Abstract

We propose a Z-scan theory for one-dimensional nonlinear photonic bandgap materials. The Z-scan characteristics for this material are analyzed. Results show that the Z-scan curves for photonic bandgap materials with nonlinear refraction are similar to those of uniform materials exhibiting both nonlinear refraction and nonlinear absorption simultaneously. Effects of nonlinear absorption on reflected and transmitted Z-scan results are also discussed.

© 2009 Optical Society of America

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2008 (1)

2007 (1)

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

2005 (1)

2004 (1)

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

2003 (1)

Q. Chen, L. Kuang, and E. H. Sargent, Appl. Phys. Lett. 83, 2115 (2003).
[CrossRef]

2001 (1)

2000 (1)

A. Haché and M. Bourgeois, Appl. Phys. Lett. 77, 4089 (2000).
[CrossRef]

1999 (1)

1997 (1)

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1989 (1)

Bennink, R. S.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

R. S. Bennink, Y.-K. Yoon, R. W. Boyd, and J. E. Sipe, Opt. Lett. 24, 1416 (1999).
[CrossRef]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Bourgeois, M.

A. Haché and M. Bourgeois, Appl. Phys. Lett. 77, 4089 (2000).
[CrossRef]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Boyd, R. W.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

R. S. Bennink, Y.-K. Yoon, R. W. Boyd, and J. E. Sipe, Opt. Lett. 24, 1416 (1999).
[CrossRef]

Chen, Q.

Q. Chen, L. Kuang, and E. H. Sargent, Appl. Phys. Lett. 83, 2115 (2003).
[CrossRef]

Chen, S.-Qi

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Dai, Q.-F.

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Gan, F. X.

Gu, D. H.

Gu, Y. Z.

Guo, Q.

Haché, A.

A. Haché and M. Bourgeois, Appl. Phys. Lett. 77, 4089 (2000).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Hu, W.

Hwang, J.

Kong, Y.-F.

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Kuang, L.

Q. Chen, L. Kuang, and E. H. Sargent, Appl. Phys. Lett. 83, 2115 (2003).
[CrossRef]

Lan, S.

Lepeshkin, N. N.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Liu, H.-Y.

Liu, S.-H.

Meng, Z.-M.

Piredda, G.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Sargent, E. H.

Q. Chen, L. Kuang, and E. H. Sargent, Appl. Phys. Lett. 83, 2115 (2003).
[CrossRef]

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Schweinsberg, A.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Sipe, J. E.

Tian, J.-G.

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Tran, P.

Trofimov, V. A.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wu, J. W.

Wu, L.-J.

Yoon, Y.-K.

Zang, W.-P.

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Zhang, W. F.

Zhou, W.-Y.

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

Q. Chen, L. Kuang, and E. H. Sargent, Appl. Phys. Lett. 83, 2115 (2003).
[CrossRef]

A. Haché and M. Bourgeois, Appl. Phys. Lett. 77, 4089 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

S.-Qi Chen, W.-P. Zang, Z.-B.Liu, W.-Y. Zhou, Y.-F. Kong, and J.-G. Tian, Opt. Commun. 274, 213 (2007).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (2)

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Linear transmission of the quarter-wave reflector. Inset, schematic of the considered configuration with 1D nonlinear PBG material. Marked are the normalized frequencies near the band edge: A = 0.8380 ω 0 , B = 0.8523 ω 0 , C = 0.8627 ω 0 , and D = 0.8683 ω 0 .

Fig. 2
Fig. 2

Z-scan curves assuming purely refractive nonlinearity. (a), (c) Open-aperture Z scan; (b), (d) closed-aperture Z scan.

Fig. 3
Fig. 3

(a) Open-aperture Z scan and (b) closed-aperture Z scan including the reflected and transmitted signal for different nonlinear absorption coefficients [solid curves, Im ( χ ( 3 ) ) = 0 ; dashed curves, Im ( χ ( 3 ) ) = 3 × 10 13 (esu)] at spectral position E = 0.872 ω 0 .

Equations (8)

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d E d z = i k H ,
d H d z = i k [ ε lin ( z ) + 12 π χ 1111 ( 3 ) | E | 2 ] E ,
E ( L ) = E t ,
H ( L ) = n 0 E t ,
E i = E i exp ( i ϕ i ) 1 2 [ E ( 0 ) + H ( 0 ) n 0 ] exp ( i ϕ t ) .
ϕ t = ϕ i arg [ E ( 0 ) + H ( 0 ) n 0 ] .
ϕ r = ϕ i arg [ E ( 0 ) + H ( 0 ) n 0 ] + arg [ E ( 0 ) H ( 0 ) n 0 ] ,
E ( z , r , t ) = E 0 ( t ) w 0 w ( z ) exp [ r 2 w 2 ( z ) i k r 2 2 R ( z ) ] exp [ i φ ( z , t ) ] ,

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