Issues

 / 

2006

 / 

October

  



Spatial dispersion and negative refraction of light

 a,  b
a Institute of Spectroscopy, Russian Academy of Sciences, ul. Fizicheskaya 5, Troitsk, Moscow, 108840, Russian Federation
b Department of Physics, The University of Texas at Dallas, Richardson, Texas, USA

Negative refraction at the interface between two media occurs as a natural consequence of wave group velocity being negative in one of the media. In this review the historical origins of this understanding are briefly described. A number of systems supporting normal electromagnetic waves (polaritons) with negative group velocity at optical frequencies are analyzed by including spatial dispersion and making use of the generalized dielectric tensor εij(ω, k), which determines the response of a medium to an electromagnetic wave of frequency ω and wave vector k. Negative group velocity polaritons occur when the medium (whether a natural one or an artificial meta-material) has a sufficiently strong spatial dispersion. Examples of bulk waves and surface waves are given both for chiral and nonchiral systems. The relationship between the εij(ω, k) approach and the more common but less comprehensive description using the dielectric permittivity ε(ω) and magnetic permeability μ(ω) is discussed.

Fulltext pdf (289 KB)
Fulltext is also available at DOI: 10.1070/PU2006v049n10ABEH006067
PACS: 42.25-p, 71.36+c, 78.20.Ci
DOI: 10.1070/PU2006v049n10ABEH006067
URL: https://ufn.ru/en/articles/2006/10/c/
000244185100003
2-s2.0-33847051663
2006PhyU...49.1029A
Citation: Agranovich V M, Gartstein Yu N "Spatial dispersion and negative refraction of light" Phys. Usp. 49 1029–1044 (2006)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Агранович В М, Гартштейн Ю Н «Пространственная дисперсия и отрицательное преломление света» УФН 176 1051–1068 (2006); DOI: 10.3367/UFNr.0176.200610c.1051

