical situation.
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665:{\displaystyle {\sqrt {\epsilon _{r}\mu _{r}}}}
153:. Other definitions include the opposition of
449:{\displaystyle n=\pm {\sqrt {\epsilon \mu }}}
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62:Learn how and when to remove this message
46:, without removing the technical details.
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1073:Microwave and Optical Technology Letters
1026:Microwave and Optical Technology Letters
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528:also depends on the chirality parameter
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145:original proposal of opposition of the
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384:{\displaystyle \epsilon _{r},\mu _{r}}
44:make it understandable to non-experts
903:"Metamaterials on antenna solutions"
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13:
14:
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901:Slyusar, Vadym I. (2009-10-10).
784:Multiple-prism dispersion theory
23:
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967:10.1070/pu1968v010n04abeh003699
861:Permeability (electromagnetism)
789:N-slit interferometric equation
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692:{\displaystyle \epsilon _{r}}
1010:10.1016/j.metmat.2008.05.001
825:Electromagnetic interactions
774:Negative index metamaterials
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1380:10.1103/PhysRevB.79.035407
1320:10.1163/156939303322226356
1149:10.1103/PhysRevB.79.235121
918:10.1109/ICATT.2009.4435103
236:Negative refractive index
719:{\displaystyle \mu _{r}}
1403:Physical Review Letters
1257:10.1126/science.1104467
624:{\displaystyle \kappa }
541:{\displaystyle \kappa }
133:Negative phase velocity
86:phenomenon where light
947:Soviet Physics Uspekhi
920:(inactive 2024-09-12).
799:Photonic metamaterials
764:Acoustic metamaterials
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1312:2003JEWA...17..695T
1249:2004Sci...306.1353P
1188:2006OptL...31.3372S
1141:2009PhRvB..79w5121M
1002:2008MetaM...2...92M
959:1968SvPhU..10..509V
504:In chiral materials
80:negative refraction
1455:Physical phenomena
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1049:10.1002/mop.20127
856:Electron mobility
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521:{\displaystyle n}
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151:Poynting vector
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926:cite journal
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878:Photo-Dember
867:Permittivity
851:EM radiation
794:Perfect lens
769:Metamaterial
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735:
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112:permeability
104:permittivity
100:metamaterial
79:
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58:
49:
33:
1080:(7): 1804.
996:(2–3): 92.
752:Snell's law
166:dot product
155:wave vector
147:wave vector
1444:Categories
1296:(5): 695.
889:References
873:Wavenumber
841:Dielectric
742:Refraction
734:and Zhang
1450:Photonics
1388:119259753
1363:0806.0823
1328:119507930
1192:CiteSeerX
1132:0903.1530
1104:117834803
1087:0806.1676
975:0038-5670
912:: 19–24.
883:Impedance
738:in 2009.
708:μ
681:ϵ
652:μ
642:ϵ
619:κ
595:κ
592:±
581:μ
571:ϵ
565:±
536:κ
442:μ
439:ϵ
434:±
373:μ
360:ϵ
322:ϵ
308:μ
296:μ
282:ϵ
222:covariant
198:→
189:⋅
183:→
96:interface
92:refracted
52:July 2020
1431:19257274
1273:13485411
1265:15550665
1214:17072427
758:See also
1411:Bibcode
1368:Bibcode
1308:Bibcode
1245:Bibcode
1237:Science
1184:Bibcode
1137:Bibcode
1057:6072651
998:Bibcode
955:Bibcode
699:and/or
232:media.
90:become
82:is the
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748:normal
736:et al.
732:et al.
728:et al.
351:where
230:chiral
139:medium
94:at an
76:optics
1384:S2CID
1358:arXiv
1346:(PDF)
1324:S2CID
1298:arXiv
1269:S2CID
1218:S2CID
1174:arXiv
1127:arXiv
1100:S2CID
1082:arXiv
1053:S2CID
1035:arXiv
906:(PDF)
631:>
268:lossy
1427:PMID
1261:PMID
1210:PMID
971:ISSN
932:link
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