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The Polariton Concept

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Semiconductor Optics 1

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

When light propagates in matter it couples to optical excitations like optical phonons, electronic transitions, excitons etc. which leads to a polarization wave accompanying the electromagnetic wave. Quantization of this mixed propagating wave results in new quasi-particles called polaritons. We review here the general properties of polaritons like their dispersion relation and resulting optical properties in the Lorentz-oscillator model for (crystalline) matter including effects of anisotropy. We explicitly discuss the validity range of the polariton concept for different ratios of the distance of Lorentz oscillators and wavelength. Then we consider the consequences of coupling of the oscillators (i.e., spatial dispersion) for the dispersion, optical functions, and experimental spectra. Finally we introduce surface polaritons and their dispersion relation.

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Notes

  1. 1.

    For electric quadrupole transitions, the matrix element varies linearly with \(\varvec{k}\). Compare (6.23), which has been truncated after the constant term for the dipole approximation.

References

  1. J. Wood, Philos. Mag. 3, 128 (1902); Phys. Z. 3, 230 (1902)

    Google Scholar 

  2. O. Lummer, E. Pringsheim, Phys. Z. 4, 430 (1903)

    Google Scholar 

  3. L. Pfaundler (ed.), Müller-Pouillets Lehrbuch der Physik und Meteorologie 2. Band, 3. Buch, (Vieweg, Braunschweig, 1909), p. 227

    Google Scholar 

  4. F. Bloch, Phys. Rev. 70, 460 (1946)

    Article  ADS  Google Scholar 

  5. J.J. Hopfield, Phys. Rev. 112, 1555 (1958)

    Article  ADS  Google Scholar 

  6. S.J. Pekar, Sov. Phys. Solid State 4, 953 (1962)

    Google Scholar 

  7. J.J. Hopfield, D.G. Thomas, Phys. Rev. 132, 563 (1963)

    Article  ADS  Google Scholar 

  8. C.G.B. Garrett, D.E. McCumber, Phys. Rev. A 1, 305 (1970)

    Article  ADS  Google Scholar 

  9. A.S. Barker, R. Loudon, Rev. Mod. Phys. 44, 18 (1972)

    Article  ADS  Google Scholar 

  10. G.S. Agarwal, Phys. Rev. B 10, 1447 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  11. A. Otto, Festkörperprobleme/Adv. Solid State Phys. 14, 1 (1974)

    Google Scholar 

  12. R. Claus, L. Merten, J. Brandmüller, Light Scattering by Phonon Polaritons. Springer Tracts in Modern Physics, vol. 75 (Springer, Berlin, 1975)

    Google Scholar 

  13. J. Lagois, K. Hümmer, Phys. Status Solidi (b) 72, 393 (1975)

    Google Scholar 

  14. R.W. Pohl, Optik und Atomphysik, 13th edn. (Springer, Berlin, 1976)

    Google Scholar 

  15. I. Broser et al., Phys. Status Solidi (b) 90, 77 (1978)

    Google Scholar 

  16. K. Hümmer, P. Gebhardt, Phys. Status Solidi (b) 85, 271 (1978)

    Google Scholar 

  17. W. Stössel, H.J. Wagner, Phys. Status Solidi (b) 89, 403 (1978)

    Google Scholar 

  18. I. Broser, M. Rosenzweig, Phys. Status Solidi (b) 95, 141 (1979)

    Google Scholar 

  19. Y. Masumoto et al., J. Phys. Soc. Jpn. 47, 1844 (1979)

    Article  ADS  Google Scholar 

  20. A. Stahl, Ch. Uhilein, Festkörperprobleme/Adv. Solid State Phys. XIX, 159 (1979)

    Google Scholar 

  21. R.G. Ulbrich, G.W. Fehrenbach, Phys. Rev. Lett. 43, 963 (1979)

    Article  ADS  Google Scholar 

  22. H. Raether, Excitation of Plasmons and Interband Transitions by Electrons. Springer Tracts in Modern Physics, vol. 88 (Springer, Berlin, 1980)

    Google Scholar 

  23. I. Balslev, Phys. Rev. B 23, 3977 (1981)

    Article  ADS  Google Scholar 

  24. T. Itho et al., Solid State Commun. 37, 925 (1981)

    Google Scholar 

  25. J. Lagois, Phys. Rev. B 23, 5511 (1981)

    Article  ADS  Google Scholar 

  26. A. Stahl, Phys. Status Solidi (b) 106, 575 (1981)

    Google Scholar 

  27. Y. Onodera, J. Phys. Soc. Jpn. 51, 2194 (1982)

    Article  ADS  Google Scholar 

  28. M. Rosenzweig, Excitonische Polaritonen – optische Eigenschaften räumlich dispersiver Medien, Dissertation, Berlin (1982)

    Google Scholar 

  29. A. Stahl, I. Balslev, Phys. Status Solidi (b) 111, 531 (1982); ibid. 113, 583 (1982)

    Google Scholar 

  30. S. Chu, S. Wong, Phys. Rev. Lett 48, 738 (1982)

    Google Scholar 

  31. V.M. Agranovich, A.A. Maradudin (eds.), Modern Problems in Condensed Matter Sciences (North Holland, Amsterdam, 1982); Surface Polaritons, vol. 1, ed. by V.M. Agranovich, D.L. Mills and Surface Excitations, vol. 9, ed. by V.M. Agranovich, R. Landon

    Google Scholar 

  32. M. Matsushito, J. Wicksted, H.Z. Cummins, Phys. Rev. B 29, 3362 (1984)

    Article  ADS  Google Scholar 

  33. V.M. Agranovich, V.L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons. Springer Series in Solid-State Sciences, vol. 42, 2nd edn. (Springer, Berlin, 1984)

    Google Scholar 

  34. P. Halevi, R. Fuchs, J. Phys. C. 17, 3869, 3889 (1984)

    Google Scholar 

  35. C. Klingshirn, Energy Transfer Processes in Condensed Matter (1983). NATO ASI Series B, vol. 114 (Plenum Press, New York, 1984), p. 285

    Google Scholar 

  36. J.E. Rothenberg, D. Grischkovsky, A.C. Balant, Phys. Rev. Lett. 53, 552 (1984)

    Article  ADS  Google Scholar 

  37. T. Shigenari, X.Z. Lu, H.Z. Cummins, Phys. Rev. B 30, 1962 (1984)

    Google Scholar 

  38. B. Hönerlage et al., Phys. Rep. 124, 161 (1985)

    Google Scholar 

  39. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings. Springer Tracts in Modern Physics, vol. 111 (Springer, Berlin, 1988)

    Google Scholar 

  40. V. Ya Reznichenko, M.I. Strashnikova, V.V. Cherny, Phys. Status Solidi (b) 152, 675 (1989)

    Google Scholar 

  41. D. Fröhlich et al., Phys. Rev. Lett. 67, 2343 (1991)

    Google Scholar 

  42. W. Kress, F.W. de Wette (eds.), Surface Phonons (Springer, Berlin, 1991)

    Google Scholar 

  43. V. Ya Reznichenko, M.I. Strashnikova, V.V. Cherny, Phys. Status Solidi (b) 167, 311 (1991)

    Google Scholar 

  44. H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd edn. (World Scientific, Singapore, 1993)

    Google Scholar 

  45. N. Peyghambarian, S.W. Koch, A. Mysyrowicz, Introduction to Semiconductor Optics (Prentice Hall, Englewood Cliffs, 1993)

    Google Scholar 

  46. G. Raithel, Phys. Bl. 50, 1149 (1994)

    Article  Google Scholar 

  47. S. Nüsse et al., Phys. Rev. B 55, 4620 (1997)

    Article  ADS  Google Scholar 

  48. A.J. Sievers, Spectroscopy and Dynamics of Collective Excitations in Solids (1995). NATO ASI Series B, vol. 356 (Plenum Press, New York, 1997), p. 227

    Chapter  Google Scholar 

  49. U. Woggon, Optical Properties of Semiconductor Quantum Dots. Springer Tracts in Modern Phyiscs, vol. 136 (Springer, Berlin, 1997)

    Google Scholar 

  50. R.v. Baltz, C. Klingshirn, Ultrafast Dynamics of Quantum Systems (1997). NATO ASI Series B, vol. 372 (Plenum Press, New York, 1998), p. 381

    Google Scholar 

  51. G. Benedek, Ultrafast Dynamics of Quantum Systems (1997). NATO ASI Series B, vol. 372 (Plenum Press, New York, 1998), p. 295

    Google Scholar 

  52. T. Ha et al., Phys. Rev. Lett. 80, 2093 (1998)

    Article  ADS  Google Scholar 

  53. C. Klingshirn, Ultrafast Dynamics of Quantum Systems (1997). NATO ASI Series B, vol. 372 (Plenum Press, New York, 1998), p. 143

    Google Scholar 

  54. A. Jolk, C. Klingshirn, R.v. Baltz, Ultrafast Dynamics of Quantum Systems (1997). NATO ASI Series B, vol. 372 (Plenum Press, New York, 1998), p. 397

    Google Scholar 

  55. U. van Bürck, Hyperfine Interact. 123/124, 483 (1999); see also ibid. 125 (1999)

    Google Scholar 

  56. T.C. Choy, Effective Medium Theory - Principles and Applications (Oxford Science, Oxford, 1999)

    Google Scholar 

  57. L.V. Hau et al., Nature 397, 594 (1999)

    Article  ADS  Google Scholar 

  58. K. Henneberger, Phys. Rev. Lett. 83, 1265 (1999)

    Article  ADS  Google Scholar 

  59. M.M. Kash et al., Phys. Rev. Lett. 82, 5229 (1999)

    Google Scholar 

  60. M. Fleischhauer, M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000)

    Article  ADS  Google Scholar 

  61. C. Klingshirn, Physik in unserer Zeit 31(4), 144 (2000)

    Article  ADS  Google Scholar 

  62. O. Kocharovskaya, Y. Rostovtsev, M.O. Scully, Phys. Rev. Lett. 86, 628 (2001)

    Article  ADS  Google Scholar 

  63. J.S. Nägerl et al., Phys. Rev. B 63, 235202 (2001)

    Google Scholar 

  64. H.C. Schneider et al., Phys. Rev. B 63, 045202 (2001)

    Google Scholar 

  65. E.A. Muljarov, R. Zimmermann, Phys. Rev. B 66, 235319 (2002)

    Google Scholar 

  66. M. Bajcsy, A.S. Zibrov, M.D. Lukin, Nature 426, 638 (2003)

    Article  ADS  Google Scholar 

  67. K. Cho, Optical Response of Nanostructures: Microscopic, Nonlocal Theory. Springer Tracts in Solid State Sciences, vol. 139 (Springer, Berlin, 2003)

    Book  Google Scholar 

  68. S. Schuhmacher et al., Phys. Rev. B 70, 235340 (2004)

    Google Scholar 

  69. A. André et al., Phys. Rev. Lett. 94, 063902 (2005)

    Google Scholar 

  70. D. Fröhlich et al., Solid State Commun. 134, 139 (2005)

    Google Scholar 

  71. G.V. Smirnov et al., Phys. Rev. A 71, 023804 (2005)

    Google Scholar 

  72. A.D. Greentree et al., Nat. Phys. 2, 856 (2006)

    Google Scholar 

  73. M.J. Hartmann, F.G.S.L. Brandão, M.B. Plenio, Nat. Phys. 2, 849 (2006); Phys. J. 9(4), 41 (2010)

    Google Scholar 

  74. L. Karpa, M. Weitz, Nat. Phys. 2, 332 (2006)

    Google Scholar 

  75. F.E. Zimmer et al., Opt. Commun. 264, 441 (2006)

    Google Scholar 

  76. D. Meschede, Optics, Light and Lasers, 2nd edn. (Wiley-VCH, Weinheim, 2007)

    Google Scholar 

  77. B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, 2nd edn. (Wiley, Hoboken, 2007)

    Google Scholar 

  78. V.M. Shalaev, S. Kawata (eds.), Nanophotonics with Surface Plasmons (Elsevier B.V., Amsterdam, 2007)

    Google Scholar 

  79. J. Otterbach et al., Phys. Rev. Lett. 104, 033903 (2010)

    Google Scholar 

  80. D. Sarid, W.A. Challener, Modern Introduction to Surface Plasmons: Theory, Mathematica Modeling, and Applications (Cambridge University Press, Cambridge, 2010)

    Google Scholar 

  81. W. Demtröder, Laser Spectroscopy 1, Basic Principles, 5th edn. (Springer, Berlin, 2014)

    Google Scholar 

  82. L.C. Oliveira, A.M. Nogueira Lima, C. Thirstrup, H.F. Neff, Surface Plasmon Resonance Sensors: A Materials Guide to Design and Optimization (Springer, Cham, 2015)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-Württemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

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  1. Heinz Kalt
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Correspondence to Heinz Kalt .

Problems

Problems

8.1

Which dispersion relations would you expect for the polariton resulting from oscillators with the dispersion relations of Fig. 7.2a, b? Do not forget that a finite coupling between photons and the oscillator necessarily implies a finite \(\Delta _{\text {LT}}\).

Check if you were right when you come to the chapters on phonon and on exciton polaritons.

8.2

Calculate the frequency shift a photon experiences when it is scattered off an atom in a backward direction. Compare with the homogenous linewidth of luminescence lines in semiconductor optics, which hardly fall below 0.1 meV.

8.3

Inform yourself about the possibility of cooling atoms by absorption and emission of photons.

8.4

What is the Mösbauer effect? How does it work?

8.5

In Na vapor it is possible to slow light down to an almost complete stop. Inform yourself with the help of some literature. Which effects apart from the extremely flat dispersion relation for large k-vectors contribute to this phenomenon?

8.6

Calculate the dispersion relation \(\omega (\varvec{k})\) from (8.7) for vanishing damping. What changes if \(\omega _0=\omega _0(\varvec{k})\) and/or if a small but finite damping \(\gamma \) are introduced?

8.7

Write down the equations of motion of two coupled harmonic oscillators and try to solve them. Find or imagine examples in classical physics and in quantum mechanical systems.

8.8

Which dependence of \(\Delta _{\text {LT}}(\varvec{k})\) do you expect for a transition that is dipole forbidden but allowed in quadrupole approximation?

8.9

Can you give an intuitive explanation as to why a photon with spin \(\pm \hbar \) can excite a quadrupole transition, e.g., from an atomic s state to a d (or s) state? Hint: Place the atom in the origin of the coordinate system and vary the impact parameter of the photon.

8.10

Sketch the dispersion of a polariton resonance with spatial dispersion and an oscillator strength which increases with \(\varvec{k}\). (Assume for simplicity zero damping). Does \(\Delta _{\text {LT}}\) then also depend on \(\varvec{k}\)?

8.11

Sketch the dispersion of the polariton for two close lying resonances A and B, with and without spatial dispersion for an order of the energies at \(\varvec{k}\,{=}\,0\) \(\hbar \omega ^A_0<\hbar \omega ^A_\text {L}< \hbar \omega ^B_0 <\hbar \omega ^B_\text {L}\). Is it possible for a single orientation of the polarization to have the sequence \(\hbar \omega ^A_0< \hbar \omega ^B_0<\hbar \omega ^A_\text {L} <\hbar \omega ^B_\text {L}\)?

8.12

Apart from the use of ATR methods see Sect. 21.1.5, it is possible to excite surface polaritons optically if a periodic structure, i.e., a grating, is formed at the interfaces. What is the principle behind this? Compare this with the statements about momentum conservation in Sects. 5.1.3 and 9.2.

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Kalt, H., Klingshirn, C.F. (2019). The Polariton Concept. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_8

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