References (64) Cited by (209) ↓

  1. Lishchuk A, Lebourg J et al Journal of Applied Physics 139 (8) (2026)
  2. Fradkin I M, Nikulin A V et al Photon. Res. 14 (3) 919 (2026)
  3. Runge M, Woerner M, Elsaesser T Phys. Rev. Research 7 (2) (2025)
  4. Song Ya, Semchenko I et al The Design of Chiral Metamaterials and Metasurfaces (2025) p. 15
  5. Solodukhin S N Physics Letters B 859 139072 (2024)
  6. Yatsyshen V V, Borodina I I Physics Of Wave Processes And Radio Systems 27 (4) 40 (2024)
  7. Korobko P O, Kuzmov A V Powder Metall Met Ceram 62 (9-10) 572 (2024)
  8. Dwivedi R, Aradian A et al Phys. Rev. A 109 (2) (2024)
  9. Makarov P, Skandakov R et al Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences 0 (5) 73 (2024)
  10. Maimistov A  I Bull. Lebedev Phys. Inst. 50 (S9) S1066 (2023)
  11. Kim Ja, Torquato S Optica 10 (8) 965 (2023)
  12. Tarasov V E Annals Of Physics 445 169082 (2022)
  13. Kovaleva N A, Mozgovoy I V 2022 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), (2022) p. 1
  14. Basdemir H D Waves In Random And Complex Media 32 (2) 696 (2022)
  15. Taya S A, Colak I et al Appl. Opt. 60 (27) 8360 (2021)
  16. Davidovich M V J. Exp. Theor. Phys. 132 (2) 159 (2021)
  17. Yatsyshen V V J. Phys.: Conf. Ser. 1889 (2) 022087 (2021)
  18. Butukhanov V P, Lomukhin Ju L, Atutov E B J. Phys.: Conf. Ser. 2140 (1) 012020 (2021)
  19. Mikki S Foundations 2 (1) 20 (2021)
  20. Khaliji K, Stauber T, Low T Phys. Rev. B 102 (12) (2020)
  21. Juárez-Reyes L, Mendoza B S, Mochán W L Physica Status Solidi (b) 257 (5) (2020)
  22. Alvarez J V, Djafari-Rouhani B, Torrent D Phys. Rev. B 102 (11) (2020)
  23. Pazynin L A, Pazynin V L, Sliusarenko H O Opt. Lett. 44 (5) 1125 (2019)
  24. Gratus J, Kinsler P, McCall M W Eur. J. Phys. 40 (2) 025203 (2019)
  25. Davidovich M V Phys.-Usp. 62 (12) 1173 (2019)
  26. TRALLE Igor, ZIĘBA Paweł Pfe 3 (1) 53 (2019)
  27. Makarov V P, Rukhadze A A Uspekhi Fizicheskikh Nauk 189 (05) (2019)
  28. Makarov V P, Rukhadze A A Phys.-Usp. 62 (5) 487 (2019)
  29. Apostolov S S, Maizelis Z A et al Low Temperature Physics 45 (8) 885 (2019)
  30. Juárez‐Reyes Lucila, Mochán W L Physica Status Solidi (b) 255 (4) (2018)
  31. McGurn A Springer Series In Optical Sciences Vol. NanophotonicsIntroduction213 Chapter 1 (2018) p. 1
  32. Davidovich M V Jetp Lett. 108 (5) 279 (2018)
  33. Amirkhizi A V, Alizadeh V Wave Motion 83 214 (2018)
  34. Davidovich M V J. Exp. Theor. Phys. 127 (1) 1 (2018)
  35. Popov A K, Myslivets S A et al Photonics 5 (2) 8 (2018)
  36. Paśko W, Tralle I et al J Mater Sci 53 (3) 2034 (2018)
  37. Chipouline A, Küppers F Springer Series In Optical Sciences Vol. Optical Metamaterials: Qualitative ModelsIntroduction to Optical Metamaterials: Motivation and Goals211 Chapter 1 (2018) p. 1
  38. Prishchenko D A, Mazurenko V G et al Phys. Rev. B 98 (20) (2018)
  39. Butko L N, Anzulevich A P et al J. Phys.: Conf. Ser. 1092 012016 (2018)
  40. Barois P, Ponsinet V et al J. Phys.: Conf. Ser. 963 012007 (2018)
  41. McGurn A Springer Series In Optical Sciences Vol. NanophotonicsMetamaterials213 Chapter 5 (2018) p. 305
  42. Popov A K, Nefedov I S, Myslivets S A ACS Photonics 4 (5) 1240 (2017)
  43. Ponsinet V, Baron A et al EPL 119 (1) 14004 (2017)
  44. Gorelik V S, Voinov Yu P et al J. Synch. Investig. 11 (1) 246 (2017)
