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Issue 9, 2026
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Reviews of topical problems


Light propagation in composite materials with gain layers

 a, b,  a, b,  a, b,  c,  a, b
a Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, ul. Izhorskaya 13/19, Moscow, 127412, Russian Federation
b Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russian Federation
c Department of Physics, Queens College of the City University of New York, Flushing, New York, USA

Light propagation through a single gain layer and a multilayer system with gain layers is studied. Results obtained using the Fresnel formulas, Airy’s series summation, and the numerical solution of the nonlinear Maxwell—Bloch equations by the finite difference time domain (FDTD) method are analyzed and compared. Normal and oblique propagation of a wave through a gain layer and a slab of a photonic crystal are examined. For the latter problem, the gain line may be situated in either the pass or stop band of the photonic crystal. It is shown that the monochromatic plane-wave approximation is generally inapplicable for active media, because it leads to results that violate causality. But the problem becomes physically meaningful and correct results can be obtained for all three approaches once the structure of the wavefront and the finite aperture of the beam are taken into account.

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Fulltext is also available at DOI: 10.3367/UFNe.0182.201211b.1157
PACS: 41.20.Jb, 42.70.Qs, 73.20.−r (all)
DOI: 10.3367/UFNe.0182.201211b.1157
URL: https://ufn.ru/en/articles/2012/11/b/
000314808600002
2-s2.0-84873896836
2012PhyU...55.1080D
Citation: Dorofeenko A V, Zyablovsky A A, Pukhov A A, Lisyansky A A, Vinogradov A P "Light propagation in composite materials with gain layers" Phys. Usp. 55 1080–1097 (2012)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 27th, October 2010, revised: 16th, July 2012, 2nd, August 2012

Оригинал: Дорофеенко А В, Зябловский А А, Пухов А А, Лисянский А А, Виноградов А П «Прохождение света через композитные материалы, содержащие усиливающие слои» УФН 182 1157–1175 (2012); DOI: 10.3367/UFNr.0182.201211b.1157

References (101) ↓ Cited by (60) Similar articles (20)

  1. Iga K IEEE J. Selected Topics Quantum Electron. 6 1201 (2000)
  2. Botez D, Scifres D R (Eds) Diode Laser Arrays (Cambridge: Cambridge Univ. Press, 2005)
  3. Kawai S (Ed.) Handbook Of Optical Interconnects (Boca Raton: CRC Press/Taylor & Francis Group, 2005)
