Abstract

We report the theoretical investigation of the Z-scan technique for characterizing the instantaneous Kerr nonlinearity of an optically thin multiphoton absorber. Based on the Huygens–Fresnel diffraction integral method, we study the characteristics of the closed-aperture Z-scan traces. Most importantly, we present the analytical formulae of the closed-aperture Z-scan transmittance with simultaneous Kerr effect and n-photon absorption. Besides, we demonstrate that the determination of the third-order nonlinear refractive index in multiphoton absorbers becomes timesaving yet unambiguously by the presented theory.

© 2010 Optical Society of America

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  3. A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
    [CrossRef] [PubMed]
  4. F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
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  6. N. Venkatram, R. Sathyavathi, and D. Narayana Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express 15, 12258–12263 (2007).
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  7. M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  25. J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235–9247 (2005).
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    [CrossRef]
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  29. B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008).
    [CrossRef] [PubMed]
  30. M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
    [CrossRef]
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    [CrossRef]

2010 (1)

B. Gu, W. Ji, H. Z. Yang, and H. T. Wang, “Theoretical and experimental studies of three-photon-induced excited-state absorption,” Appl. Phys. Lett. 96, 081104 (2010).
[CrossRef]

2009 (8)

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. L. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4∕DMSO,” J. Opt. Soc. Am. B 26, 754–761 (2009).
[CrossRef]

R. Y. Chen, M. D. B. Charlton, and P. G. Lagoudakis, “Chi 3 dispersion in planar tantalum pentoxide waveguides in the telecommunications window,” Opt. Lett. 34, 1135–1137 (2009).
[CrossRef] [PubMed]

G. Boudebs and K. Fedus, “Linear optical characterization of transparent thin films by the Z-scan technique,” Appl. Opt. 48, 4124–4129 (2009).
[CrossRef] [PubMed]

B. Gu, H. T. Wang, and W. Ji, “Z-scan technique for investigation of the noninstantaneous optical Kerr nonlinearity,” Opt. Lett. 34, 2769–2771 (2009).
[CrossRef] [PubMed]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

2008 (2)

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008).
[CrossRef] [PubMed]

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

2007 (4)

2005 (5)

2004 (1)

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

2003 (2)

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

2001 (1)

2000 (1)

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

1999 (2)

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of themal refraction in liquids in the transient regime,” Opt. Express 4, 315–327 (1999).
[CrossRef] [PubMed]

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 24, 5168–5180 (1999).
[CrossRef]

1997 (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1979 (1)

Badu Reddy, J. N.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

Bhat, H. L.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

Boudebs, G.

Chapple, P. B.

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

Charlton, M. D. B.

Chatterjee, U.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

Chattopadhyay, M.

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

Chen, J.

Chen, R. Y.

Ciattoni, A.

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

Cohanoschi, I.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Corrêa, D. S.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Crosignani, B.

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

De Boni, L.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Ding, J. P.

Elizabeth, S.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

Fakis, M.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

Fan, Y. X.

Fedus, K.

Fejer, M. M.

Ganeev, R. A.

R. A. Ganeev, “Nonlinear refraction and nonlinear absorption of various media,” J. Opt. A, Pure Appl. Opt. 7, 717–733 (2005).
[CrossRef]

Giannetas, V.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

Gu, B.

Hagan, D. J.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 24, 5168–5180 (1999).
[CrossRef]

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of themal refraction in liquids in the transient regime,” Opt. Express 4, 315–327 (1999).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

He, C.

He, J.

Hermann, J. A.

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

Hernandez, F. E.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Huang, X. Q.

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008).
[CrossRef] [PubMed]

Hurlbut, W. C.

Ji, W.

B. Gu, W. Ji, H. Z. Yang, and H. T. Wang, “Theoretical and experimental studies of three-photon-induced excited-state absorption,” Appl. Phys. Lett. 96, 081104 (2010).
[CrossRef]

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

B. Gu, H. T. Wang, and W. Ji, “Z-scan technique for investigation of the noninstantaneous optical Kerr nonlinearity,” Opt. Lett. 34, 2769–2771 (2009).
[CrossRef] [PubMed]

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008).
[CrossRef] [PubMed]

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235–9247 (2005).
[CrossRef] [PubMed]

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

Kikpatrick, S.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, second ed. (Marcel Dekker, 2003).
[CrossRef]

Kobayashi, T.

Kovsh, D. I.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 24, 5168–5180 (1999).
[CrossRef]

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of themal refraction in liquids in the transient regime,” Opt. Express 4, 315–327 (1999).
[CrossRef] [PubMed]

Kumbhakar, P.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

Kuo, P. S.

Lagoudakis, P. G.

Lee, Y. S.

Li, H. P.

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235–9247 (2005).
[CrossRef] [PubMed]

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

Li, Y.

Liu, M.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Liu, Z. B.

Mckay, T. J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

McLean, D. G.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, second ed. (Marcel Dekker, 2003).
[CrossRef]

Mendonça, C. R.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Mi, J.

Miller, D. A. B.

Misoguti, L.

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Mitra, A. K.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

Naik, V. B.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

Narayana Rao, D.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

N. Venkatram, R. Sathyavathi, and D. Narayana Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express 15, 12258–12263 (2007).
[CrossRef] [PubMed]

Persephonis, P.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

Polyakov, S.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

S. Polyakov, F. Yoshino, and G. Stegeman, “Interplay between self-focusing and high-order multiphoton absorption,” J. Opt. Soc. Am. B 18, 1891–1895 (2001).
[CrossRef]

Polyzos, I.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

Porto, P. D.

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

Qu, Y. L.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Sarkar, R.

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

Sathyavathi, R.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Shi, G.

Smith, S. D.

Song, Y. L.

Staromlynska, J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

Stegeman, G.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

S. Polyakov, F. Yoshino, and G. Stegeman, “Interplay between self-focusing and high-order multiphoton absorption,” J. Opt. Soc. Am. B 18, 1891–1895 (2001).
[CrossRef]

Sutherland, R. L.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, second ed. (Marcel Dekker, 2003).
[CrossRef]

Tan, S. Q.

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

Tang, S. H.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

Tian, J. G.

Tiwary, C. S.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, U. Chatterjee, and T. Kobayashi, “Three-photon-induced four-photon absorption and nonlinear refraction in ZnO quantum dots,” Opt. Lett. 34, 3644–3646 (2009).
[CrossRef] [PubMed]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

Tsigaridas, G.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

Van Stryland, E. W.

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of themal refraction in liquids in the transient regime,” Opt. Express 4, 315–327 (1999).
[CrossRef] [PubMed]

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 24, 5168–5180 (1999).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Venkatram, N.

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

N. Venkatram, R. Sathyavathi, and D. Narayana Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express 15, 12258–12263 (2007).
[CrossRef] [PubMed]

Vodopyanov, K. L.

Wang, C. H.

Wang, H. T.

Wang, J.

Wang, M.

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

Wang, Y.

Weaire, D.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wherrett, B. S.

Yan, X. Q.

Yang, H. Z.

B. Gu, W. Ji, H. Z. Yang, and H. T. Wang, “Theoretical and experimental studies of three-photon-induced excited-state absorption,” Appl. Phys. Lett. 96, 081104 (2010).
[CrossRef]

Yang, K.

Yang, S.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 24, 5168–5180 (1999).
[CrossRef]

Yariv, A.

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

Yin, M.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

Yoshino, F.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

S. Polyakov, F. Yoshino, and G. Stegeman, “Interplay between self-focusing and high-order multiphoton absorption,” J. Opt. Soc. Am. B 18, 1891–1895 (2001).
[CrossRef]

Zang, W. P.

Zhang, X.

Zhou, W. Y.

Zou, R.

Appl. Opt. (3)

Appl. Phys. B: Lasers Opt. (2)

B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B: Lasers Opt. 95, 375–381 (2009).
[CrossRef]

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B: Lasers Opt. 70, 587–591 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

B. Gu, W. Ji, H. Z. Yang, and H. T. Wang, “Theoretical and experimental studies of three-photon-induced excited-state absorption,” Appl. Phys. Lett. 96, 081104 (2010).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Appl. Phys. (2)

J. N. Badu Reddy, V. B. Naik, S. Elizabeth, H. L. Bhat, N. Venkatram, and D. Narayana Rao, “Multiphoton absorption in CsLiB6O10 with femtosecond infrared laser pulses,” J. Appl. Phys. 104, 053108 (2008).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, A. K. Mitra, and U. Chatterjee, “Multiphoton absorption and refraction in Mn2+ doped ZnS quantum dots,” J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, and T. J. Mckay, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6, 251–293 (1997).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

R. A. Ganeev, “Nonlinear refraction and nonlinear absorption of various media,” J. Opt. A, Pure Appl. Opt. 7, 717–733 (2005).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Commun. 225, 253–268 (2003).
[CrossRef]

D. S. Corrêa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonça, “Z-scan theoretical analysis for three-, four- and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. B (1)

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, “Nonlinear refraction and multiphoton absorption in polydiacetylenes from 1200to2200 nm,” Phys. Rev. B 69, 115421 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, “Observation of three-photon enhanced four-photon absorption,” Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Other (1)

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, second ed. (Marcel Dekker, 2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Open-aperture and (b) closed-aperture ( S = 0.01 ) Z-scan traces for multiphoton absorbers with the parameters presented in Table 1. The lines are the numerical simulations, while the scatters are the analytical results by Eqs. (17, 11) in (a) and (b) respectively. Insert of (b) is the asymmetric parameter A versus n.

Fig. 2
Fig. 2

Influence of the linear transmittance of the aperture S on the Z-scan traces for the concurrence of Kerr nonlinearity ( Φ 0 = 0.20 ) and 3PA ( Ψ 3 = 0.79 ) . The lines are the numerical simulations, while the scatters are obtained by Eq. (12). The inset is Δ T P V versus S for n-photon absorber with the nonlinear parameters ( Φ 0 and Ψ n ) listed in Table 1.

Fig. 3
Fig. 3

Open-aperture (squares from [31]) and closed-aperture (circles) Z-scans for 2,4,5TA in acetone with a concentration of 0.02 M at (a) I 0 = 116 GW cm 2 and (b) 160 GW cm 2 . The dashed curves are the theoretical fitting by the Z-scan theory on 3PA [23], while the solid curves and crosses are the best-fit curves by employing Eqs. (10, 11), respectively.

Tables (1)

Tables Icon

Table 1 Excitation Wavelength λ, Optical Intensity I 0 , Third-order Nonlinear Refraction Index γ, Multiphoton Absorption Coefficient α n PA , Nonlinear Refraction Phase Shift Φ 0 , and Nonlinear Absorption Phase Shift Ψ n for Different Multiphoton Absorbers in the Z-scan Simulations

Equations (17)

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E ( r , z ; t ) = E 0 ω 0 ω ( z ) exp [ r 2 ω 2 ( z ) j k r 2 2 R ( z ) ] exp ( t 2 2 τ 2 ) ,
I ( r , z ; t ) = I 0 1 + z 2 z 0 2 exp [ 2 r 2 ω 2 ( z ) ] exp ( t 2 τ 2 ) ,
d Δ ϕ ( r , z ; t ) d z = k γ I ( r , z ; t ) ,
d I ( r , z ; t ) d z = α n I n ( r , z ; t ) ,
E e ( r , z ; t ) = E ( r , z ; t ) [ 1 + ψ n n 1 ( r , z ; t ) ] 1 2 ( n 1 ) exp [ j Ω ( r , z ; t ) ] ,
Ω ( r , z ; t ) = ( n 1 ) ϕ ( r , z ; t ) ( n 2 ) ψ n n 1 ( r , z ; t ) { [ 1 + ψ n n 1 ( r , z ; t ) ] ( n 2 ) ( n 1 ) 1 } ,
ψ n ( r , z ; t ) = Ψ n 1 + z 2 z 0 2 exp [ 2 r 2 ω 2 ( z ) ] exp ( t 2 τ 2 ) ,
ϕ ( r , z ; t ) = Φ 0 1 + z 2 z 0 2 exp [ 2 r 2 ω 2 ( z ) ] exp ( t 2 τ 2 ) .
E a ( r a , z ; t ) = 2 π j λ ( d z ) exp [ j π r a 2 λ ( d z ) ] 0 + E e ( r , z ; t ) exp [ j π r 2 λ ( d z ) ] J 0 [ 2 π r r a λ ( d z ) ] r d r ,
T ( z , S ) = 4 π 1 2 I 0 ω 0 2 τ S + d t 0 R a | E a ( r a , z ; t ) | 2 r a d r a .
T ( x , S 0 ) = 1 + k γ I 0 L 2 1 2 4 x ( x 2 + 1 ) ( x 2 + 9 ) α n I 0 n 1 L n 1 2 x 2 + ( 2 n 1 ) ( x 2 + 1 ) n 1 [ x 2 + ( 2 n 1 ) 2 ] + 4 ( k γ I 0 L ) 2 3 1 2 3 x 2 5 ( x 2 + 1 ) 2 ( x 2 + 9 ) ( x 2 + 25 ) + ( α n I 0 n 1 L ) 2 2 ( 2 n 1 ) 1 2 ( x 2 + 1 ) 2 ( n 1 ) [ x 2 + 1 x 2 + ( 2 n 1 ) 2 + ( 2 n 1 ) ( x 2 + 4 n 3 ) x 2 + ( 4 n 3 ) 2 ] k γ I 0 L α n I 0 n 1 L ( n + 1 ) 1 2 2 n + 1 x ( x 2 + 1 ) n [ x 2 + ( 2 n + 1 ) 2 ] .
T ( x , S ) = 1 k γ I 0 L 2 1 2 ( x 2 + 1 ) ( 1 S ) μ S sin ξ α n I 0 n 1 L n 3 2 ( x 2 + 1 ) n 1 S [ 1 ( 1 S ) η cos ζ ] ,
μ = 2 ( x 2 + 3 ) x 2 + 9 ,
ξ = 4 x ln ( 1 S ) x 2 + 9 ,
η = n ( x 2 + 2 n 1 ) x 2 + ( 2 n 1 ) 2 ,
ζ = 2 n ( n 1 ) x x 2 + ( 2 n 1 ) 2 ln ( 1 S ) .
T OA ( x ) = 1 1 n 3 2 α n I 0 n 1 L ( x 2 + 1 ) n 1 + n 2 ( 2 n 1 ) 3 2 ( α n I 0 n 1 L ) 2 ( x 2 + 1 ) 2 ( n 1 ) .

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