  45. Sous J, Berciu M, Krems R V Phys. Rev. A 96 (6) (2017)
  46. Forcella D, Prada C, Carminati R Phys. Rev. Lett. 118 (13) (2017)
  47. Fisanov V V Russ Phys J 59 (9) 1395 (2017)
  48. Apostolov S S, Havrilenko V I et al Low Temperature Physics 43 (2) 296 (2017)
  49. Chipouline A, Küppers F J. Opt. Soc. Am. B 34 (8) 1597 (2017)
  50. Gorelik V S, Bi D, Fei G T J. Adv. Dielect. 07 (06) 1750038 (2017)
  51. Rudenko S P, Stetsenko M O et al Opt. Spectrosc. 120 (4) 540 (2016)
  52. Maimistov A I, Lyashko E I Opt. Spectrosc. 121 (4) 635 (2016)
  53. Tutorials in Metamaterials 0 (2016) p. 239
  54. Bykov N V, Maimistov A I Bull. Russ. Acad. Sci. Phys. 80 (7) 770 (2016)
  55. Tarasov V E Mod. Phys. Lett. B 30 (10) 1650132 (2016)
  56. Gomez-Graña S, Le Beulze A et al Mater. Horiz. 3 (6) 596 (2016)
  57. Markel V A, Tsukerman I Phys. Rev. B 93 (22) (2016)
  58. Šindler M, Kadlec C et al Opt. Express 24 (16) 18340 (2016)
  59. Jiang Bing-feng, Hou De-fu, Li Jia-rong Phys. Rev. D 94 (7) (2016)
  60. Toptygin I N, Levina K Uspekhi Fizicheskikh Nauk 186 (2) 146 (2016)
  61. (Asia-Pacific Conference on Fundamental Problems of Opto- and Microelectronics) Vol. Asia-Pacific Conference on Fundamental Problems of Opto- and MicroelectronicsFormation of the reflected and refracted s-polarized electromagnetic waves in the Fresnel problem for the boundary vacuum-metamaterial from the viewpoint of molecular opticsYuri N.KulchinRoman V.RomashkoAlexander V.SyuyB. B.AverbukhI. B.Averbukh10176 (2016) p. 101760I
  62. Stetsenko M O, Maksimenko L S et al Nanoscale Res Lett 11 (1) (2016)
  63. Averbukh B B, Averbukh I B Russ Phys J 58 (12) 1760 (2016)
  64. Gorelik V S, Shchavlev V V Bull. Lebedev Phys. Inst. 43 (6) 189 (2016)
  65. Khokhlov Yu K Bull. Lebedev Phys. Inst. 43 (1) 49 (2016)
  66. Maimistov A I, Kazantseva E V Springer Series In Optical Sciences Vol. Contemporary OptoelectronicsOppositely Directional Coupler: Example of the Forward Backward Waves Interaction in the Metamaterials199 Chapter 11 (2016) p. 181
  67. Zhuravlev V M, Zolotovskii I O, Mironov P P Opt. Spectrosc. 121 (5) 744 (2016)
  68. Bychanok D, Plyushch A et al 2015 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS), (2015) p. 1
  69. Compaijen P J, Malyshev V A, Knoester Ja Opt. Express 23 (3) 2280 (2015)
  70. Shafeeque A A K, Nithyanandan K, Porsezian K Physics Letters A 379 (3) 223 (2015)
  71. Bychanok D, Plyushch A et al 2015 International Conference on Electromagnetics in Advanced Applications (ICEAA), (2015) p. 43
  72. Maimistov A I, Gabitov I R, Lyashko E I J. Phys.: Conf. Ser. 613 012012 (2015)
  73. Kazantseva E V, Maimistov A I Quantum Electron. 45 (12) 1137 (2015)
  74. Gorlach M A, Belov P A Phys. Rev. B 92 (8) (2015)
  75. Maimistov A I, Lyashko E I Opt. Spectrosc. 118 (5) 803 (2015)
  76. Lu X, Shapiro M A, Temkin R J Phys. Rev. ST Accel. Beams 18 (8) (2015)
  77. Gubin M Yu, Leksin A Yu et al Opt. Spectrosc. 119 (3) 497 (2015)
  78. Porvatkina O V, Tishchenko A A, Strikhanov M N J. Phys.: Conf. Ser. 643 012074 (2015)
  79. Mahapatra S J. High Energ. Phys. 2015 (1) (2015)
  80. Huang Y, Chen W Q et al AIP Advances 5 (2) (2015)
  81. Electromagnetic Phenomena in Matter 1 (2015) p. 689
  82. Lyashko E I, Maimistov A I Quantum Electron. 45 (11) 1050 (2015)
