Abstract

Group delay for a reflected light pulse from a weakly absorbing dielectric slab is theoretically investigated, and large negative group delay is found for weak absorption near a resonance of the slab [Re(kd)=mπ]. The group delay for both the reflected and transmitted pulses will be saturated with an increase of the absorption.

© 2006 Optical Society of America

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  1. R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E.Wolf, ed. (Elsevier, 1997), Vol. 37, pp. 345-405.
    [CrossRef]
  2. G. Nimtz, Prog. Quantum Electron. 27, 417 (2003).
    [CrossRef]
  3. R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530.
    [CrossRef]
  4. P. W. Milloni, J. Phys. B 35, R31 (2002).
    [CrossRef]
  5. M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
    [CrossRef]
  6. V. S. C. Manga Rao, S. Dutta Gupta, and G. S. Agarwal, Opt. Lett. 29, 307 (2004).
    [CrossRef] [PubMed]
  7. L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
    [CrossRef]
  8. S. Longhi, Phys. Rev. E 64, 037601 (2001).
    [CrossRef]
  9. S. Longhi, Phys. Rev. E 72, 056614 (2005).
    [CrossRef]
  10. C. F. Li and Q. Wang, Phys. Lett. A 275, 287 (2000).
    [CrossRef]
  11. C. F. Li and H. Spieker, Opt. Commun. 259, 158 (2006).
    [CrossRef]
  12. R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
    [CrossRef]
  13. S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
    [CrossRef]
  14. S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
    [CrossRef]
  15. A. H. Gevorgyan, Opt. Spectrosc. 96, 877 (2004).
    [CrossRef]
  16. C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
    [CrossRef] [PubMed]
  17. L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
    [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).
  19. L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
    [CrossRef] [PubMed]
  20. A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
    [CrossRef] [PubMed]
  21. E. P. Wigner, Phys. Rev. 98, 145 (1955).
    [CrossRef]
  22. H. G. Winful, Phys. Rev. Lett. 90, 023901 (2003).
    [CrossRef] [PubMed]
  23. T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
    [CrossRef]
  24. G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
    [CrossRef]
  25. G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
    [CrossRef]

2006 (1)

C. F. Li and H. Spieker, Opt. Commun. 259, 158 (2006).
[CrossRef]

2005 (2)

2004 (4)

V. S. C. Manga Rao, S. Dutta Gupta, and G. S. Agarwal, Opt. Lett. 29, 307 (2004).
[CrossRef] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
[CrossRef]

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

A. H. Gevorgyan, Opt. Spectrosc. 96, 877 (2004).
[CrossRef]

2003 (4)

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

H. G. Winful, Phys. Rev. Lett. 90, 023901 (2003).
[CrossRef] [PubMed]

G. Nimtz, Prog. Quantum Electron. 27, 417 (2003).
[CrossRef]

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

2002 (3)

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

P. W. Milloni, J. Phys. B 35, R31 (2002).
[CrossRef]

G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
[CrossRef]

2001 (2)

R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 037601 (2001).
[CrossRef]

2000 (1)

C. F. Li and Q. Wang, Phys. Lett. A 275, 287 (2000).
[CrossRef]

1998 (1)

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

1994 (2)

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
[CrossRef]

1962 (1)

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

1955 (1)

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

Agarwal, G. S.

Belmonte, M.

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

Blaauboer, M.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

Boyd, R. W.

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

Brodowsky, H. M.

G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
[CrossRef]

Chen, H.

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E.Wolf, ed. (Elsevier, 1997), Vol. 37, pp. 345-405.
[CrossRef]

Crespi, P.

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

Dutta Gupta, S.

Gauthier, D. J.

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

Gevorgyan, A. H.

A. H. Gevorgyan, Opt. Spectrosc. 96, 877 (2004).
[CrossRef]

Haibel, A.

G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
[CrossRef]

R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
[CrossRef]

Hartman, T. E.

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

Kofman, A. G.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Kozhekin, A. E.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Kurizki, G.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Laporta, P.

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

Lenstra, D.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Li, C. F.

C. F. Li and H. Spieker, Opt. Commun. 259, 158 (2006).
[CrossRef]

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

C. F. Li and Q. Wang, Phys. Lett. A 275, 287 (2000).
[CrossRef]

Lin, Q.

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Liu, N.-H.

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Lodder, A.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Rev. E 72, 056614 (2005).
[CrossRef]

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 037601 (2001).
[CrossRef]

Manga Rao, V. S. C.

Marano, M.

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

Milloni, P. W.

P. W. Milloni, J. Phys. B 35, R31 (2002).
[CrossRef]

Nimtz, G.

G. Nimtz, Prog. Quantum Electron. 27, 417 (2003).
[CrossRef]

G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
[CrossRef]

R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
[CrossRef]

G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
[CrossRef]

Spieker, H.

C. F. Li and H. Spieker, Opt. Commun. 259, 158 (2006).
[CrossRef]

G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E.Wolf, ed. (Elsevier, 1997), Vol. 37, pp. 345-405.
[CrossRef]

Vetter, R. M.

R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
[CrossRef]

Vetter, R.-M.

G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
[CrossRef]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
[CrossRef]

Wang, L-G.

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Wang, Q.

C. F. Li and Q. Wang, Phys. Lett. A 275, 287 (2000).
[CrossRef]

Wigner, E. P.

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

Winful, H. G.

H. G. Winful, Phys. Rev. Lett. 90, 023901 (2003).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

Zhu, S. Y.

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
[CrossRef]

Zhu, S-Y.

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, IEEE J. Sel. Top. Quantum Electron. 9, 4 (2003).
[CrossRef]

J. Appl. Phys. (1)

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

J. Phys. (France) (1)

G. Nimtz, H. Spieker, and H. M. Brodowsky, J. Phys. (France) 4, 1379 (1994).
[CrossRef]

J. Phys. B (1)

P. W. Milloni, J. Phys. B 35, R31 (2002).
[CrossRef]

Opt. Commun. (1)

C. F. Li and H. Spieker, Opt. Commun. 259, 158 (2006).
[CrossRef]

Opt. Lett. (2)

Opt. Spectrosc. (1)

A. H. Gevorgyan, Opt. Spectrosc. 96, 877 (2004).
[CrossRef]

Phys. Lett. A (1)

C. F. Li and Q. Wang, Phys. Lett. A 275, 287 (2000).
[CrossRef]

Phys. Rev. (1)

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

Phys. Rev. A (2)

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (7)

G. Nimtz, A. Haibel, and R.-M. Vetter, Phys. Rev. E 66, 037602 (2002).
[CrossRef]

L-G. Wang, N.-H. Liu, Q. Lin, and S-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

R. M. Vetter, A. Haibel, and G. Nimtz, Phys. Rev. E 63, 04671 (2001).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, M. Belmonte, and P. Crespi, Phys. Rev. E 65, 045602(R) (2002).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Rev. E 70, 066602 (2004).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 037601 (2001).
[CrossRef]

S. Longhi, Phys. Rev. E 72, 056614 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

H. G. Winful, Phys. Rev. Lett. 90, 023901 (2003).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

G. Nimtz, Prog. Quantum Electron. 27, 417 (2003).
[CrossRef]

Other (3)

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

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E.Wolf, ed. (Elsevier, 1997), Vol. 37, pp. 345-405.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the weakly absorbing dielectric slab.

Fig. 2
Fig. 2

(a) Group delay τ r , (b) absolute value of the reflection coefficient, and (c) relative phase ϕ r as functions of angular frequency ω with thickness d = 6 μ m and ε r = 3.0 . Solid curves, ε i = 0.01 ; dashed–dotted curves, ε i = 0.02 ; dashed curves, ε i = 0.05 . Dotted curves are for the lossless slab ( ε i = 0 ) .

Fig. 3
Fig. 3

(a) Dependence of the reflected (solid curve) and transmitted (dashed curve) group delay on slab thickness d with ε = 3.0 + 0.02 i and ω c 2 π = 129.9 THz . (b) Group delays τ r , t and (c) absolute values r , t as functions of absorptive parameter ε i at fixed thickness d = 6 μ m . Note the different time scales for τ r , t in (b). Other parameters are as in Fig. (a).

Equations (7)

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[ cos ( k d ) i sin ( k d ) q i q sin ( k d ) cos ( k d ) ] ,
r ( ω , d ) = ( i 2 ) ( 1 ε ε ) sin ( k d ) cos ( k d ) ( i 2 ) ( 1 ε + ε ) sin ( k d ) ,
t ( ω , d ) = 1 cos ( k d ) ( i 2 ) ( 1 ε + ε ) sin ( k d ) .
τ r , t = ( ϕ r , t ω ) ω = ω c ,
τ t = d c { 4 n i 2 ( ε 1 ) cos [ 2 Re ( k d ) ] 4 n r 2 ( ε + 1 ) cosh [ 2 Im ( k d ) ] + n i [ ( ε 1 ) 2 4 n i 2 ] sin [ 2 Re ( k d ) ] n r [ ( ε + 1 ) 2 + 4 n r 2 ] sinh [ 2 Im ( k d ) ] } { [ ( ε 1 ) 2 4 n i 2 ] cos [ 2 Re ( k d ) ] [ ( ε + 1 ) 2 + 4 n r 2 ] cosh [ 2 Im ( k d ) ] 4 n i ( ε 1 ) sin [ 2 Re ( k d ) ] 4 n r ( ε + 1 ) sinh [ 2 Im ( k d ) ] } .
τ r = τ t + τ 1 ,
τ 1 ϕ 2 ω = d c n i sin [ 2 Re ( k d ) ] n r sinh [ 2 Im ( k d ) ] cosh [ 2 Im ( k d ) ] cos [ 2 Re ( k d ) ] .

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