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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, 141701, 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.

Fulltext pdf (749 KB)
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)
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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 (57) 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. Veselago V G 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. Vinogradov A P, Dorofeenko A V, Zukhdi S Usp. Fiz. Nauk 178 511 (2008); Vinogradov A P, Dorofeenko A V, Zouhdi S Phys. Usp. 51 485 (2008)
  29. Vinogradov A P, Dorofeenko A V, Merzlikin A M, Lisyanskii A A Usp. Fiz. Nauk 180 249 (2010); Vinogradov A P, Dorofeenko A V, Merzlikin A M, Lisyansky A A Phys. Usp. 53 243 (2010)
  30. Shatrov A D Radiotekhnika Elektronika 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. Lagar’kov A N i dr. 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. Khanin Ya I Osnovy Dinamiki Lazerov (M.: Fizmatlit, 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); Solimeno S, Krozin’yani B, Di Porto P Difraktsiya i Volnovodnoe Rasprostranenie Opticheskogo Izlucheniya (M.: Mir, 1989)
  40. Kolokolov A A Usp. Fiz. Nauk 169 1025 (1999); Kolokolov A A Phys. Usp. 42 931 (1999)
  41. Vainshtein L A Usp. Fiz. Nauk 118 339 (1976); Vainshtein L A Sov. Phys. Usp. 19 189 (1976)
  42. Kolokolov A A Pis’ma ZhETF 21 660 (1975); Kolokolov A A JETP Lett. 21 312 (1975)
  43. Romanov G N, Shakhidzhanov S S Pis’ma ZhETF 16 298 (1972); Romanov G N, Shakhidzhanov S S JETP Lett. 16 210 (1972)
  44. Boiko B B, Petrov N S Otrazhenie Sveta ot Usilivayushchikh i Nelineinykh Sred (Minsk: Nauka i tekhnika, 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. Lavrent’ev M A, Shabat B V Metody Teorii Funktsii Kompleksnogo Peremennogo (M.: Nauka, 1965)
  57. Lagarkov A N, Kissel V N Phys. Rev. Lett. 92 077401 (2004)
  58. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Fizmatlit, 2003); Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  59. Lebedev S A, Volkov V M, Kogan B Ya Optika Spektroskopiya 35 976 (1973)
  60. Kogan B Ya, Volkov V M, Lebedev S A Pis’ma ZhETF 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. Andrianov E S, Pukhov A A, Dorofeenko A V, Vinogradov A P Radiotekhnika Elektronika 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. Kolokolov A A, Skrotskii G V Usp. Fiz. Nauk 162 (12) 165 (1992); Kolokolov A A, Skrotskii G V Sov. Phys. Usp. 35 1089 (1992)
  73. Vinogradov A P, Dorofeenko A V Radiotekhnika Elektronika 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); Mandel’ L, Vol’f E Opticheskaya Kogerentnost’ i Kvantovaya Optika (M.: Fizmatlit, 2000)
  77. Heitler W The Quantum Theory Of Radiation (Oxford: Clarendon Press, 1954); Gaitler V Kvantovaya Teoriya Izlucheniya (M.: IL, 1956)
  78. Oraevskii A N Kvantovaya Elektronika 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); Pantel R, Putkhof G Osnovy Kvantovoi Elektroniki (M.: Mir, 1972)
  80. Scully M O, Zubairy M S Quantum Optics (Cambridge: Cambridge Univ. Press, 1997); Skalli M O, Zubairi M S Kvantovaya Optika (M.: Fizmatlit, 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. Zyablovskii A A, Dorofeenko A V, Pukhov A A, Vinogradov A P Radiotekhnika Elektronika 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); Yariv A Kvantovaya Elektronika (M.: Sov. radio, 1980)
  87. Jackson J D Classical Electrodynamics (New York: Wiley, 1962); Dzhekson D Klassicheskaya Elektrodinamika (M.: Mir, 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. Vladimirov V S Obobshchennye Funktsii v Matematicheskoi Fizike (M.: Nauka, 1979)
  92. Vladimirov V S Uravneniya Matematicheskoi Fiziki (M.: Nauka, 1981); Vladimirov V S Equations Of Mathematical Physics (Moscow: Mir, 1984)
  93. Sivukhin D V Obshchii Kurs Fiziki T. 4 Optika (M.: Fizmatlit, MFTI, 2002)
  94. Butikov E I Optika (M.: Vysshaya shkola, 1986)
  95. Born M, Wolf E Principles Of Optics (Oxford: Pergamon Press, 1969); Born M, Vol’f E Osnovy Optiki (M.: Nauka, 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); Zommerfel’d A Optika (M.: IL, 1953)
  97. Vaganov R B, Katsenelenbaum B Z Osnovy Teorii Difraktsii (M.: Nauka, 1982)
  98. Vainshtein L A Otkrytye Rezonatory i Otkrytye Volnovody (M.: Sov. radio, 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. Mantsyzov B I Kogerentnaya i Nelineinaya Optika Fotonnykh Kristallov (M.: Fizmatlit, 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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