Abstract

We theoretically investigate slow and fast light propagation and pulse velocity control in a nanocavity containing a single quantum dot side-coupled to a planar-photonic-crystal waveguide. We demonstrate that low coupling strength (i.e., the weak coupling regime) between a cavity and a dot, under on-resonance condition, can lead to delays of about +90ps for a pulse 1e-width of 280ps. The group delay dependence on the various coupling parameters suggests achievable delays of +300ps and consequently very slow light speeds of around 5000ms in a 1.5μm cavity-waveguide section. We also show that under off-resonant condition one can achieve significant pulse advancement of 60ps.

© 2007 Optical Society of America

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  1. R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530.
    [CrossRef]
  2. L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
    [CrossRef]
  3. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
    [CrossRef] [PubMed]
  4. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
    [CrossRef] [PubMed]
  5. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  6. M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
    [CrossRef] [PubMed]
  7. J. B. Khurgin, J. Opt. Soc. Am. B 22, 1062 (2005).
    [CrossRef]
  8. E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
    [CrossRef]
  9. D. Gerace and L. C. Andreani, Opt. Express 13, 4939 (2005).
    [CrossRef] [PubMed]
  10. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  11. Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
    [CrossRef] [PubMed]
  12. V. S. C. Manga Rao, S. Dutta Gupta, and G. S. Agarwal, Opt. Lett. 29, 307 (2003).
    [CrossRef]
  13. A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
    [CrossRef] [PubMed]
  14. H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
    [CrossRef]
  15. S. Hughes and H. Kamada, Phys. Rev. B 70, 195313 (2004).
    [CrossRef]
  16. E. P. Wigner, Phys. Rev. 98, 145 (1955).
    [CrossRef]
  17. E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006).
    [CrossRef] [PubMed]
  18. L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
    [CrossRef] [PubMed]
  19. S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef] [PubMed]
  20. T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
    [CrossRef]
  21. See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
    [CrossRef]

2006 (4)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef] [PubMed]

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
[CrossRef]

2005 (8)

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

J. B. Khurgin, J. Opt. Soc. Am. B 22, 1062 (2005).
[CrossRef]

D. Gerace and L. C. Andreani, Opt. Express 13, 4939 (2005).
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

2004 (2)

S. Hughes and H. Kamada, Phys. Rev. B 70, 195313 (2004).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

1955 (1)

E. P. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

Agarwal, G. S.

Altug, H.

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Andreani, L. C.

Arakawa, Y.

See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
[CrossRef]

Atature, M.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Badolato, A.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Behroozi, C.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530.
[CrossRef]

Briggs, A.

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Deng, L.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Dreiser, J.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Elsaesser, T.

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Fan, S.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Gaeta, A. L.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530.
[CrossRef]

Gerace, D.

Gupta, S. Dutta

Hagley, E.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Hennessy, K.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Hu, E.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Hughes, S.

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

S. Hughes and H. Kamada, Phys. Rev. B 70, 195313 (2004).
[CrossRef]

Imamoglu, A.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Kako, S.

See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
[CrossRef]

Kamada, H.

S. Hughes and H. Kamada, Phys. Rev. B 70, 195313 (2004).
[CrossRef]

Khurgin, J. B.

Kozuma, M.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Kuga, T.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[CrossRef] [PubMed]

Lienau, C.

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Manga Rao, V. S. C.

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Mueller, K.

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Nakaoka, T.

See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
[CrossRef]

Notomi, M.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Petroff, P. M.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Shimizu, Y.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

Shiokawa, N.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Sipe, J. E.

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Unold, T.

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Vuckovic, J.

E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef] [PubMed]

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Waks, E.

E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef] [PubMed]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

Wigner, E. P.

E. P. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

Yamamoto, N.

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

Yanik, M. F.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Young, J. Y.

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (2)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

E. P. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

Phys. Rev. B (3)

See, for example, T. Nakaoka, S. Kako, and Y. Arakawa, Phys. Rev. B 73, 121305 (2006).
[CrossRef]

S. Hughes and H. Kamada, Phys. Rev. B 70, 195313 (2004).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

Phys. Rev. Lett. (6)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. Hagley, Phys. Rev. Lett. 89, 233001 (2002).
[CrossRef] [PubMed]

E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef] [PubMed]

S. Hughes, L. Ramunno, J. Y. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. Briggs, Phys. Rev. Lett. 92, 157401 (2006).
[CrossRef]

Science (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[CrossRef] [PubMed]

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).
[CrossRef] [PubMed]

Other (1)

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the waveguide/nanocavity coupling scheme using a planar photonic crystal. The quantum dot (QD) is placed near the field antinode location of the nanocavity. The propagating field excites the defect cavity e c , which couples to the propagating Bloch mode e k and to the embedded QD.

Fig. 2
Fig. 2

(a) Intensity transmission T 2 of a PPC waveguide coupled to a nanocavity system with the QD (solid curve) and without the QD (dashed curve) as a function of cavity detuning [ δ = ( ω ω c ) 2 π ] . The parameters are as follows: Γ c 2 π = 28.8 GHz ( Γ c 0.12 meV ) , Γ 0 2 π = 2.9 GHz , γ 2 π = 0.5 GHz , Ω 2 π = 6.3 GHz . (b) Corresponding group delay τ T . (c) Transmitted pulse shape (solid curve) compared with the reference pulse (dashed curve normalized to the peak of the transmitted pulse) for an input Gaussian pulse with width τ = 280 ps and carrier chosen at cavity resonance.

Fig. 3
Fig. 3

Group delay τ T dependence on the coupling parameters using a pulse carrier tuned at cavity resonance (a) versus cavity-dot coupling Ω, (b) versus cavity waveguide coupling Γ c . The other parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

Advancement in the transmitted pulse shape (solid curve) compared with the reference pulse (dashed curve) with width τ = 250 ps and the carrier tuned near the cavity resonance. The other parameters are the same as in Fig. 2.

Equations (4)

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

T ( w ) = 1 + i ω Γ c ω c 2 ω 2 i ω ( Γ c + Γ 0 ) ω c Σ ,
A T ( t ) = d ω T ( ω ) A I ( ω ) e i ω t ,
T = 1 Γ c γ 2 Ω 2 + ( Γ c + Γ 0 ) γ ,
τ T = ( 2 Ω 2 γ 2 ) Γ c [ 2 Ω 2 + γ Γ 0 ] [ 2 Ω 2 + γ ( Γ 0 + Γ c ) ] .

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