  4. Yu S F Analysis And Design Of Vertical Cavity Surface Emitting Lasers (Hoboken, NJ: Wiley-Interscience, 2003)
  5. Wilmsen C W, Temkin H, Coldren L A (Eds) Vertical-Cavity Surface-Emitting Lasers: Design, Fabrication, Characterization, And Applications (Cambridge: Cambridge Univ. Press, 1999)
  6. Cheng J, Dutta N K (Eds) Vertical-Cavity Surface-Emitting Lasers (Amsterdam: Gordon & Breach, 2000)
  7. Asatryan A A et al. Phys. Rev. B 57 13535 (1998)
  8. Bulgakov S A, Nieto-Vesperinas M Waves Random Media 10 373 (2000)
  9. Frank R, Lubatsch A, Kroha J Phys. Rev. B 73 245107 (2006)
  10. Heinrichs J Phys. Rev. B 56 8674 (1997)
  11. Jiang X, Li Q, Soukoulis C M Phys. Rev. B 59 R9007 (1999)
  12. Joshi S K, Jayannavar A M Phys. Rev. B 56 12038 (1997)
  13. Nam C-K, Zhang Z-Q Phys. Rev. B 66 073101 (2002)
  14. Paasschens J C J, Misirpashaev T Sh, Beenakker C W J Phys. Rev. B 54 11887 (1996)
  15. Ramakrishna S A et al. Phys. Rev. B 62 256 (2000)
  16. Yamilov A et al. Phys. Rev. B 71 092201 (2005)
  17. Datta P K Phys. Rev. B 59 10980 (1999)
  18. Dowling J P et al. J. Appl. Phys. 75 1896 (1994)
  19. Jiang X, Soukoulis C M Phys. Rev. Lett. 85 70 (2000)
  20. Feng Y, Ueda K Opt. Express 12 3307 (2004)
  21. Pendry J B Phys. Rev. Lett. 85 3966 (2000)
  22. ’E’?с’?’?’?’?’? ’E ’I Usp. Fiz. Nauk 92 517 (1967); Veselago V G Sov. Phys. Usp. 10 509 (1968)
  23. Ramakrishna S A, Pendry J B Phys. Rev. B 67 201101(R) (2003)
  24. Fang A, Koschny T, Soukoulis C M J. Opt. 12 024013 (2010)
  25. Xiao S et al. Nature 466 735 (2010)
  26. Cai W, Shalaev V Optical Metamaterials. Fundamentals And Applications (New York: Springer, 2010)
  27. Wuestner S et al. Phys. Rev. Lett. 105 127401 (2010)
  28. ’E’?’?’?’?р’?’?’?’? ’B ’z, ’K’?р’?ф’?’?’?’?’? ’B ’E, ’Oуkh’?’? ’l Usp. Fiz. Nauk 178 511 (2008); Vinogradov A P, Dorofeenko A V, Zouhdi S Phys. Usp. 51 485 (2008)
  29. ’E’?’?’?’?р’?’?’?’? ’B ’z, ’K’?р’?ф’?’?’?’?’? ’B ’E, ’a’?р’?’?’?’?’?’? ’B ’a, ’’’?сya’?с’?’?’? ’B ’B Usp. Fiz. Nauk 180 249 (2010); Vinogradov A P, Dorofeenko A V, Merzlikin A M, Lisyansky A A Phys. Usp. 53 243 (2010)
  30. Sh’?тр’?’? ’B ’K ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 52 1430 (2007); Shatrov A D J. Commun. Technol. Electron. 52 1324 (2007)
  31. Mozjerin I et al. Opt. Lett. 35 3240 (2010)
  32. Sarychev A K, Pukhov A A, Tartakovsky G PIERS Online 3 1264 (2007)
  33. Sarychev A K, Tartakovsky G Phys. Rev. B 75 085436 (2007)
  34. Gabitov I R, Kennedy B, Maimistov A I IEEE J. Selected Topics Quantum Electron. 16 401 (2010)
  35. ’’’?’?’?рь’?’?’? ’B ’v ’? ’?р. Usp. Fiz. Nauk 179 1018 (2009); Lagarkov A N et al. Phys. Usp. 52 959 (2009)
  36. Noginov M A et al. Opt. Express 16 1385 (2008)
  37. Kh’?’?’?’? Ya ’R ’dс’?’?’?ы ’?’?’?’?’?’?’?’? ’?’?’?’?р’?’? (’a.: ’s’?’?’?’?т’?’?т, 1999)
  38. Hu X et al. Phys. Rev. B 77 205104 (2008)
  39. Solimeno S, Crosignani B, DiPorto P Guiding, Diffraction, And Confinement Of Optical Radiation (Orlando: Academic Press, 1986); ’l’?’?’?’?’?’?’? ’l, ’Fр’?’?’?’?ьya’?’? ’G, ’K’? ’z’?рт’? ’z ’K’?фр’?’?ts’?ya ’? ’?’?’?’?’?’?’?’?’?’?’? р’?с’?р’?стр’?’?’?’?’?’? ’?’?т’?ch’?с’?’?’?’? ’?’?’?уch’?’?’?ya (’a.: ’a’?р, 1989)
  40. ’F’?’?’?’?’?’?’?’? ’B ’B Usp. Fiz. Nauk 169 1025 (1999); Kolokolov A A Phys. Usp. 42 931 (1999)
  41. ’E’?’?’?shт’?’?’? ’’ ’B Usp. Fiz. Nauk 118 339 (1976); Vainshtein L A Sov. Phys. Usp. 19 189 (1976)
  42. ’F’?’?’?’?’?’?’?’? ’B ’B ’z’?сь’?’? Zh’e’n’s 21 660 (1975); Kolokolov A A JETP Lett. 21 312 (1975)
  43. ’i’?’?’?’?’?’? ’I ’v, Sh’?kh’?’?zh’?’?’?’? ’l ’l ’z’?сь’?’? Zh’e’n’s 16 298 (1972); Romanov G N, Shakhidzhanov S S JETP Lett. 16 210 (1972)
  44. ’G’?’?’?’? ’G ’G, ’z’?тр’?’? ’v ’l ’dтр’?zh’?’?’?’? с’?’?т’? ’?т ус’?’?’?’?’?yushch’?kh ’? ’?’?’?’?’?’?’?’?ыkh ср’?’? (’a’?’?с’?: ’v’?у’?’? ’? т’?kh’?’?’?’?, 1988)
  45. Dolling G et al. Opt. Lett. 31 1800 (2006)
  46. Wegener M et al. Opt. Express 16 19785 (2008)
  47. Meinzer N et al. Opt. Express 18 24140 (2010)
  48. Dong Z-G et al. Appl. Phys. Lett. 96 044104 (2010)
  49. Fang A et al. Phys. Rev. B 79 241104(R) (2009)
  50. Fang A, Koschny Th, Soukoulis C M Phys. Rev. B 82 121102(R) (2010)
  51. Chen X et al. Phys. Rev. E 70 016608 (2004)
  52. Smith D R et al. Phys. Rev. E 71 036617 (2005)
  53. Menzel C et al. Phys. Rev. B 77 195328 (2008)
  54. Franceschetti G Alta Frequenza 36 757 (1967)
  55. Smith D R, Schurig D Phys. Rev. Lett. 90 077405 (2003)
  56. ’’’?’?р’?’?ть’?’? ’a ’B, Sh’?’?’?т ’G ’E ’a’?т’?’?ы т’?’?р’?’? фу’?’?ts’?’? ’?’?’?’?’?’?’?с’?’?’?’? ’?’?р’?’?’?’?’?’?’?’? (’a.: ’v’?у’?’?, 1965)
  57. Lagarkov A N, Kissel V N Phys. Rev. Lett. 92 077401 (2004)
  58. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’e’?’?’?тр’?’?’?’?’?’?’?’?’? с’?’?’?sh’?ыkh ср’?’? (’a.: ’s’?’?’?’?т’?’?т, 2003); Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  59. ’’’?’?’?’?’?’? ’l ’B, ’E’?’?’?’?’? ’E ’a, ’F’?’?’?’? ’G Ya ’d’?т’?’?’? с’?’?’?тр’?с’?’?’?’?ya 35 976 (1973)
  60. ’F’?’?’?’? ’G Ya, ’E’?’?’?’?’? ’E ’a, ’’’?’?’?’?’?’? ’l ’B ’z’?сь’?’? Zh’e’n’s 16 144 (1972); Kogan B Ya, Volkov V M, Lebedev S A JETP Lett. 16 100 (1972)
  61. Goos F, Hänchen H Ann. Physik 436 333 (1947)
  62. Goos F, Lindberg-Hänchen H Ann. Physik 440 251 (1949)
  63. Bergman D J, Stockman M I Phys. Rev. Lett. 90 027402 (2003)
  64. Andrianov E S et al. Opt. Express 19 24849 (2011)
  65. Andrianov E S et al. Opt. Lett. 36 4302 (2011)
  66. Andrianov E S et al. Phys. Rev. B 85 165419 (2012)
  67. Andrianov E S et al. Phys. Rev. B 85 035405 (2012)
  68. Lisyansky A A et al. Phys. Rev. B 84 153409 (2011)
  69. Stockman M I Phil. Trans. R. Soc. A 369 3510 (2011)
  70. ’B’?’?р’?’?’?’?’? ’M ’l, ’zуkh’?’? ’B ’B, ’K’?р’?ф’?’?’?’?’? ’B ’E, ’E’?’?’?’?р’?’?’?’? ’B ’z ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 57 114 (2012); Andrianov E S, Pukhov A A, Dorofeenko A V, Vinogradov A P J. Commun. Technol. Electron. 57 106 (2012)
  71. Plum E et al. Opt. Express 17 8548 (2009)
  72. ’F’?’?’?’?’?’?’?’? ’B ’B, ’l’?р’?ts’?’?’? ’I ’E Usp. Fiz. Nauk 162 (12) 165 (1992); Kolokolov A A, Skrotskii G V Sov. Phys. Usp. 35 1089 (1992)
  73. ’E’?’?’?’?р’?’?’?’? ’B ’z, ’K’?р’?ф’?’?’?’?’? ’B ’E ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 50 1246 (2005); Vinogradov A P, Dorofeenko A V J. Commun. Technol. Electron. 50 1153 (2005)
  74. Vinogradov A P et al. Phys. Rev. B 80 235106 (2009)
  75. Vinogradov A P, Dorofeenko A V Opt. Commun. 256 333 (2005)
  76. Mandel L, Wolf E Optical Coherence And Quantum Optics (Cambridge: Cambridge Univ. Press, 1995); ’a’?’?’?’?’?ь ’’, ’E’?’?ьф ’e ’d’?т’?ch’?с’?’?ya ’?’?’?’?р’?’?т’?’?сть ’? ’?’?’?’?т’?’?’?ya ’?’?т’?’?’? (’a.: ’s’?’?’?’?т’?’?т, 2000)
  77. Heitler W The Quantum Theory Of Radiation (Oxford: Clarendon Press, 1954); ’I’?’?т’?’?р ’E ’F’?’?’?т’?’?’?ya т’?’?р’?ya ’?’?’?уch’?’?’?ya (’a.: ’R’’, 1956)
  78. ’dр’?’?’?с’?’?’? ’B ’v Kvantovaya Elektron. 29 (11) 137 (1999); Oraevsky A N Quantum Electron. 29 975 (1999)
  79. Pantell R H, Puthoff H E Fundamentals Of Quantum Electronics (New York: Wiley, 1969); ’z’?’?т’?’? ’i, ’zутkh’?ф ’I ’dс’?’?’?ы ’?’?’?’?т’?’?’?’? э’?’?’?тр’?’?’?’?’? (’a.: ’a’?р, 1972)
  80. Scully M O, Zubairy M S Quantum Optics (Cambridge: Cambridge Univ. Press, 1997); ’l’?’?’?’?’? ’a ’d, ’Oу’?’?’?р’? ’a ’l ’F’?’?’?т’?’?’?ya ’?’?т’?’?’? (’a.: ’s’?’?’?’?т’?’?т, 2003)
  81. Lukš A, Peřinová V Quantum Aspects Of Light Propagation (Dordrecht: Springer, 2009)
  82. Erneux T, Glorieux P Laser Dynamics (New York: Cambridge Univ. Press, 2010)
  83. Zyablovsky A A, Dorofeenko A V, Vinogradov A P, Pukhov A A Photon. Nanostruct. Fundament. Appl. 9 398 (2011)
  84. Kivshar Y S, Agrawal G P Optical Solitons: From Fibers To Photonic Crystals (Amsterdam: Academic Press, 2003)
  85. ’Oya’?’?’?’?с’?’?’? ’B ’B, ’K’?р’?ф’?’?’?’?’? ’B ’E, ’zуkh’?’? ’B ’B, ’E’?’?’?’?р’?’?’?’? ’B ’z ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 56 1142 (2011); Zyablovsky A A, Dorofeenko A V, Pukhov A A, Vinogradov A P J. Commun. Technol. Electron. 56 1139 (2011)
  86. Yariv A Quantum Electronics (New York: Wiley, 1975); Yaр’?’? ’B ’F’?’?’?т’?’?’?ya э’?’?’?тр’?’?’?’?’? (’a.: ’l’?’?. р’?’?’?’?, 1980)
  87. Jackson J D Classical Electrodynamics (New York: Wiley, 1962); ’Kzh’?’?с’?’? ’K ’F’?’?сс’?ch’?с’?’?ya э’?’?’?тр’?’?’?’?’?’?’?’?’? (’a.: ’a’?р, 1965)
  88. Airy G B Philos. Mag. 2 20 (1833)
  89. Sturrock P A Phys. Rev. 112 1488 (1958)
  90. Skaar J Phys. Rev. E 73 026605 (2006)
  91. ’E’?’?’?’?’?’?р’?’? ’E ’l ’d’?’?’?shch’?’?’?ы’? фу’?’?ts’?’? ’? ’?’?т’?’?’?т’?ch’?с’?’?’? ф’?’?’?’?’? (’a.: ’v’?у’?’?, 1979)
  92. ’E’?’?’?’?’?’?р’?’? ’E ’l ’pр’?’?’?’?’?’?ya ’?’?т’?’?’?т’?ch’?с’?’?’? ф’?’?’?’?’? (’a.: ’v’?у’?’?, 1981); Vladimirov V S Equations Of Mathematical Physics (Moscow: Mir, 1984)
  93. ’l’?’?уkh’?’? ’K ’E ’d’?shch’?’? ’?урс ф’?’?’?’?’? ’n. 4 ’d’?т’?’?’? (’a.: ’s’?’?’?’?т’?’?т, ’a’s’n’R, 2002)
  94. ’Gут’?’?’?’? ’M ’R ’d’?т’?’?’? (’a.: ’Eысsh’?ya sh’?’?’?’?, 1986)
  95. Born M, Wolf E Principles Of Optics (Oxford: Pergamon Press, 1969); ’G’?р’? ’a, ’E’?’?ьф ’e ’dс’?’?’?ы ’?’?т’?’?’? (’a.: ’v’?у’?’?, 1970)
  96. Sommerfeld A Vorlesungen über Theoretische Physik Bd. 4 Optik (Wiesbaden: Dieterich, 1950); Sommerfeld A Lectures On Theoretical Physics Vol. 4 Optics (New York: Academic Press, 1954); ’O’?’?’?’?рф’?’?ь’? ’B ’d’?т’?’?’? (’a.: ’R’’, 1953)
  97. ’E’?’?’?’?’?’? ’i ’G, ’F’?ts’?’?’?’?’?’?’?’?у’? ’G ’O ’dс’?’?’?ы т’?’?р’?’? ’?’?фр’?’?ts’?’? (’a.: ’v’?у’?’?, 1982)
  98. ’E’?’?’?shт’?’?’? ’’ ’B ’dт’?рыты’? р’?’?’?’?’?т’?ры ’? ’?т’?рыты’? ’?’?’?’?’?’?’?’?ы (’a.: ’l’?’?. р’?’?’?’?, 1966); Weinstein L A Open Resonators And Open Waveguides (Boulder, Colo.: Golem Press, 1969)
  99. Bahlouli H et al. Phys. Rev. B 72 094304 (2005)
  100. ’a’?’?tsы’?’?’? ’G ’R ’F’?’?’?р’?’?т’?’?ya ’? ’?’?’?’?’?’?’?’?’?ya ’?’?т’?’?’? ф’?т’?’?’?ыkh ’?р’?ст’?’?’?’?’? (’a.: ’s’?’?’?’?т’?’?т, 2009)
  101. Kurizki G et al. Progress In Optics Vol. 42 (Ed. E Wolf) (Amsterdam: North-Holland, 2001) p. 93; Kurizki G et al. nlin/0007007
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