OSA's Digital Library

Advances in Optics and Photonics

Advances in Optics and Photonics


  • Editor: Bahaa E. A. Saleh
  • Vol. 2, Iss. 3 — Sep. 30, 2010

Slow light in various media: a tutorial

Jacob B. Khurgin  »View Author Affiliations

Advances in Optics and Photonics, Vol. 2, Issue 3, pp. 287-318 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1796 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



I consider the physical basics of slow light propagation in atomic media, photonic structures, and optical fibers. I show similarities and differences between all of the above media and develop set of criteria that are then used to compare different media. Special attention is given to dispersion of group velocity and loss, which are shown to limit the bandwidth and delay capacity of all the slow light schemes.

© 2010 Optical Society of America

ToC Category:
Nonlinear Optics

Original Manuscript: October 26, 2009
Revised Manuscript: February 4, 2010
Manuscript Accepted: February 8, 2010
Published: March 23, 2010

Virtual Issues
(2010) Advances in Optics and Photonics

Jacob B. Khurgin, "Slow light in various media: a tutorial," Adv. Opt. Photon. 2, 287-318 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–596 (1999). [CrossRef]
  2. D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001). [CrossRef]
  3. R. W. Boyd, D. J. Gauthier, “Slow and fast light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497–530. [CrossRef]
  4. P. W. Milonni, “Controlling the speed of light pulses,” J. Phys. B 35, R31–R56 (2002). [CrossRef]
  5. P. W. Milonni, Fast Light, Slow Light, and Left-Handed Light (Institute of Physics, 2005).
  6. J. B. Khurgin, R. S. Taylor, Slow Light: Science and Applications (Taylor & Francis, 2009).
  7. H. A. Lorentz, “Uber die Beziehung zwischen der Fortpflanzung des Lichtes und der Körperdichte,” Wiedemann Ann. 9, 641–664 (1880). [CrossRef]
  8. J. R. Pierce, Traveling Wave Tubes (Van Nostrand, 1950).
  9. S. L. McCall, E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967). [CrossRef]
  10. D. Grischkowsky, “Adiabatic following and slow optical pulse propagation in rubidium vapor,” Phys. Rev. A 7, 2096 (1973). [CrossRef]
  11. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005). [CrossRef]
  12. A. B. Matsko, D. V. Strekalov, L. Maleki, “On the dynamic range of optical delay lines based on coherent atomic media,” Opt. Express 13, 2210–2223 (2005). [CrossRef] [PubMed]
  13. J. B. Khurgin, “Optical buffers based on slow light in EIT media and coupled resonator structures—comparative analysis,” J. Opt. Soc. Am. B 22, 1062–1074 (2005). [CrossRef]
  14. S. Chu, S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982). [CrossRef]
  15. S. Chu, S. Wong, “Linear pulse propagation in an absorbing medium—response,” Phys. Rev. Lett. 49, 1293 (1982). [CrossRef]
  16. B. Segard, B. Macke, “Observation of negative velocity pulse propagation,” Phys. Lett. A 109, 213–216 (1985). [CrossRef]
  17. S. E. Harris, J. E. Field, A. Imamoglu, “Nonlinear optics using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990). [CrossRef]
  18. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999). [CrossRef]
  19. R. M. Camacho, M. V. Pack, J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73, 063812 (2006). [CrossRef]
  20. R. M. Camacho, M. V. Pack, J. C. Howell, A. Schweinsberg, R. W. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007). [CrossRef] [PubMed]
  21. M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003). [CrossRef] [PubMed]
  22. M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003). [CrossRef] [PubMed]
  23. R. M. Camacho, M. V. Pack, J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74, 0338012006. [CrossRef]
  24. K-J. Boller, A. Imamoglu, S. E. Harris, “Observation of EIT,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]
  25. S. E. Harris, J. E. Field, A. Kasapi, “Dispersive properties of EIT,” Phys. Rev. A. 46, R39–R321992. [CrossRef]
  26. A. Kasapi, M. Jain, G. Y. Jin, S. E. Harris, “EIT: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995). [CrossRef] [PubMed]
  27. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, 2002. “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2002). [CrossRef] [PubMed]
  28. M. D. Lukin, A. Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000). [CrossRef] [PubMed]
  29. F. E. Zimmer, A. Andre, M. D. Lukin, M. Fleischhauer, “Coherent control of stationary light pulses,” Opt. Commun. 264, 441–453 (2006). [CrossRef]
  30. O. Firstenberg, M. Shuker, N. Davidson, A. Ron, “Elimination of the diffraction of arbitrary images imprinted on slow light,” Phys. Rev. Lett. 102, 043601 (2009). [CrossRef] [PubMed]
  31. R. M. Camacho, C. J. Broadbent, I. Ali-Khan, J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007). [CrossRef] [PubMed]
  32. Z. Shi, R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Am. 25, 136–139 (2008). [CrossRef]
  33. Z. Shi, R. W. Boyd, D. J. Gauthier, C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007). [CrossRef] [PubMed]
  34. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007). [CrossRef]
  35. P. K. Kondratko, S. W. Chang, H. Su, S. L. Chuang, “Slow light with tunable bandwidth in p-doped and intrinsic quantum dot electro-absorbers,” Appl. Phys. Lett. 90, 251108 (2007). [CrossRef]
  36. F. Ohman, K. Yivind, J. Mork, “Voltage-controlled slow light in an integrated semiconductor structure with net gain,” Opt. Express 14, 9955–9962 (2006). [CrossRef] [PubMed]
  37. F. G. Sedgwick, B. Pesala, J. Y. Lin, W. S. Ko, X. X. Zhao, C. J. Chang-Hasnain, “THz-bandwidth tunable slow light in semiconductor optical amplifiers,” Opt. Express 15, 747–753 (2007). [CrossRef] [PubMed]
  38. R. S. Tucker, P. C. Ku, C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005). [CrossRef]
  39. D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007). [CrossRef]
  40. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]
  41. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008). [CrossRef]
  42. T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007). [CrossRef]
  43. N. M. Litchinitser, B. J. Eggleton, G. P. Agrawal, “Dispersion of cascaded fiber gratings in WDM lightwave systems,” J. Lightwave Technol. 16, 1523–1529 (1999). [CrossRef]
  44. S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovitch, V. Grubsky, D. S. Starodubov, Feinberg, “Group velocity dispersion cancellation and additive group delays by cascaded fiber Bragg gratings in transmission,” IEEE Microw. Guid. Wave Lett. 8, 327–329 (1998). [CrossRef]
  45. J. B. Khurgin, J. U. Kang, Y. J. Ding, “Ultrabroad-bandwidth electro-optic modulator based on a cascaded Bragg grating,” Opt. Lett. 25, 70–72 (2000). [CrossRef]
  46. D. Mori, T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide.,” Opt. Express 13, 9398–9408 (2005). [CrossRef] [PubMed]
  47. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13, 7145–7159 (2005). [CrossRef] [PubMed]
  48. D. Mori, S. Kubo, H. Sasaki, T. Baba, “Experimental demonstration of wideband dispersion-compensated slow light by a chirped photonic crystal directional coupler,” Opt. Express 15, 5264–5270 (2007). [CrossRef] [PubMed]
  49. S. C. Huang, M. Kato, E. Kuramochi, C. P. Lee, M. Notomi, “Time-domain and spectral-domain investigation of inflection-point slow-light modes in photonic crystal coupled waveguides,” Opt. Express 15, 3543–3549 (2007). [CrossRef] [PubMed]
  50. T. Kawasaki, D. Mori, T. Baba, “Experimental observation of slow light in photonic crystal coupled waveguides,” Opt. Express 15, 10274–10281 (2007). [CrossRef] [PubMed]
  51. J. B. Khurgin, “Light slowing down in Moiré fiber gratings and its implications for nonlinear optics,” Phys Rev A 62, 3821–3824 (2000). [CrossRef]
  52. S. Longhi, D. Janner, G. Galzerano, G. Della Valle, D. Gatti, P. Laporta, “Optical buffering in phase-shifted fibre gratings,” Electron. Lett. 41, 1075–1077 (2005). [CrossRef]
  53. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]
  54. C. K. Madsen, G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10, 994–9961998. [CrossRef]
  55. A. Melloni, F. Morichetti, M. Martnelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–378 (2003). [CrossRef]
  56. Z. Wang, S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003). [CrossRef]
  57. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 63804 (2004). [CrossRef]
  58. J. E. Heebner, R. W. Boyd, “‘Slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002). [CrossRef]
  59. S. Mookhejea, “Dispersion characteristics of coupled-resonator optical waveguides,” Opt. Lett. 30, 2406–2408 (2005). [CrossRef]
  60. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]
  61. F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007). [CrossRef]
  62. A. B. Matsko, A. A. Savchenlov, L. Maleki, “Vertically coupled whispering-gallery-mode resonator waveguide,” Opt. Lett.3066–3068 (2005). [CrossRef] [PubMed]
  63. J. B. Khurgin, “Dispersion and loss limitations on the performance of optical delay lines based on coupled resonant structures,” Opt. Lett. 32, 163–165 (2007). [CrossRef]
  64. J. B. Khurgin, “Expanding the bandwidth of slow-light photonic devices based on coupled resonators,” Opt. Lett. 30, 513–515 (2005). [CrossRef] [PubMed]
  65. M. F. Yanik, S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004). [CrossRef] [PubMed]
  66. M. F. Yanik, S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]
  67. M. F. Yanik, S. Fan, “Dynamic photonic structures: stopping, storage, and time-reversal of light,” Stud. Appl. Math. 115, 233–253 (2005). [CrossRef]
  68. Z. S. Yang, N. H. Kwong, R. Binder, A. L. Smirl, “Distortionless light pulse delay in quantum-well Bragg structures,” Opt. Lett. 30, 2790–2792 (2005). [CrossRef] [PubMed]
  69. Z. S. Yang, N. H. Kwong, R. Binder, A. L. Smirl, “Stopping, storing, and releasing light in quantum-well Bragg structures,” J. Opt. Soc. Am B 22, 2144–2156 (2005). [CrossRef]
  70. J. B. Khurgin, “Adiabatically tunable optical delay lines and their performance limitations,” Opt. Lett. 30, 2778–2780 (2005). [CrossRef] [PubMed]
  71. R. S. Tucker, “The role of optics and electronics in high-capacity routers,” J. Lightwave Technol. 24, 4655–4673 (2006). [CrossRef]
  72. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  73. J. B. Khurgin, “Performance limits of delay lines based on optical amplifiers,” Opt. Lett. 31, 948–950 (2006). [CrossRef] [PubMed]
  74. K. Y. Song, M. G. Herráez, L. Thevenaz, “Observation of pulse delaying and advancementin optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]
  75. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. oyd, A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]
  76. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005). [CrossRef] [PubMed]
  77. A. Minardo, R. Bernini, L. Zeni, “Low distortion Brillouin slow light in optical fibers sing AM modulation,” Opt. Express 14, 5866–5876 (2006). [CrossRef] [PubMed]
  78. Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for increased fractional delay with high data fidelity,” Opt. Lett. 32, 1986–1988 (2007). [CrossRef] [PubMed]
  79. K. Y. Song, K. S. Abedin, K. Hotate, M. G. Herraez, L. Thevenaz, “Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber,” Opt. Express 14, 5860–5865 (2006). [CrossRef] [PubMed]
  80. A. Zadok, A. Eyal, M. Tur, “Extended delay of broadband signals in stimulated rillouin cattering slow light using synthesized pump chirp,” Opt. Express 14, 8498–8505 (2006). [CrossRef] [PubMed]
  81. T. Schneider, R. Henker, K. U. Lauterbach, M. Junker, “Comparison of delay enhancement mechanisms for SBS-based slow light systems,” Opt. Express 15, 9606–9613 (2007). [CrossRef] [PubMed]
  82. M. G. Herraez, K. Y. Song, L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006). [CrossRef]
  83. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25, 201–206 (2007). [CrossRef]
  84. T. Schneider, M. Junker, K.-U. Lauterbach, “Potential ultra wide slow-light bandwidth enhancement,” Opt. Express 14, 11082–11087 (2006). [CrossRef] [PubMed]
  85. K. Y. Song, K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32, 217–219 (2007). [CrossRef] [PubMed]
  86. L. Yi, L. Zhan, W. Hu, Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007). [CrossRef]
  87. L. Thevenaz, “Slow light in optical fibers,” Nat. Photonics 2, 474–481 (2008). [CrossRef]
  88. J. E. Sharping, Y. Okawachi, A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef] [PubMed]
  89. Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, M. Lipson, “All-optical slow-light on a photonic chip,” Opt. Express 14, 2317–2322 (2006). [CrossRef] [PubMed]
  90. A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006). [CrossRef]
  91. H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q.-H. Park, D. J. Gauthier, “Reducing pulse distortion in fast-light pulse propagation through an erbium-doped fiber amplifier,” Opt. Lett. 32, 906–908 (2007). [CrossRef] [PubMed]
  92. D. Dahan, G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13, 6234–6249 (2005). [CrossRef] [PubMed]
  93. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, B. J. Kirby, “Low-light level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006). [CrossRef]
  94. K. L. Tsakmakidis, A. D. Boardman, O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited