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Linear optical properties of semiconductor microcavities with embedded quantum wells

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Book cover Confined Photon Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 531))

Abstract

An overview of the theory of the linear optical response of planar semiconductor microcavities with embedded quantum wells is presented. In particular, the optical properties close to the excitonic transition in the strong coupling regime are addressed and the formalism of exciton polaritons is used. First, the transfer matrix formalism is introduced in order to solve Maxwell equations for the Fabry-Pérot microcavity with distributed Bragg reflectors and to study the cavity mode features. Then, the coupling to a quantum well excitonic resonance is included within the semiclassical formalism for the optical response. The main qualitative and quantitative features of microcavity polaritons are illustrated through several calculated optical spectra and, afterwards, a more formal description of the polariton modes is provided. Finally, the problem of the full quantum description of the exciton photon coupling is briefly addressed. The quasimode formalism is introduced and, as an example of application, a simple model for microcavity photoluminescence under nonresonant continuous wave excitation is presented.

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References

  1. Abram I., Sermage B., Long S., Bloch J., Planel R., Thierry-Mieg V. (1996): Spontaneous emission dynamics in planar semiconductor microcavities, in Microcavities and Photonic Bandgaps, J. Rarity and C. Weisbuch eds., 69 (Kluwer, Dordrecht)

    Google Scholar 

  2. Agarwal G. S., Phys. Rev. Lett. 51, 550 (1984).

    Google Scholar 

  3. Agranovich V. M., Dubowskii A. O. (1966): Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals. Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (JETP Lett. 3, 233)

    Google Scholar 

  4. Andreani L. C., Tassone F., Bassani F. (1991): Radiative lifetime of free excitons in quantum wells. Solid State Commun. 77, 641

    Article  ADS  Google Scholar 

  5. Andreani L. C. (1994): Exciton-polaritons in superlattices. Physics Letters A 192, 99

    Article  ADS  Google Scholar 

  6. Andreani L. C. (1995): Optical transitions, excitons and polaritons in bulk and low-dimensional semiconductor structures: in E. Burstein and C. Weisbuch (Eds.), Confined Electrons and Photons: new Physics and Devices, Plenum Press, New York

    Google Scholar 

  7. Andreani L. C., Panzarini G., Kavokin A. V., Vladimirova M. V. (1998): Effect of inhomogeneous broadening on optical properties of excitons in quantum wells. Phys. Rev. B 57, 4670

    Article  ADS  Google Scholar 

  8. Barnett S. M., Radmore P. M. (1988): Quantum theory of cavity quasimodes. Optics Commun. 68, 364

    Article  ADS  Google Scholar 

  9. Bassani F., Altarelli M. (1983): Interaction of radiation with condensed matter. In E. E. Koch (Ed.), Handbook on Syncrotron Radiation, North Holland, Amsterdam, 463–606

    Google Scholar 

  10. Baumberg J. J., Armitage A., Skolnick M. S., Roberts J. S. (1998): Suppressed polariton scattering in semiconductor microcavities. Phys. Rev. Lett. 81, 661

    Article  ADS  Google Scholar 

  11. Bastard G. (1989). Wave Mechanics Applied to Semiconductor Heterostructures. Les Editions de Physique, Les Ulis, Paris

    Google Scholar 

  12. Benisty H., De Neve H., Weisbuch C. (1998): Impact of planar microcavity effects on light extraction. IEEE J. of Quantum Elec. 34, 146

    Google Scholar 

  13. Born M., Wolf E. (1993), Principles of Optics, sixth ed., (Pergamon Press, Oxford)

    Google Scholar 

  14. Brinkmann D., Rossi F., Kock S. W., Thomas P. (1996): Phonon-induced dephasing of localized optical excitations. Phys. Rev. B 54, 2561

    Article  ADS  Google Scholar 

  15. Brinkmann D., Bott K., Koch S. W., Thomas P. (1998): Disorder-induced dephasing of excitons in semiconductor heterostructures. Phys. Stat. Sol. (b) 206, 493

    Article  ADS  Google Scholar 

  16. E. Burstein and C. Weisbuch (Eds.), Confined Electrons and Photons: new Physics and Devices, (Plenum Press, New York, 1995).

    Google Scholar 

  17. Carmichael H. J., Brecha R. J., Raizen M. G., Kimble H. J., Rice P. R. (1989): Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators. Phys. Rev. A 40, 5516

    Article  ADS  Google Scholar 

  18. Citrin D. S. (1993): Radiative lifetimes of excitons in quantum wells: Localization and phase-coherenece effects. Phys. Rev. B 47, 3832

    Article  ADS  Google Scholar 

  19. Citrin D. S. (1994): Exciton radiative decay and polaritons in multiquantum wells: quantum well to superlattice crossover. Solid State Commun. 89, 139 (1994).

    Article  ADS  Google Scholar 

  20. Citrin D. S. (1996): Time-domain theory of resonant Rayleigh scattering by quantum wells: Early-time evolution. Phys. Rev. B 54, 14572

    Article  ADS  Google Scholar 

  21. Citrin D. S. (1996): Coherence transfer via resonance Rayleigh scattering of exciton polaritons in a semiconductor microcavity. Phys. Rev. B 54, 16425

    Article  ADS  Google Scholar 

  22. Ciuti C., Savona V., Piermarocchi C., Quattropani A., Schwendimann P. (1998): Threshold behavior in the collision broadening of microcavity polaritons. Phys. Rev. B. 58, R10123

    Google Scholar 

  23. Cohen-Tannoudji C., Dupont-Roc J., Grynberg G. (1988): Processus d’interaction entre photons et atomes, Editions du CNRS, Paris

    Google Scholar 

  24. Ebeling K. J. (1993): Integrated optoelectronics: waveguide optics, photonics, semiconductors. Springer-Verlag, Berlin

    Google Scholar 

  25. Eberly J. H., Wódkiewicz K. (1977): The time-dependent physical spectrum of light. J. Opt. Soc. Am. 67, 1252

    Article  ADS  Google Scholar 

  26. C. Ell, J. Prineas, T. R. Nelson, Jr., S. Park, H. M. Gibbs, G. Khitrova, S. W. Koch, and R. Houdré. Influence of structural disorder and light coupling on the excitonic response of semiconductor microcavities. Phys. Rev. Lett. 80, 4795 (1998).

    Article  ADS  Google Scholar 

  27. Fano U. (1961): Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866

    Article  MATH  ADS  Google Scholar 

  28. Fisher T. A., Afshar A. M., Whittaker D. M., Skolnick M. S., Kinsler P., Roberts J. S., Hill G., Pate M. A. (1996): Magnetic and electric field effects in semiconductor quantum microcavity structures. In J. Rarity and C. Weisbuch (eds.), Microcavities and Photonic Bandgaps, Kluwer, The Netherlands

    Google Scholar 

  29. Gérard J. M., Sermage B., Gayral B., Legrand B., Costard E., Thierry-Mieg V. (1998): Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity. Phys. Rev. Lett. 81, 1110

    Article  ADS  Google Scholar 

  30. Glutsch S., Bechstedt F. (1994): Theory of asymmetric broadening and shift of excitons in quantum structures with rough interfaces. Phys. Rev. B 50, 7733

    Article  ADS  Google Scholar 

  31. Glutsch S., Chemla D. S., Bechstedt F. (1996): Numerical calculation of the optical absorption in semiconductor quantum structures. Phys. Rev. B 54, 11592

    Article  ADS  Google Scholar 

  32. Haroche S. (1992): Cavity quantum electrodynamics. In Dalibard J., Raymond J. M., Zinn-Justin J. (eds.), Fundamental systems in quantum optics, London Science Publishers, Amsterdam

    Google Scholar 

  33. Haug H., Koch S. W. (1994): Quantum theory of the optical and electronic properties of semiconductors. 3rd edn., World Scientific, Singapore

    MATH  Google Scholar 

  34. Hellwege A. M., Madelung O. (eds.) (1982). Physics of Group IV Elements and III–V Compounds, Landolt-Börnstein, New Series, Group III, 17, Springer-Verlag, Berlin

    Google Scholar 

  35. Hood C. J., Chapman M. S., Lynn T. W., Kimble H. J. (1998): Real-time cavity QED with single atoms. Phys. Rev. Lett. 80, 4157

    Article  ADS  Google Scholar 

  36. Hopfield J. J. (1958): Theory of the contribution of excitons to the complex dielectric constant of crystals. Phys. Rev. 112, 1555

    Article  MATH  ADS  Google Scholar 

  37. Houdré R., Gibernon J. L., Pellandini P., Stanley R. P., Oesterle U., Weisbuch C., O’Gorman J., Roycroft B., Ilegems M. (1995): Saturation of the strong-coupling regime in a semiconductor microcavity: Free-carrier bleaching of cavity polaritons. Phys. Rev. B 52, 7810

    Article  ADS  Google Scholar 

  38. Jackson J. D., Classical Electrodynamics. Wiley, New York

    Google Scholar 

  39. Jahnke F., Kira M. Koch S. W., Khitrova G., Lindmark E. K., Nelson T. R., Jr., Wick D. V., Berger J. D., Lyngnes O., Gibbs H. M., Tai K. (1996): Excitonic nonlinearities of semiconductor microcavities in the nonperturbative regime. Phys. Rev. Lett. 77, 5257

    Article  ADS  Google Scholar 

  40. Jahnke F., Kira M., Koch S. W. (1997): Linear and nonlinear optical properties of excitons in semiconductor quantum wells and microcavities. Z. Phys. B 104, 559

    Article  ADS  Google Scholar 

  41. Jorda S., Rössler U., Broido D. (1993): Fine structure of excitons and polariton dispersion in quantum wells. Phys. Rev. B 48, 1669

    Article  ADS  Google Scholar 

  42. Kaluzny, Y., P. Goy, M. Gross, J. M. Raymond and S. Haroche (1983). Observation of self-induced Rabi oscillations in two-level atoms excited inside a resonant cavity: The ringing regime of superradiance. Phys. Rev. Lett., 51, 1175

    Article  ADS  Google Scholar 

  43. A. V. Kavokin. Motional narrowing of inhomogeneously broadened excitons in a semiconductor microcavity: semiclassical treatment. Phys. Rev. B 57, 3757 (1998)

    Article  ADS  Google Scholar 

  44. Knox, R. S. (1963). Theory of Excitons. In F. Seitz and D. Turnbull (eds.), Solid State Physics, Academic Press, New York

    Google Scholar 

  45. Ley M., Loudon R. (1987): Quantum theory of high-resolution length measurement with a Fabry-Pérot interferometer. J. of Mod. Optics 34, 227

    Article  ADS  Google Scholar 

  46. Lindberg M., Koch S. W. (1988): Effective Bloch equations for semiconductors. Phys. Rev. B 38, 3342

    Article  ADS  Google Scholar 

  47. Lyngnes O., Berger J. D., Prineas J. P., Park S., Khitrova G., Gibbs H. M., Jahnke F., Kira M., Koch S. W. (1997): Nonlinear emission dynamics from semiconductor microcavities in the nonperturbative regime. Solid State Commun. 104, 297

    Article  ADS  Google Scholar 

  48. McLeod H. A. (1986): Thin-Film Optical Filters. second ed., Hilger

    Google Scholar 

  49. Meystre P. (1992): Cavity quantum optics and the quantum measurement process. Progress in Optics XXX 261

    Article  MathSciNet  Google Scholar 

  50. Piermarocchi C, Tassone F., Savona V., Quattropani A., Schwendimann P. (1996): Nonequilibrium dynamics of free quantum-well excitons in time-resolved photoluminescence. Phys. Rev. B 53, 15834

    Article  ADS  Google Scholar 

  51. Piermarocchi C, Tassone F., Savona V., Quattropani A., Schwendimann P. (1997): Exciton formation rates in GaAs/AlxGa1−x As quantum wells. Phys. Rev. B 55, 1333

    Article  ADS  Google Scholar 

  52. Purcell E. M. (1946): Spontaneous emission probabilities at radiofrequencies. Phys. Rev. 69, 681

    Article  Google Scholar 

  53. Quochi F., Bongiovanni G., Mura A., Staehli J. L., Deveaud B., Stanley R. P., Oesterle U., Houdré R. (1998): Strongly driven semiconductor microcavities: From the polariton doublet to an ac Stark triplet. Phys. Rev. Lett. 80, 4733

    Article  ADS  Google Scholar 

  54. Microcavities and Phtonic Bandgaps, J. Rarity and C. Weisbuch eds., (Kluwer, Dordrecht, 1996)

    Google Scholar 

  55. Rhee J.-K., Citrin D. S., Norris T. B., Arakawa Y., Nishioka M. (1996): Femtosecond dynamics of semiconductor-microcavity polaritons in the nonlinear regime. Solid. State Commun. 97, 941

    Article  ADS  Google Scholar 

  56. Sanchez-Mondragon J. J., Narozhny N. B., Eberly J. H. (1983): Theory of spontaneous emission line shape in an ideal cavity. Phys. Rev. Lett. 51, 550

    Article  ADS  Google Scholar 

  57. Savona V., Andreani L. C., Schwendimann P., Quattropani A. (1995): Quantum well excitons in semiconductor microcavities: Unified treatment of weak and strong coupling regimes. Solid State Commun. 93 (1995), 733

    Article  ADS  Google Scholar 

  58. Savona V., Tassone F., Piermarocchi C., Quattropani A., Schwendimann P. (1996): Theory of polariton photoluminescence in arbitrary semiconductor microcavity structures. Phys. Rev. B 53, 13051

    Article  ADS  Google Scholar 

  59. Savona V., Weisbuch C. (1996): Theory of time-resolved light emission from polaritons in a semiconductor microcavity under resonant excitation. Phys. Rev. B 54, 10835

    Article  ADS  Google Scholar 

  60. Savona V., Piermarocchi C., Quattropani A., Tassone F., Schwendimann P. (1997): Microscopic theory of motional narrowing of microcavity polaritons in a disordered potential. Phys. Rev. Lett. 78, 4470

    Article  ADS  Google Scholar 

  61. Savona V., Piermarocchi C. (1997): Microcavity polaritons: homogeneous and inhomogeneous broadening in the strong coupling regime. Phys. Stat. Sol. (a) 164, 45

    Article  ADS  Google Scholar 

  62. Schnabel R. F., Zimmermann R., Bimberg D., Nickel H., Lösch R., Schlapp W. (1992): Influence of exciton localization on recombination line shapes: InxGa1−x As/GaAs quantum wells as a model. Phys. Rev. B 46, 9873

    Article  ADS  Google Scholar 

  63. Schulteis L., Honold A., Kuhl J., Köler K., Tu C. W. (1986): Optical dephasing of homogeneously broadened two-dimensional exciton transitions in GaAs quantum wells. Phys. Rev. B 34, 9027

    Article  ADS  Google Scholar 

  64. Sermage B., Long S., Abram I., Marzin J. Y., Bloch J., Planel R., Thierry-Mieg V. (1996): Time resolved spontaneous emission of excitons in a microcavity: Behavior of the individual exciton-photon mixed states. Phys. Rev. B 53, 16516

    Article  ADS  Google Scholar 

  65. Stanley R. P.: Unpublished

    Google Scholar 

  66. Stanley R. P., Houdré R., Oesterle U., Ilegems M., Weisbuch C. (1993): Impurity modes in one-dimensional periodic systems: The transition from photonic band gaps to microcavities. Phys. Rev. A 48, 2246

    Article  ADS  Google Scholar 

  67. Stanley R. P., Houdré R., Weisbuch C., Oesterle U., Ilegems M. (1996): Cavity-polariton photoluminescence in semiconductor microcavities: Experimental evidence, Phys. Rev. B 53, 10995

    Article  ADS  Google Scholar 

  68. Stanley R. P., Houdré R., Oesterle U., Ilegems M. (1997): Semiconductor microcavity polaritons: photoquenching of inhomogeneous broadening and acoustic phonon broadening. Presented to the OSA-ILX Interdisciplinary Laser Conference, Long Beach, October 1997

    Google Scholar 

  69. Sumi H. (1976): On the exciton luminescence at low temperatures: Importance of the polariton viewpoint. J. Phys. Soc. Jpn 21, 1936

    Google Scholar 

  70. Tassone F., Bassani F., Andreani, L. C. (1990): Resonant and surface polaritons in quantum wells. Il Nuovo Cimento 12D, 1673

    Article  ADS  Google Scholar 

  71. Tassone F., Bassani F., Andreani L. C. (1992): Quantum-well reflectivity and exciton-polariton dispersion. Phys. Rev. B 45, 6023

    Article  ADS  Google Scholar 

  72. Tassone F., Piermarocchi C., Savona V., Schwendimann P., Quattropani A. (1996): Photoluminescence decay times in strong-coupling semiconductor microcavities. Phys. Rev. B 53, R7642

    Google Scholar 

  73. Tassone F., Piermarocchi C., Savona V., Quattropani A., Schwendimann P. (1997): Bottleneck effects in the relaxation and photoluminescence of microcavity polaritons. Phys. Rev. B 56, 7554

    Article  ADS  Google Scholar 

  74. Thompson R. J., Rempe G., Kimble H. J. (1992): Observation of normal-mode splitting for an atom in an optical cavity. Phys. Rev. Lett. 68, 1132

    Article  ADS  Google Scholar 

  75. Ulbrich R. G., Fehrenbach G. W. (1979): Polariton wave packet propagation in the exciton resonance of a semiconductor. Phys. Rev. Lett. 43, 963

    Article  ADS  Google Scholar 

  76. Weisbuch C., Ulbrich R. G. (1977): Resonant polariton fluorescence in gallium arsenide. Phys. Rev. Lett. 39, 654

    Article  ADS  Google Scholar 

  77. Weisbuch C., Ulbrich R. G. (1979): Spatial and spectral features of polariton fluorescence. J. Lumin. 18/19, 27

    Article  Google Scholar 

  78. Weisbuch C., Dingle R., Gossard A. C., Wiegmann W. (1981): Optical characterization of interface disorder in GaAs-Ga1−x AlxAs multi-quantum well structures. Solid State Commun. 38, 709

    Article  ADS  Google Scholar 

  79. Weisbuch C., Ulbrich R. G. (1982): Resonant light scattering mediated by excitonic polaritons in semiconductors. In M. Cardona and G. Güntherodt (eds.), Light scattering in solids III, Springer-Verlag, Berlin

    Google Scholar 

  80. Weisbuch C., Nishioka M., Ishikawa A., Arakawa Y. (1992): Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett., 69, 3314

    Article  ADS  Google Scholar 

  81. Whittaker D. M., Skolnick M. S., Fisher T. A., Armitage A., Baxter D., Astratov V. N. (1997): Excitons and polaritons in semiconductor microcavities. Phys. Stat. Sol. (a) 164, 13

    Article  ADS  Google Scholar 

  82. Whittaker D. M. (1998): What determines inhomogeneous linewidth in semiconductor microcavities? Phys. Rev. Lett. 80, 4791

    Article  ADS  Google Scholar 

  83. Yokoyama H., Nishi K., Anan T., Yamada H., Bronson S. D., Ippen E. P. (1990): Enhanced spontaneous emission from GaAs quantum wells in monolithic microcavities. Appl. Phys. Lett. 57, 2814

    Article  ADS  Google Scholar 

  84. Zhu Y., Gauthier D. J., Morin S. E., Wu Q., Carmichael H. J., Mossberg T. W. (1990): Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations. Phys. Rev. Lett. 64, 2499

    Article  ADS  Google Scholar 

  85. Zimmermann R. (1992): Theory of dephasing in semiconductor optics. Phys. Stat. Sol. (b) 173, 129

    Article  ADS  Google Scholar 

  86. Zimmermann R. (1995): Theory of resonant Rayleigh scattering of excitons in semiconductor quantum wells. Il Nuovo Cimento D 17, 1801

    Article  ADS  Google Scholar 

  87. Zimmermann R., Runge E. (1997): Excitons in narrow quantum wells: Disorder localization and luminescence kinetics. Phys. Status Sol. (a) 164, 511

    Article  ADS  Google Scholar 

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  1. Institut de Physique Théorique, Ecole Polytechnique Fédérale, CH-1015, Lausanne, Switzerland

    Vincenzo Savona

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  1. Vincenzo Savona
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Henri Benisty Claude Weisbuch École Polytechnique Jean-Michel Gérard Romuald Houdré John Rarity

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Savona, V. (1999). Linear optical properties of semiconductor microcavities with embedded quantum wells. In: Benisty, H., Weisbuch, C., Polytechnique, É., Gérard, JM., Houdré, R., Rarity, J. (eds) Confined Photon Systems. Lecture Notes in Physics, vol 531. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104383

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