Abstract

Fourier methods are used to model the propagation of ultrashort pulses of light through GaAs/AlGaAs microcavities. Resonance effects are seen in the time dependence of field amplitude in the cavity, with the electric-field amplitude in the cavity center increasing in a similar time to the pulse duration but then decaying at a much slower rate, with a longer decay time for more reflective distributed Bragg mirrors, in agreement with experimental measurements. Two separate sets of novel transient peaks are quantitatively studied. Pulses longer than 100 fs produce peaks with decreasing period for increased detuning between pulse wavelength and cavity length. Shorter pulses with spectral content broader than the range of wavelengths for which the mirrors are highly reflective show transient peaks with period independent of detuning. These peaks could affect a wide range of experiments using ultrafast pulses to study microcavities.

© 1998 Optical Society of America

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References

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  1. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).
  2. S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).
  10. M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, San Diego, Calif., 1982).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  16. T. Sale, Vertical Cavity Surface Emitting Lasers (Research Studies Press, Taunton, UK, 1995).
  17. G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
    [CrossRef]
  18. F. Jahnke and S. Koch, Z. Phys. B 104, 559 (1997).
    [CrossRef]

1997

M. Kira, F. Jahnke, and S. W. Koch, Solid State Commun. 102, 703 (1997).
[CrossRef]

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

F. Jahnke and S. Koch, Z. Phys. B 104, 559 (1997).
[CrossRef]

1996

S. C. Hagness, R. M. Joseph, and A. Taflove, Radio Sci. 31, 931 (1996).
[CrossRef]

1995

J. L. Volakis and L. C. Kempel, IEEE Comput. Sci. Eng. 2(4), 24 (1995).
[CrossRef]

S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
[CrossRef]

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

1994

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

1993

Y. Yamamoto and R. Slusher, Phys. Today 28, 66 (1993).
[CrossRef]

1989

S. Haroche and D. Kleppner, Phys. Today 24(1), 24 (1989).
[CrossRef]

Arakawa, Y.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Bongiovanni, G.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Chow, W. W.

S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
[CrossRef]

Guertler, S.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Hagness, S. C.

S. C. Hagness, R. M. Joseph, and A. Taflove, Radio Sci. 31, 931 (1996).
[CrossRef]

Haroche, S.

S. Haroche and D. Kleppner, Phys. Today 24(1), 24 (1989).
[CrossRef]

Houdre, R.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Ishira, T.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Jahnke, F.

F. Jahnke and S. Koch, Z. Phys. B 104, 559 (1997).
[CrossRef]

M. Kira, F. Jahnke, and S. W. Koch, Solid State Commun. 102, 703 (1997).
[CrossRef]

S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
[CrossRef]

Joseph, R. M.

S. C. Hagness, R. M. Joseph, and A. Taflove, Radio Sci. 31, 931 (1996).
[CrossRef]

Kempel, L. C.

J. L. Volakis and L. C. Kempel, IEEE Comput. Sci. Eng. 2(4), 24 (1995).
[CrossRef]

Kira, M.

M. Kira, F. Jahnke, and S. W. Koch, Solid State Commun. 102, 703 (1997).
[CrossRef]

Kleppner, D.

S. Haroche and D. Kleppner, Phys. Today 24(1), 24 (1989).
[CrossRef]

Koch, S.

F. Jahnke and S. Koch, Z. Phys. B 104, 559 (1997).
[CrossRef]

Koch, S. W.

M. Kira, F. Jahnke, and S. W. Koch, Solid State Commun. 102, 703 (1997).
[CrossRef]

S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
[CrossRef]

Lee, Y.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Mura, A.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Nakamura, T.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Nishioka, M.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Norris, T. B.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Oesterle, U.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Quochi, F.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Rhee, J. K.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Slusher, R.

Y. Yamamoto and R. Slusher, Phys. Today 28, 66 (1993).
[CrossRef]

Staehli, J. L.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Stanley, R. P.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Sung, C. Y.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Taflove, A.

S. C. Hagness, R. M. Joseph, and A. Taflove, Radio Sci. 31, 931 (1996).
[CrossRef]

Takamatsu, W.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Tanaka, K.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Tassone, F.

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

Volakis, J. L.

J. L. Volakis and L. C. Kempel, IEEE Comput. Sci. Eng. 2(4), 24 (1995).
[CrossRef]

Weisbuch, C.

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto and R. Slusher, Phys. Today 28, 66 (1993).
[CrossRef]

Yamanishi, M.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

IEEE Comput. Sci. Eng.

J. L. Volakis and L. C. Kempel, IEEE Comput. Sci. Eng. 2(4), 24 (1995).
[CrossRef]

Phys. Rev. B

G. Bongiovanni, A. Mura, F. Quochi, S. Guertler, J. L. Staehli, F. Tassone, R. P. Stanley, U. Oesterle, and R. Houdre, Phys. Rev. B 55, 7084 (1997).
[CrossRef]

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 55, 14663 (1994).
[CrossRef]

Phys. Rev. Lett.

K. Tanaka, T. Nakamura, W. Takamatsu, M. Yamanishi, Y. Lee, and T. Ishira, Phys. Rev. Lett. 74, 3380 (1995).
[CrossRef] [PubMed]

Phys. Today

Y. Yamamoto and R. Slusher, Phys. Today 28, 66 (1993).
[CrossRef]

S. Haroche and D. Kleppner, Phys. Today 24(1), 24 (1989).
[CrossRef]

Radio Sci.

S. C. Hagness, R. M. Joseph, and A. Taflove, Radio Sci. 31, 931 (1996).
[CrossRef]

Semicond. Sci. Technol.

S. W. Koch, F. Jahnke, and W. W. Chow, Semicond. Sci. Technol. 10, 739 (1995).
[CrossRef]

Solid State Commun.

M. Kira, F. Jahnke, and S. W. Koch, Solid State Commun. 102, 703 (1997).
[CrossRef]

Z. Phys. B

F. Jahnke and S. Koch, Z. Phys. B 104, 559 (1997).
[CrossRef]

Other

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

T. Sale, Vertical Cavity Surface Emitting Lasers (Research Studies Press, Taunton, UK, 1995).

R. T. Phillips, Coherent Optical Interactions in Semiconductors: Proceedings of a NATO ARW Held in Cambridge, United Kingdom, August 11–14, 1993 (Plenum, New York, 1994).

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer-Verlag, Berlin, 1996).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).

M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, San Diego, Calif., 1982).

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Figures (5)

Fig. 1
Fig. 1

Input pulse and corresponding amplitude response at the center of a cavity made with highly reflective mirrors (maximum reflectivity 99.94%).

Fig. 2
Fig. 2

Effect of the reflectivity of the cavity mirrors (R) on the cavity response. The input pulse has unit amplitude as in Fig. 1.

Fig. 3
Fig. 3

(a) Cavity response for increasingly detuned pulses. The input pulse has unit amplitude as in Fig. 1. The maximum reflectivities of the two mirrors are 96.9% and 99.2%. (b) Detail of (a) showing the transient peaks.

Fig. 4
Fig. 4

For shorter pulses, increased detuning has no effect on the period of the transient peaks. The input pulse has unit amplitude as in Fig. 1.

Fig. 5
Fig. 5

(a) Transient peaks from shorter tuned pulses of unit amplitude. (b) Spectral content of the pulses used in (a) and the reflectivity of the cavity and the first DBR. When the input pulse contains components in the region of transmission for the mirror, transients appear in the cavity response.

Equations (5)

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

Re[A(z)]=2A0 cos[k0(z-z0)]exp(z-z0)σ+exp(-z+z0)σ,
Im[A(z)]=2A0 sin[k0(z-z0)]exp(z-z0)σ+exp(-z+z0)σ.
m(nλ-λcav)=λcav.
τ=nλλcavc|nλ-λcav|.
τ=λ1λ2c(λ1-λ2).

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