Abstract

A theory for carrier decay rates and a technique for measuring them are reported. Modification of the spontaneous emission rate of carriers by a semiconductor microcavity is investigated with 100-nm-thick bulk GaAs. Reabsorption makes the cavity-mode photoluminescence (PL) decay much faster than the square of the carrier density. Here reabsorption distortion is avoided by collecting PL that escapes the microcavity directly without multiple reflections: a ZnSe prism glued to the top mirror allows PL to escape at angles beyond the cutoff angle for total internal reflection without the prism. At these steep angles, the stop band of the top mirror has shifted to higher energy, so that it does not impede PL emission. Removal of most of the bottom mirror decreases the true carrier decay rate by only ≈25%, showing that the large enhancements deduced from cavity-mode PL are incorrect. Fully quantum mechanical computation including guided modes corroborates this conclusion. The prism technique could be used to study carrier dynamics and competition between guided and cavity modes in microcavities below and near threshold.

© Optical Society of America

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References

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  1. P. Goy, J. M. Raimond, M. Gross, and S. Haroche, "Observation of cavity-enhanced single-atom spontaneous emission," Phys. Rev. Lett. 50, 1903-1906 (1983).
    [CrossRef]
  2. S. Haroche and J. M. Raimond, "Radiative properties of Rydberg states in resonant cavities," 347-411 in B. Bederson and D. R. Bates, eds., Advances in Atomic and Molecular Physics 20 (Academic, New York, 1985).
    [CrossRef]
  3. H. J. Kimble, "Structure and dynamics in cavity quantum electrodynamics," 203-266 in P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, Boston, 1994).
  4. M. Kira, F. Jahnke, and S. W. Koch, "Microscopic theory of excitonic signatures in semiconductor photoluminescence," Phys. Rev. Lett. 81, 3263-3266 (1998).
    [CrossRef]
  5. L. C. Andreani, F. Tassone, and F. Bassani, "Radiative lifetime of free excitons in quantum wells," Solid State Commun. 77, 641-645 (1991).
    [CrossRef]
  6. D. S. Citrin, "Radiative lifetimes of excitons in semiconductor quantum wells," Comments Cond. Mat. Phys. 16(5), 263-280 (1993).
  7. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, "Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity," Phys. Rev. Lett. 69, 3314-3317 (1992).
    [CrossRef] [PubMed]
  8. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, "Nonlinear optics of normal-mode-coupling semiconductor microcavities," Rev. Mod. Phys., to be published.
  9. M. Kira, F. Jahnke, W Hoyer, and S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Electron., to be published.
  10. M. Kira, F. Jahnke, S. W. Koch, J. D. Berger, D. V. Wick, T. R. Nelson, Jr., G. Khitrova, and H. M. Gibbs, "Quantum theory of nonlinear semiconductor microcavity luminescence explaining "Boser" experiments," Phys. Rev. Lett. 79, 5170-5173 (1997).
    [CrossRef]
  11. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
  12. Cavity Quantum Electrodynamics, edited by P. R. Berman, (Academic Press, New York, 1994).
  13. G. Bj�rk, S. Machida, and K. Igata, "Modification of spontaneous emission rate in planar dielectric microcavity structures," Phys. Rev. A, 44, 669-681 (1991).
    [CrossRef] [PubMed]
  14. Y. Yamamoto, S. Machida, Y. Horikoshi, K. Igeta, and G. Bj�rk, "Enhanced and inhibited spontaneous emission of free excitons in GaAs quantum wells in a microcavity," Opt. Commun. 80, 337-342 (1991).
    [CrossRef]
  15. D. L. Huffaker, C. Lei, D. G. Deppe, C. J. Pinzone, J. G. Neff, and R. D. Dupuis, "Controlled spontaneous emission in room-temperature semiconductor microcavities," Appl. Phys. Lett. 60, 3203-3205 (1992).
    [CrossRef]
  16. K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishihara, "Cavity-induced changes of spontaneous emission lifetime in one-dimensional semiconductor microcavities," Phys. Rev. Lett. 74, 3380-3383 (1995).
    [CrossRef] [PubMed]
  17. L. A. Graham, D. L. Huffaker, Q. Deng, and D. G. Deppe, "Controlled spontaneous lifetime in microcavity confined InGaAlAs/GaAs quantum dots," Appl. Phys. Lett. 72, 1670-1672 (1998).
    [CrossRef]
  18. R. Jin, M. S. Tobin, R. P. Leavitt, H. M. Gibbs, G. Khitrova, D. Boggavarapu, O. Lynnes, E. Lindmark, F. Jahnke, and S. W. Koch, "Order of magnitude enhanced spontaneous emission from room-temperature bulkGaAs," in Microcavities and Photonic Bandgaps: Physics and Applications, J. Rarity, and C. Weisbuch, ed. (Kluwer, Dordrecht,1996), p. 43.
  19. H. K. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, "Enhanced spontaneous emission from GaAs quantum wells in monolithic microcavities," Appl. Phys. Lett. 57, 2814-2816 (1990).
    [CrossRef]
  20. Y. Hanamaki, H. Kinoshita, H. Akiyama, N. Ogasawara, and Y. Shirki, "Spontaneous emission lifetime alteration in InGaAs/GaAs vertical-cavity surface-emitting laser structures," Phys. Rev. B 56, R4379-4382 (1997).
    [CrossRef]
  21. C. C. Lin, D. G. Deppe, and C. Lei, "Role of waveguide light emission in planar microcavities," IEEE J. Quantum Electron. 30, 2304-2312 (1994).
    [CrossRef]
  22. Analysis shows that reabsorption distortion can be avoided if a stationary carrier density is maintained in the active layer, e.g., by means of cw pumping. In this case, PL dynamics of this sample subjected to a weak perturbation (e.g., to a short pump pulse) will exactly reproduce dynamics of carriers (provided that the perturbation is sufficiently small).
  23. I. Abram, S. Iung, R. Kuszelewicz, G. Le Roux, C. Licoppe, J. L. Oudar, and E. V. K. Rao, "Nonguiding half-wave semiconductor microcavities displaying the exciton-photon mode splitting," Appl. Phys. Lett. 65, 2516-2518 (1994).
    [CrossRef]
  24. E. F. Schubert, N. E. J. Hunt, M. Micovic, R. J. Malik, D. L. Sivco, A. Y. Cho, and G. J. Zydzik, "Highly efficient light-emitting diodes with microcavities," Science 265, 943-945 (1994).
    [CrossRef] [PubMed]
  25. H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Van Daele, and G. Borghs, "High efficiency planar microcavity LEDs: comparison of design and experiment," IEEE Phot. Tech. Lett. 7, 287-289 (1995).
    [CrossRef]
  26. H. De Neve, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, and G. Borghs, "Recycling of guided mode light emission in planar microcavity light emitting diodes," Appl. Phys. Lett. 70, 799-801 (1997).
    [CrossRef]
  27. H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, "Radiative and guided wave emission of Er 3+ atoms located in planar multidielectric structures," Phys. Rev. A 55, 1497-1502 (1997).
    [CrossRef]
  28. H. Rigneault, S. Robert, C. Amra, F. Lamarque, S. Monneret, B. Jacquier, P. Moretti, A. M. Jurdyc, and A. Belarouci, "Spontaneous emission of rare earth ions confined in planar multilayer dielectric microcavities," SPIE 3133, 78-87 (1997).
    [CrossRef]
  29. R. P. Stanley, R. Houdr�, C. Weisbuch, U. Oesterle, and M. Ilegems, "Cavity-polariton photoluminescence in semiconductor microcavities: experimental evidence," Phys. Rev. B 53, 10995-11007 (1996).
    [CrossRef]
  30. E. Spiller, "Saturable resonator for visible light," J. Opt. Soc. Am. 61, 669 (1971) and "Saturable optical resonator," J. Appl. Phys. 43, 1673-1681 (1972).
  31. D. L. Huffaker and D. G. Deppe, "Spontaneous coupling to planar and index-confined quasimodes of Fabry-P�rot microcavities," Appl. Phys. Lett. 67, 2594-2596 (1995).
    [CrossRef]
  32. D. G. Deppe, T. -H. Oh, and D. L. Huffaker, "Eigenmode confinement in the dielectrically apertured Fabry-Perot microcavity," IEEE Photon. Tech. Lett. 9, 713-715 (1997).
    [CrossRef]
  33. F. Jahnke, M. Kira, and S. W. Koch, "Linear and nonlinear optical properties of excitons in semiconductor quantum well and microcavities," Z. Physik B 104, 559-572 (1997).
    [CrossRef]
  34. J. M. G�rard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity", Phys. Rev. Lett. 81, 1110- 1113 (1998).
    [CrossRef]

Other (34)

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, "Observation of cavity-enhanced single-atom spontaneous emission," Phys. Rev. Lett. 50, 1903-1906 (1983).
[CrossRef]

S. Haroche and J. M. Raimond, "Radiative properties of Rydberg states in resonant cavities," 347-411 in B. Bederson and D. R. Bates, eds., Advances in Atomic and Molecular Physics 20 (Academic, New York, 1985).
[CrossRef]

H. J. Kimble, "Structure and dynamics in cavity quantum electrodynamics," 203-266 in P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, Boston, 1994).

M. Kira, F. Jahnke, and S. W. Koch, "Microscopic theory of excitonic signatures in semiconductor photoluminescence," Phys. Rev. Lett. 81, 3263-3266 (1998).
[CrossRef]

L. C. Andreani, F. Tassone, and F. Bassani, "Radiative lifetime of free excitons in quantum wells," Solid State Commun. 77, 641-645 (1991).
[CrossRef]

D. S. Citrin, "Radiative lifetimes of excitons in semiconductor quantum wells," Comments Cond. Mat. Phys. 16(5), 263-280 (1993).

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, "Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity," Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, "Nonlinear optics of normal-mode-coupling semiconductor microcavities," Rev. Mod. Phys., to be published.

M. Kira, F. Jahnke, W Hoyer, and S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Electron., to be published.

M. Kira, F. Jahnke, S. W. Koch, J. D. Berger, D. V. Wick, T. R. Nelson, Jr., G. Khitrova, and H. M. Gibbs, "Quantum theory of nonlinear semiconductor microcavity luminescence explaining "Boser" experiments," Phys. Rev. Lett. 79, 5170-5173 (1997).
[CrossRef]

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

Cavity Quantum Electrodynamics, edited by P. R. Berman, (Academic Press, New York, 1994).

G. Bj�rk, S. Machida, and K. Igata, "Modification of spontaneous emission rate in planar dielectric microcavity structures," Phys. Rev. A, 44, 669-681 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, Y. Horikoshi, K. Igeta, and G. Bj�rk, "Enhanced and inhibited spontaneous emission of free excitons in GaAs quantum wells in a microcavity," Opt. Commun. 80, 337-342 (1991).
[CrossRef]

D. L. Huffaker, C. Lei, D. G. Deppe, C. J. Pinzone, J. G. Neff, and R. D. Dupuis, "Controlled spontaneous emission in room-temperature semiconductor microcavities," Appl. Phys. Lett. 60, 3203-3205 (1992).
[CrossRef]

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishihara, "Cavity-induced changes of spontaneous emission lifetime in one-dimensional semiconductor microcavities," Phys. Rev. Lett. 74, 3380-3383 (1995).
[CrossRef] [PubMed]

L. A. Graham, D. L. Huffaker, Q. Deng, and D. G. Deppe, "Controlled spontaneous lifetime in microcavity confined InGaAlAs/GaAs quantum dots," Appl. Phys. Lett. 72, 1670-1672 (1998).
[CrossRef]

R. Jin, M. S. Tobin, R. P. Leavitt, H. M. Gibbs, G. Khitrova, D. Boggavarapu, O. Lynnes, E. Lindmark, F. Jahnke, and S. W. Koch, "Order of magnitude enhanced spontaneous emission from room-temperature bulkGaAs," in Microcavities and Photonic Bandgaps: Physics and Applications, J. Rarity, and C. Weisbuch, ed. (Kluwer, Dordrecht,1996), p. 43.

H. K. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, "Enhanced spontaneous emission from GaAs quantum wells in monolithic microcavities," Appl. Phys. Lett. 57, 2814-2816 (1990).
[CrossRef]

Y. Hanamaki, H. Kinoshita, H. Akiyama, N. Ogasawara, and Y. Shirki, "Spontaneous emission lifetime alteration in InGaAs/GaAs vertical-cavity surface-emitting laser structures," Phys. Rev. B 56, R4379-4382 (1997).
[CrossRef]

C. C. Lin, D. G. Deppe, and C. Lei, "Role of waveguide light emission in planar microcavities," IEEE J. Quantum Electron. 30, 2304-2312 (1994).
[CrossRef]

Analysis shows that reabsorption distortion can be avoided if a stationary carrier density is maintained in the active layer, e.g., by means of cw pumping. In this case, PL dynamics of this sample subjected to a weak perturbation (e.g., to a short pump pulse) will exactly reproduce dynamics of carriers (provided that the perturbation is sufficiently small).

I. Abram, S. Iung, R. Kuszelewicz, G. Le Roux, C. Licoppe, J. L. Oudar, and E. V. K. Rao, "Nonguiding half-wave semiconductor microcavities displaying the exciton-photon mode splitting," Appl. Phys. Lett. 65, 2516-2518 (1994).
[CrossRef]

E. F. Schubert, N. E. J. Hunt, M. Micovic, R. J. Malik, D. L. Sivco, A. Y. Cho, and G. J. Zydzik, "Highly efficient light-emitting diodes with microcavities," Science 265, 943-945 (1994).
[CrossRef] [PubMed]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Van Daele, and G. Borghs, "High efficiency planar microcavity LEDs: comparison of design and experiment," IEEE Phot. Tech. Lett. 7, 287-289 (1995).
[CrossRef]

H. De Neve, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, and G. Borghs, "Recycling of guided mode light emission in planar microcavity light emitting diodes," Appl. Phys. Lett. 70, 799-801 (1997).
[CrossRef]

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, "Radiative and guided wave emission of Er 3+ atoms located in planar multidielectric structures," Phys. Rev. A 55, 1497-1502 (1997).
[CrossRef]

H. Rigneault, S. Robert, C. Amra, F. Lamarque, S. Monneret, B. Jacquier, P. Moretti, A. M. Jurdyc, and A. Belarouci, "Spontaneous emission of rare earth ions confined in planar multilayer dielectric microcavities," SPIE 3133, 78-87 (1997).
[CrossRef]

R. P. Stanley, R. Houdr�, C. Weisbuch, U. Oesterle, and M. Ilegems, "Cavity-polariton photoluminescence in semiconductor microcavities: experimental evidence," Phys. Rev. B 53, 10995-11007 (1996).
[CrossRef]

E. Spiller, "Saturable resonator for visible light," J. Opt. Soc. Am. 61, 669 (1971) and "Saturable optical resonator," J. Appl. Phys. 43, 1673-1681 (1972).

D. L. Huffaker and D. G. Deppe, "Spontaneous coupling to planar and index-confined quasimodes of Fabry-P�rot microcavities," Appl. Phys. Lett. 67, 2594-2596 (1995).
[CrossRef]

D. G. Deppe, T. -H. Oh, and D. L. Huffaker, "Eigenmode confinement in the dielectrically apertured Fabry-Perot microcavity," IEEE Photon. Tech. Lett. 9, 713-715 (1997).
[CrossRef]

F. Jahnke, M. Kira, and S. W. Koch, "Linear and nonlinear optical properties of excitons in semiconductor quantum well and microcavities," Z. Physik B 104, 559-572 (1997).
[CrossRef]

J. M. G�rard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity", Phys. Rev. Lett. 81, 1110- 1113 (1998).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Arrangement for pumping and detecting PL. A prism glued on the top of the sample permits the observation of PL that is free from multiple-layer interference; without the prism, it undergoes total internal reflection and goes into guided modes.

Fig. 2.
Fig. 2.

The 110 K PL spectrum including both the emission by the cavity mode and emission at steep angles through the prism. A normal-incidence reflection spectrum of the sample measured at room temperature is shown in the inset.

Fig. 3.
Fig. 3.

Experimental setup for steep-angle PL lifetime measurements undistorted by reabsorption by the GaAs layer.

Fig. 4.
Fig. 4.

PL decay times as a function of pump power at 110 K. (a) Decay times of steep- angle PL for two different reflectivities of the bottom mirror, ~78% and 99.9%. (b) Corresponding decay times of the cavity-mode PL emitted through the bottom mirror for the same mirror reflectivities.

Fig. 5.
Fig. 5.

Angular distribution of PL intensity emitted through the top mirror at room temperature (no prism). (a) Without and (b) with integration over the annulus shown in the inset.

Fig. 6.
Fig. 6.

Angular distribution of the PL intensity integrated over an annulus.

Fig. 7.
Fig. 7.

The calculated spectral position of the cavity peak with respect to the bulk GaAs PL measured at room temperature for (a) θ=0° and (b) θ=70°.

Fig. 8.
Fig. 8.

Microscopically computed electron-hole recombination rates γeh(N) for microcavities as used herein with different number N of quarterwave pairs in the bottom mirror. The top mirror has 22 pairs. A carrier density of 2×1011 cm-2 is assumed.

Fig. 9.
Fig. 9.

Electron-hole recombination rate as a function of the number of layers in the top mirror of Yokoyama et al. [19], showing very little cavity-QED enhancement.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

t b q h k e k + q = ( ε k , q ħ ω q i γ ) b q h k e k + q + ( f k + q e + f k h 1 ) Ω k , q + f k h f k + q e Ω q SE ,
t b q , q e q + q = i ( ω q ω q′ ) b q , q b q′ , q + 1 ħ k [ F q b q′ e k + q h k + F q′ b q h k e k + q ] ,
t f k e = 2 ħ q , q Re [ d cv * F q b q , q h k q e k ] ,
t f k h = 2 ħ q , q Re [ d cv * F q b q , q h k e k + q ] ,
Ω q SE = i F q d cv ,
Ω k , q = d cv [ q i F q b q b q , q k P d cv * b q h k e k + q ] + k V k k b q h k e k + q ,
γ eh = 2 ħ S n o k q , q Re [ d cv * F q b q , q h k q e k ] ,

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