  83. Rai B, McGurn A R Phys. Rev. B 91 (8) (2015)
  84. Shevelev M, Konkov A, Aryshev A Phys. Rev. A 92 (5) (2015)
  85. Antonets I V, Kotov L N et al J. Commun. Technol. Electron. 60 (8) 904 (2015)
  86. Popov A K Springer Series In Materials Science Vol. Nonlinear, Tunable and Active MetamaterialsNonlinear Optics with Backward Waves200 Chapter 10 (2015) p. 193
  87. Korovai O V Phys. Solid State 57 (7) 1456 (2015)
  88. Naimi E K, Vekilov Yu Kh Phys. Solid State 57 (1) 111 (2015)
  89. Bobrov V B, Sokolov I M, Trigger S A Jetp Lett. 101 (5) 299 (2015)
  90. Antonets I V, Kotov L N et al Tech. Phys. Lett. 40 (7) 584 (2014)
  91. (Photonic and Phononic Properties of Engineered Nanostructures IV) Vol. Photonic and Phononic Properties of Engineered Nanostructures IVTransmission in a 1D split-ring resonator metamaterial containing a nonlinear barrier: soliton modesAliAdibiShawn-YuLinAxelSchererArthur R.McGurn8994 (2014) p. 89941C
  92. Forcella D, Mezzalira A, Musso D J. High Energ. Phys. 2014 (11) (2014)
  93. Fedorov V Yu, Nakajima T J. Opt. 16 (3) 035103 (2014)
  94. Forcella D, Zaanen Ja et al Phys. Rev. B 90 (3) (2014)
  95. Tralle I, Ziȩba P, Paśko W Journal of Applied Physics 115 (23) (2014)
  96. Porvatkina O V, Tishchenko A A, Strikhanov M N J. Phys.: Conf. Ser. 541 012024 (2014)
  97. Gevorgyan A H, Matinyan G K J. Exp. Theor. Phys. 118 (5) 771 (2014)
  98. Taya S Opto-Electronics Review 22 (4) (2014)
  99. Chern R-L, Han D Opt. Express 22 (4) 4817 (2014)
  100. Smolyakov A, Fourkal E Phys. Rev. A 87 (1) (2013)
  101. Chern R-L Opt. Express 21 (14) 16514 (2013)
  102. Amariti A, Forcella D, Mariotti A J. High Energ. Phys. 2013 (1) (2013)
  103. Zuo Zh-W, Ling D-B et al Physics Letters A 377 (40) 2909 (2013)
  104. Li X, Arnoldus H F Physics Letters A 377 (34-36) 2235 (2013)
  105. Liu Ya, Guenneau S, Gralak B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2158) (2013)
  106. Jiang Bing-feng, Hou De-fu et al Phys. Rev. D 88 (4) (2013)
  107. Mankov Yu I Phys. Solid State 55 (5) 924 (2013)
  108. Markel V A, Tsukerman I Phys. Rev. B 88 (12) (2013)
  109. Vendik I B, Vendik O G Tech. Phys. 58 (1) 1 (2013)
  110. Kazantseva E V, Maimistov A I Quantum Electron. 43 (9) 807 (2013)
  111. Naumenko G A, Potylitsyn A P et al Proceedings of the International Conference Days on Diffraction 2013, (2013) p. 105
  112. Kudyshev Zh, Gabitov I, Maimistov A Phys. Rev. A 87 (6) (2013)
  113. Alexopoulos A, Yau K S B Physics Letters A 377 (15) 1143 (2013)
  114. Dai Zh, Xu Y et al Phys. Rev. A 87 (5) (2013)
  115. Wormeester H, Oates T W H Ellipsometry at the Nanoscale Chapter 6 (2013) p. 225
  116. Tarasov V E Physics of Plasmas 20 (10) (2013)
  117. Gorelik V S Bull. Lebedev Phys. Inst. 40 (6) 150 (2013)
  118. Liu Ya, Guenneau S, Gralak B Phys. Rev. B 88 (16) (2013)
  119. Afanas’ev S A, Sannikov D G, Sementsov D I Phys. Solid State 54 (2) 332 (2012)
  120. Brée C Nonlinear Optics in the Filamentation Regime Springer Theses Chapter 2 (2012) p. 7
  121. Tatsing P H, Mohamadou A et al J. Opt. Soc. Am. B 29 (12) 3218 (2012)
  122. Ostroukhova E I, Maimistov A I Opt. Spectrosc. 112 (2) 255 (2012)
  123. Radovanović Je, Ilić I et al Appl. Phys. A 109 (4) 997 (2012)
  124. Popov A K, Shalaev M I et al Appl. Phys. A 109 (4) 835 (2012)
  125. Prokhorov A V, Barinov I O, Arakelian S M Opt. Spectrosc. 113 (3) 305 (2012)
  126. Tarapov S I, Belozorov D P Low Temperature Physics 38 (7) 603 (2012)
  127. Byrdin V M J. Commun. Technol. Electron. 57 (1) 75 (2012)
  128. Partovi T Chemistry Letters 41 (8) 760 (2012)
  129. Jiang Hai-tao, Zhang Jie-fei et al Physics Letters A 376 (17) 1509 (2012)
  130. Maimistov A I, Kazantseva E V Opt. Spectrosc. 112 (2) 264 (2012)
  131. Kim K-Y, Kim Ju et al Phys. Rev. A 85 (2) (2012)
  132. Kuroda N, Tsugawa K, Yokoi H J. Phys. Soc. Jpn. 81 (11) 114706 (2012)
  133. Amariti A, Forcella D et al J. High Energ. Phys. 2011 (4) (2011)
  134. Makarov V P, Rukhadze A A Uspekhi Fizicheskikh Nauk 181 (12) 1357 (2011)
  135. Rockstuhl C, Menzel C et al Phys. Rev. B 83 (24) (2011)
  136. Ilić I, Beličev P P et al Physics Letters A 375 (10) 1357 (2011)
  137. Tcherniega N V, Samoilovich M I et al Inorg Mater 47 (9) 1043 (2011)
  138. Jiang Hai-tao, Wang Zi-li et al Physics Letters A 375 (6) 1014 (2011)
  139. Reyes-Avendaño J A, Algredo-Badillo U et al New J. Phys. 13 (7) 073041 (2011)
  140. Oates T W H, Wormeester H, Arwin H Progress In Surface Science 86 (11-12) 328 (2011)
  141. Amariti A, Forcella D et al J. High Energ. Phys. 2011 (10) (2011)
  142. Shalashov A G, Gospodchikov E D Uspekhi Fizicheskikh Nauk 181 (2) 151 (2011)
  143. Wang H, Zhang X Phys. Rev. A 83 (5) (2011)
  144. Maimistov A I, Kazantseva E V, Ozhenko S S Bull. Russ. Acad. Sci. Phys. 75 (2) 165 (2011)
  145. Lagarkov A N, Kisel V N et al High Temp 48 (6) 983 (2010)
  146. Grochol M, Kessler E M, Piermarocchi C NanoScience And Technology Vol. Optical Generation and Control of Quantum Coherence in Semiconductor NanostructuresExciton and spin coherence in quantum dot lattices0 Chapter 9 (2010) p. 181
  147. Kravets V G, Schedin F et al Opt. Express 18 (10) 9780 (2010)
  148. Belozorov D, Khodzitsky M et al 2010 INTERNATIONAL KHARKOV SYMPOSIUM ON PHYSICS AND ENGINEERING OF MICROWAVES, MILLIMETER AND SUBMILLIMETER WAVES, (2010) p. 1
  149. Gorelik V S, Shchavlev V V Bull. Lebedev Phys. Inst. 37 (12) 374 (2010)
  150. Markel V A, Schotland J C J. Opt. 12 (1) 015104 (2010)
  151. Makarov V P, Rukhadze A A, Samokhin A A Plasma Phys. Rep. 36 (13) 1129 (2010)
  152. Kriegler Ch E, Rill M S et al IEEE J. Select. Topics Quantum Electron. 16 (2) 367 (2010)
  153. Alexopoulos A Phys. Rev. E 81 (4) (2010)
  154. Maimistov A I, Gabitov I R Optics Communications 283 (8) 1633 (2010)
  155. Fedyanin D Yu, Arsenin A V et al J. Opt. 12 (1) 015002 (2010)
  156. Chipouline A, Petschulat J et al 2010 International Conference on Advanced Optoelectronics and Lasers, (2010) p. 81
  157. Lagarkov A N, Kisel V N, Sarychev A K J. Opt. Soc. Am. B 27 (4) 648 (2010)
  158. Wei Sh, Dong Yu et al Phys. Rev. A 81 (5) (2010)
  159. Li X, Arnoldus H F Physics Letters A 374 (43) 4479 (2010)
  160. Simovski C R, Tretyakov S A Photonics And Nanostructures - Fundamentals And Applications 8 (4) 254 (2010)
  161. Rosanov N N Opt. Spectrosc. 107 (5) 768 (2009)
  162. Chern R-L, Chen Yu-T Phys. Rev. B 80 (7) (2009)
  163. Kazantseva E V, Maimistov A I, Ozhenko S S Phys. Rev. A 80 (4) (2009)
  164. Agranovich V M, Gartstein Yu N Metamaterials 3 (1) 1 (2009)
  165. Tikhodeev S G Bull. Russ. Acad. Sci. Phys. 73 (1) 88 (2009)
  166. Zhang X Materials Today 12 (12) 44 (2009)
  167. Averkov Yu O, Kats A V, Yakovenko V M Tech. Phys. 54 (9) 1245 (2009)
  168. Ramm A G Nonlinear Analysis: Theory, Methods & Applications 71 (12) e186 (2009)
  169. Liu H, Lv Q et al J. Opt. A: Pure Appl. Opt. 11 (10) 105103 (2009)
  170. Thu L M, Voskoboynikov O Phys. Rev. B 80 (15) (2009)
  171. Wegener M, Linden S Physics 2 (2009)
  172. Lagar’kov A N, Sarychev A K et al Uspekhi Fizicheskikh Nauk 179 (9) 1018 (2009)
  173. Zolotovskii I O, Sementsov D I, Barykina E I Opt. Spectrosc. 107 (1) 117 (2009)
  174. Adamashvili G T, Adamashvili N T et al Opt. Spectrosc. 106 (6) 863 (2009)
  175. Plum E, Zhou J et al Phys. Rev. B 79 (3) (2009)
  176. Dong Yu, Zhang X Journal of Applied Physics 105 (5) (2009)
  177. Ioanid A, Dafinei A S 2009 International Semiconductor Conference, (2009) p. 139
  178. Feigenbaum E, Kaminski N, Orenstein M Opt. Express 17 (21) 18934 (2009)
  179. Merlin R Proc. Natl. Acad. Sci. U.S.A. 106 (6) 1693 (2009)
  180. Tikhodeev S G, Gippius N A Uspekhi Fizicheskikh Nauk 179 (9) 1003 (2009)
  181. Tankeyev A P, Smagin V V et al Phys. Metals Metallogr. 107 (3) 229 (2009)
  182. Alexopoulos A Physics Letters A 373 (35) 3190 (2009)
  183. Cho D J, Wang F et al Phys. Rev. B 78 (12) (2008)
  184. Maimistov A I, Gabitov I R Bull. Russ. Acad. Sci. Phys. 72 (5) 704 (2008)
  185. Wang Zh, Zhang Zh et al Materials & Design 29 (9) 1777 (2008)
  186. Zhang Ya Physics Letters A 372 (29) 4962 (2008)
  187. Ramm A G Physics Letters A 372 (13) 2319 (2008)
  188. Kessler E M, Grochol M, Piermarocchi C Phys. Rev. B 77 (8) (2008)
  189. Yunxia D, Xiangdong Zh 2008 International Workshop on Metamaterials, (2008) p. 216
  190. Xu J, Zhang X Physics Letters A 372 (7) 1129 (2008)
  191. Adamashvili G T Physics Letters A 373 (1) 156 (2008)
  192. Litchinitser N M, Gabitov I R et al Progress In Optics Vol. Progress in Optics Volume 51Chapter 1 Negative refractive index metamaterials in optics51 (2008) p. 1
  193. Liu N, Hou X-D, Zhang X J. Phys.: Condens. Matter 20 (33) 335210 (2008)
  194. Elyutin S O, Ozhenko S S, Maĭmistov A I J. Opt. Technol. 75 (10) 625 (2008)
  195. Ramm A G Physics Letters A 372 (43) 6518 (2008)
  196. Biancalana F, Creatore C Opt. Express 16 (19) 14882 (2008)
  197. Urzhumov Ya A, Shvets G Solid State Communications 146 (5-6) 208 (2008)
  198. Dong Yu, Zhang X Opt. Express 16 (21) 16950 (2008)
  199. Kozlov A V, Mozhaev V G Physics Letters A 372 (26) 4718 (2008)
  200. Maĭmistov A I, Gabitov I R, Litchinitser N M Opt. Spectrosc. 104 (2) 253 (2008)
  201. Brodin G, Marklund M et al Physics Letters A 367 (3) 233 (2007)
  202. Ivanov A V, Shalygin A N et al Jetp Lett. 85 (11) 565 (2007)
  203. de Medeiros F F, Albuquerque E L et al J. Phys.: Condens. Matter 19 (49) 496212 (2007)
  204. Darmanyan S A, Kobyakov A, Chowdhury D Q Physics Letters A 363 (1-2) 159 (2007)
  205. Shvartsburg A B, Kuzmiak V, Petite G Physics Reports 452 (2-3) 33 (2007)
  206. Plum E, Fedotov V A et al Applied Physics Letters 90 (22) (2007)
  207. Ramm A G Physics Letters A 370 (5-6) 522 (2007)
  208. Perel’man M E Physics Letters A 370 (5-6) 528 (2007)
  209. Kästel J, Fleischhauer M, Juzeliūnas G Phys. Rev. A 76 (6) (2007)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions