Skip to main content

Localization of Light in Disordered and Periodic Dielectrics

  • Chapter
Confined Electrons and Photons

Part of the book series: NATO ASI Series ((NSSB,volume 340))

Abstract

Photon localization and photonic bandgaps is a new branch of pure and applied science, bringing together the disciplines of condensed matter physics, quantum optics, chemistry and engineering 1–6. Electromagnetism is the fundamental mediator of interactions in condensed matter and atomic physics. Photonic bandgap materials constitute a fundamentally new class of dielectric materials in which this basic interaction is controllably altered, and in some cases completely removed over certain frequency and length scales. This leads to a host of new physical phenomena. From the standpoint of applied science, localized modes of light act as ideal high Q optical cavities important in the design of low threshold microlasers for use in optoelectronic devices and optical communication networks. The ability to tailor the radiative properties of atoms and molecules by means of the structural characteristics of the dielectric host also has applications in photochemistry and catalysis of chemical reactions. The potential significance of this subject may be compared to that of semiconductor physics. Photonic bandgap materials are the photonic analogues of semiconductors in the electronics industry. Rather than a periodic array of atoms which scatters and modifies the energy-momentum relation of electrons, these materials consist of periodically modulated dielectrics with periodicity on the scale of the wavelength of light. This constitutes an important and unexplored regime of mesoscopic physics with new technological applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. S. John, Ph.D. thesis Harvard University (1984) “Localization of Waves in a Disordered Medium”

    Google Scholar 

  2. S. John, Physics Today (May 1991) pg. 32 and cover story, “Localization of Light”

    Google Scholar 

  3. P. St. John Russell, Physics World (August 1992), pg. 37, “Photonic Bandgaps”

    Google Scholar 

  4. “Photonic Bandgaps and Localization” edited by C.M. Soukoulis, NATO ASI series B in Physics, vol. 308, Plenum Press (1993)

    Google Scholar 

  5. “Scattering and Localization of Classical Waves in Random Media” edited by Ping Sheng, World Scientific Series on Directions in Condensed Matter Physics — vol. 8, World Scientific Press (1990).

    Google Scholar 

  6. “Development and Application of Materials Exhibiting Photonic Bandgaps”, feature issue of Journal of the Optical Society of America B (January 1993)

    Google Scholar 

  7. P.W. Anderson, Phys. Rev. 109, 1492 (1958) “Absence of Diffusion in Certian Random Lattices”

    Article  Google Scholar 

  8. S. John and M.J. Stephen, Physical Review B28, 6358 (1983). “Wave Propagation and Localization in a Long-range Correlated Random Potential”

    Google Scholar 

  9. S. John, H. Sompolinsky and M.J. Stephen, Physical Review 27, 5592 (1983) “Localization in a Disordered Elastic Medium Near Two Dimensions”

    Google Scholar 

  10. S. John, Physical Review Letters 53, 2169, (1984) “Electromagnetic Absorption in a Disordered Medium Near a Photon Mobility Edge”

    Article  Google Scholar 

  11. P.W. Anderson, Philosophical Magazine B52, 505 (1985) “On the Question of Classical Localization: A Theory of White Paint?”

    Google Scholar 

  12. M.P. van Albada and A. Lagendijk, Physical Review Letters 55, 2692 (1985), “Observation of Weak Localization of Light in a Random Medium”

    Article  Google Scholar 

  13. P.E. Wolf and G. Maret, Physical Review Letters 55, 2696 (1985), “Weak Localization and Coherent Backscattering of Photons in Disordered Media”

    Article  Google Scholar 

  14. E. Yablonovitch, Physical Review Letters 58, 2059 (1987), “Inhibited Spontaneous Emission in Solid-State Physics and Electronics”

    Article  Google Scholar 

  15. S. John, Physical Review Letters 58, 2486 (1987) “Strong Localization of Photons in Certain Dielectric Superlattices”

    Article  Google Scholar 

  16. see for instance N.F. Mott, “Metal-Insulator Transitions”; Taylor and Francis Publishers, London (1974)

    Google Scholar 

  17. I. Freund, M. Rosenbluh, R. Berkovits and M. Kaveh, Physical Review Letters 61, 1214 (1989), “Coherent Backscat tering of Light in a Quasi-Two-Dimensional System”

    Article  Google Scholar 

  18. see for instance J.D. Jackson, “Classical Electrodynamics”, published by J. Wiley (1975)

    Google Scholar 

  19. A.F. Ioffe and A.R. Regel, Prog. Semicond. 4, 237 (1960)

    Google Scholar 

  20. H.C. van de Hülst, “Light Scattering by Small Particles”, Dover Publications Inc. (1981)

    Google Scholar 

  21. C.F. Bohren and D.R. Huffman, “Absorption and Scattering of Light by Small Particles”, J. Wiley Interscience Publication (1983)

    Google Scholar 

  22. A.Z. Genack, Physical Review Letters 58, 2043 (1987), “Optical Transmission in Disordered Media”

    Article  Google Scholar 

  23. M. Drake and A.Z. Genack, Physical Review Letters 63, 259 (1989), “Observation of Nonclassical Optical Diffusion”

    Article  Google Scholar 

  24. “Statistical Mechanics”, section 16.3, D. McQuarrie, Harper and Row Publishers, (1976)

    Google Scholar 

  25. “Solid State Physics”, N. Ashcroft and D. Mermin; Holt, Rinehart and Winston Publishers, (1976)

    Google Scholar 

  26. R. Car and M. Parrinello, Physical Review Letters 60, 1988; “Structural, Dynamical, and Electronic Properties of Amorphous Silicon: An Ab Initio Molecular-Dynamics Study”

    Google Scholar 

  27. see for instance P. Chaikin et. al. “Colloidal Crystals” in “Physics of Complex and Supermolecular Fluids” edited by S. Safran and N.A. Clark, Wiley-Interscience Publications (1987)

    Google Scholar 

  28. see for instance “Elementary Quantum Mechanics”, D. Saxon, Holden-Day Publishing (1968)

    Google Scholar 

  29. E. Yablonovitch and T.J. Gmitter, Physical Review Letters 63, 1950 (1989), “Photonic Band Structure: The Face-Centered-Cubic Case”

    Article  Google Scholar 

  30. K.M. Leung and Y.F. Lui, Physical Reivew Letters 65, 2646 (1990) “Full Vector Wave Calculation of Photonic Band Structures in fcc Dielectric Media”

    Article  Google Scholar 

  31. Z. Zhang and S. Satpathy, Physical Review Letters 65, 2650 (1990) “Electromagnetic Wave Propagation in Periodic Structures: Bloch Wave Solution to Maxwell’s Equations”

    Article  Google Scholar 

  32. K.M. Ho, C.T. Chan, and C.M. Soukoulis, Physical Review Letters 65, 3152 (1990) “Existence of Photonic Bandgap in Periodic Dielectric Structures”

    Article  Google Scholar 

  33. E. Yablonovitch, T.J. Gmitter, and K.M. Leung, Physical Review Letters 67, 2295 (1991) “Photonic Band Strucutre: the fcc case employing nonspherical atoms”

    Article  Google Scholar 

  34. R.D. Meade, A.M. Rappe, K.D. Brommer and J.D. Joannopoulos. Physical Review B44, 10961 (1991), “Electromagnetic Bloch Waves at the Surface of a Photonic Crystal”

    Google Scholar 

  35. E.N. Economou and M.M. Sigalas, Physical Review B48, 13434 (1993) “Spectral Gaps for Classical Waves in Periodic Structures”

    Google Scholar 

  36. M.M. Sigalas, E.N. Economou and M. Kafesaki, Physical Review B (in press) “Spectral Gaps for Electromagnetic and Scalar Waves: Possible explanation for certain differences”

    Google Scholar 

  37. for a review see “Models of Disorder”, J. Ziman, Section 9.6, Cambridge University Press (1979)

    Google Scholar 

  38. J. He and M. Cada, IEEE J. Quantum Electron 27, 1182 (1991)

    Article  Google Scholar 

  39. For a general discussion of nonlinear optical susceptibilities see “The Elements of Nonlinear Optics”, P.N. Butcher and D. Cotter, Cambridge University Press (1990)

    Google Scholar 

  40. D.L. Mills and S.E. Trullinger, Physical Review B36, 947 (1987) “Gap Solitons in Nonlinear Periodic Structures”

    Google Scholar 

  41. S. John and N. Akozbek, Physical Review Letters 71, 1168 (1993), “Nonlinear Optical Solitary Waves in a Photonic Band Gap”

    Article  Google Scholar 

  42. E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan; Physical Review Letters 42, 673 (1979), “Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions”

    Article  Google Scholar 

  43. D. Vollhardt and P. Wölfle, Physical Review B22, 4666 (1980), “Diagrammatic, self-consistent treatment of the Anderson localizaiton problem”

    Google Scholar 

  44. F.C. MacKintosh and S. John, Physical Review B40, 2383 (1989) “Diffusingwave spectroscopy and multiple scattering of light in correlated random media”

    Google Scholar 

  45. Gerd Bergmann, Physics Reports 107, 1, (1984), “Weak localization in Thin Films: a time of flight experiment with conduction electrons”

    Article  Google Scholar 

  46. E. Akkermans, P.E. Wolf and R. Maynard, Physical Review Letters 56, 1471 (1986) “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape”

    Article  Google Scholar 

  47. M.J. Stephen and G. Cwilich, Physical Review B 34, 7564 (1986) “Rayleigh Scattering and Weak Localization: Effects of Polarization”

    Article  Google Scholar 

  48. F.C. MacKintosh and S. John, Phys. Rev. B37, 1884 (1988), “Coherent Backscattering of Light in the Presence of Time-reversal Non-invariant and Parity Violating Media”

    Google Scholar 

  49. E.E. Gorodnichev, S.L. Dudarev, D.B. Rogozkin, and M.I. Ryazanov, Soviet Physics JETP 69, 1017 (1989), “Weak Localization of Waves in Incoherent Scattering in Crystals”

    Google Scholar 

  50. D.C. Licciardello and D.J. Thouless, Physical Review Letters 35, 1475 (1975); “Constancy of Minimum Metallic Conductivity in Two Dimensions”

    Article  Google Scholar 

  51. J.T. Edwards and D.J. Thouless, J. Phys. C5, 807 (1972); “Numerical studies of localization in disordered systems”

    Google Scholar 

  52. N. Garcia and A.Z. Genack, Physical Review Letters 66, 1850 (1991), “Anomalous Photon Diffusion at the Threshold of the Anderson Localization Transition”

    Article  Google Scholar 

  53. A.Z. Genack and N. Garcia, Physical Review Letters 66, 2064 (1991), “Observation of Photon Localization in a Three-Dimensional Disordered System”

    Article  Google Scholar 

  54. B.A. van Tiggelen, A. Lagendijk, M.P. van Albada and A. Tip, Physical Review B45, 12, 233 (1992), “Speed of Light in Random Media”

    Google Scholar 

  55. see for instance N.F. Mott and E.A. Davis “Electronic Processes in Noncrystalline Materials” Clarendon Press, Oxford (1979)

    Google Scholar 

  56. S. John and J. Wang, Physical Review Letters “Quantum Electrodynamics near a Photonic Bandgap: Photon Bound States and Dressed Atoms”

    Google Scholar 

  57. S. John and J. Wang, “Quantum Optics of Localized Light”, Physical Review B43, 12772, (1991)

    Google Scholar 

  58. M.G. Raizen, R.J. Thompson, R.J. Brecha, H.J. Kimble and H.J. Carmichael, Physical Review Letters 63, 240 (1989), “Normal-Mode Splitting and Linewidth Averaging for Two-State Atoms in an Optical Cavity”

    Article  Google Scholar 

  59. S. John and Tran Quang, Physical Review A (in press) “Spontaneous Emission near the Edge of a Photonic Band Gap”

    Google Scholar 

  60. S. John and Tran Quang, submitted to Physical Review Letters, “Localization of Superradiance near a Photonic Band Edge”

    Google Scholar 

  61. “Molecular Quantum Electrodynamics” D.P. Craig and T. Thirunamachandran, Academic Press (1984)

    Google Scholar 

  62. “Elements of Advanced Quantum Theory” J.M. Ziman, Cambridge University Press (1969)

    Google Scholar 

  63. H.A. Bethe, Physical Review 72, 339 (1947) “The Electromagnetic Shift of Energy Levels”

    Article  MATH  Google Scholar 

  64. B.R. Mollow, Physical Review 188, 1969 (1969), “Power Spectrum of Light Scattered by Two-Level Systems”

    Article  Google Scholar 

  65. Th. Basche and W.E. Moerner, Nature voluem 355, 355 (January 23, 1992) “Optical Modification of a Single Impurity Molecule in a Solid”

    Google Scholar 

  66. A detailed discussion of exciton lineshapes in solids due to phonon interaction may be found in “The Physics of Elementary Excitations”, S. Nakajima, Y. Toyozawa, and R. Abe, Springer-Verlag Publishers, Berlin (1980)

    Google Scholar 

  67. see for instance “Optical Resonance and Two-Level Atoms”, L. Allen and J.H. Eberly, Dover Publications Inc., New York (1987)

    Google Scholar 

  68. R.H. Dicke Physical Review 93, 99 (1954), “Coherence in Spontaneous Radiation Processes”

    Article  MATH  Google Scholar 

  69. M. Tavis and F.W. Cummings, Physical Review 170, 379 (1968), “Exact Solution for an N-Molecule-Radiation-Field Hamiltonian”

    Article  Google Scholar 

  70. K. Hepp and E.H. Lieb, Annals of Physics, 360 (1973), “On the Superradiant Phase Transition for Molecules in a Quantized Radiation Field: the Dicke Maser Model”

    Google Scholar 

  71. for an elementary derivation using coherent states see Y.K. Wang and F.T. Hioe, Physical Review A7, 831 (1973) “Phase Transition in the Dicke Model of Superradiance”.

    Google Scholar 

  72. S.F. Edwards and P.W. Anderson, Journal of Physics F5, 965 (1975)

    Article  Google Scholar 

  73. “Spin Glasses and Other Frustrated Systems” Debashish Chowdhury, Princeton Series in Physics, Princeton University Press

    Google Scholar 

  74. K. Binder, Reviews of Modern Physics 58, 801, (1986), “Spin Glasses; Experimental Facts, Theoretical Concepts and Open Questions”

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media New York

About this chapter

Cite this chapter

John, S. (1995). Localization of Light in Disordered and Periodic Dielectrics. In: Burstein, E., Weisbuch, C. (eds) Confined Electrons and Photons. NATO ASI Series, vol 340. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1963-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-1963-8_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5807-7

  • Online ISBN: 978-1-4615-1963-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics