Abstract

We experimentally study the spectra of the transient Faraday and Kerr effects near exciton resonances of a GaAs multiple quantum well. A multilayer calculation with a transfer matrix model accounts quantitatively for the linear transmission (reflectivity) spectra and the Faraday (Kerr) spectra. The Faraday and Kerr spectra do not obey a Kramers–Kronig relation. This phenomenon was found to be due to the multiple reflection effects on the Kerr spectra.

© 2005 Optical Society of America

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  1. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
    [CrossRef] [PubMed]
  2. W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
    [CrossRef]
  3. C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
    [CrossRef]
  4. S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
    [CrossRef]
  5. T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
    [CrossRef]
  6. A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
    [CrossRef]
  7. C. L. Mitsas and D. I. Siapkas, Appl. Opt. 34, 1678 (1995).
    [CrossRef] [PubMed]
  8. M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
    [CrossRef]

2001 (3)

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
[CrossRef]

2000 (1)

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

1997 (2)

C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
[CrossRef]

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

1995 (1)

1991 (1)

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Awschalom, D. D.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Baumberg, J. J.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Bentivegna, F.

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

Buhrman, R. A.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Chtchelkanova, A. Y.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Cibert, J.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
[CrossRef]

Crooker, S. A.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Daughton, J. M.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Eccleston, R.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Flack, F.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Flinn, G. P.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Gaj, J. A.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Golnik, A.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Harley, R. T.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Hashimoto, Y.

T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
[CrossRef]

Karczewski, G.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Kimel, A. V.

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

Kossacki, P.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Kossut, J.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Kuroda, T.

T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
[CrossRef]

Mac, W.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Maslana, W.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Minami, F.

T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
[CrossRef]

Mitsas, C. L.

Pavlov, V. V.

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

Phillips, C. C.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Pisarev, R. V.

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

Plaut, A. S.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Rasing, Th.

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

Rigaux, C.

C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
[CrossRef]

Roukes, M. L.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Samarth, N.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Siapkas, D. I.

Snelling, M. J.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

Tatarenko, S.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Testelin, C.

C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
[CrossRef]

Treger, D. M.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Tropper, A. C.

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

von Molnar, S.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Wojtowicz, T.

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

Wolf, S. A.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Lumin. (1)

T. Kuroda, Y. Hashimoto, and F. Minami, J. Lumin. 94–95, 551 (2001).
[CrossRef]

Phys. Rev. B (5)

A. V. Kimel, V. V. Pavlov, R. V. Pisarev, F. Bentivegna, and Th. Rasing, Phys. Rev. B 62, R10610 (2000).
[CrossRef]

M. J. Snelling, G. P. Flinn, A. S. Plaut, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C. Phillips, Phys. Rev. B 44, 11345 (1991).
[CrossRef]

W. Maslana, W. Mac, J. A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, and J. Kossut, Phys. Rev. B 63, 165318 (2001).
[CrossRef]

C. Testelin, C. Rigaux, and J. Cibert, Phys. Rev. B 55, 2360 (1997).
[CrossRef]

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, Phys. Rev. B 56, 7574 (1997).
[CrossRef]

Science (1)

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Energy-shift-induced Faraday and Kerr effect spectra calculated for a slab of a nonlinear medium. Reflection from the front interface alone is considered for the Kerr effect. An energy shift of 0.1 γ is used, where γ is the full width at half-maximum linewidth of the resonance.

Fig. 2
Fig. 2

Schematic setup for the transient Faraday rotation measurements. An additional quarter-wave plate ( λ 4 ) is inserted for the Faraday ellipticity measurement. Kerr measurements are performed in reflection geometry, which is not shown in the figure. PBS, polarizing beam splitter.

Fig. 3
Fig. 3

Measured (filled circles) and calculated (solid curves) linear reflectivity spectra near hh and lh exciton resonances (indicated by dashed lines). Spectra in (a) and (b) correspond to different sample thicknesses, which are described in the text.

Fig. 4
Fig. 4

Measured (open circles) and calculated (solid curves) Faraday and Kerr effect spectra. Spectra in (a)–(d) are obtained for a sample thickness the same as that in Fig. 3(a); spectra in (e)–(h) are for a slightly different sample thickness, the same as that in Fig. 3(b).

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