Abstract

We observe mixed two- and three-photon absorption in bulk rutile (TiO2) around 800 nm using the open aperture Z-scan technique. We fit the data with an extended model that includes multiphoton absorption, beam quality, and ellipticity. The extracted two- and three-photon absorption coefficients are below 1 mm/GW and 2 mm3/GW2, respectively. We observe negligible two-photon absorption for 813-nm light polarized along the extraordinary axis. We measure the nonlinear index of refraction and obtain two-photon nonlinear figures of merit greater than 1.1 at 774 nm and greater than 12 at 813 nm. Similarly, we obtain three-photon figures of merit that allow operational intensities up to 0.57 GW/mm2. We conclude that rutile is a promising material for all-optical switching applications around 800 nm.

©2012 Optical Society of America

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2012 (1)

J. Wang, B. Gu, X.-W. Ni, and H.-T. Wang, “Z-scan theory with simultaneous two- and three-photon absorption saturation,” Opt. Laser Technol. 44(2), 390–393 (2012).
[Crossref]

2011 (1)

T. Sarma, P. K. Panda, P. T. Anusha, and S. V. Rao, “Dinaphthoporphycenes: synthesis and nonlinear optical studies,” Org. Lett. 13(2), 188–191 (2011).
[Crossref] [PubMed]

2010 (4)

2009 (4)

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(23), 3644–3646 (2009).
[Crossref] [PubMed]

H. Long, G. Yang, A. Chen, Y. Li, and P. Lu, “Femtosecond Z-scan measurement of third-order optical nonlinearities in anatase TiO2 thin films,” Opt. Commun. 282(9), 1815–1818 (2009).
[Crossref]

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films 517(19), 5601–5604 (2009).
[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 95(2), 375–381 (2009).
[Crossref]

2008 (3)

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93(9), 091114 (2008).
[Crossref]

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[Crossref]

L. Irimpan, B. Krishnan, V. P. N. Nampoori, and P. Radhakrishnan, “Luminescence tuning and enhanced nonlinear optical properties of nanocomposites of ZnO-TiO2.,” J. Colloid Interface Sci. 324(1-2), 99–104 (2008).
[Crossref] [PubMed]

2007 (4)

2005 (3)

2004 (3)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[Crossref]

G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses,” Opt. Commun. 232(1-6), 417–423 (2004).
[Crossref]

A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
[Crossref]

2003 (3)

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, “Ultrafast optical nonlinearity in poly(methylmethacrylate)-TiO2 nanocomposites,” Appl. Phys. Lett. 82(16), 2691–2693 (2003).
[Crossref]

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[Crossref]

B. Imangholi, M. P. Hasselbeck, and M. Sheik-Bahae, “Absorption spectra of wide-gap semiconductors in their transparency region,” Opt. Commun. 227(4-6), 337–341 (2003).
[Crossref]

2000 (1)

M. Kyoung and M. Lee, “Z-scan studies on the third-order optical nonlinearity of Au nanoparticles embedded in TiO2,” Bull. Korean Chem. Soc. 21, 26–28 (2000).

1999 (1)

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
[Crossref]

1998 (2)

1997 (2)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay, and R. G. McDuff, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6(3), 251–293 (1997).
[Crossref]

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

1996 (2)

S. M. Mian, B. Taheri, and J. P. Wicksted, “Effects of beam ellipticity on Z-scan measurements,” J. Opt. Soc. Am. B 13(5), 856–863 (1996).
[Crossref]

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. Lond. A 354(1708), 745–756 (1996).
[Crossref]

1995 (2)

Y. Watanabe, M. Ohnishi, and T. Tsuchiya, “Measurement of nonlinear absorption and refraction in titanium dioxide single crystal by using a phase distortion method,” Appl. Phys. Lett. 66(25), 3431–3432 (1995).
[Crossref]

P. Sathy and A. Penzkofer, “Three-photon absorption and its limitation of third-order nonlinear optical effects in rutile,” Appl. Phys. B 61(2), 127–134 (1995).
[Crossref]

1994 (1)

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn. 67(3), 653–660 (1994).
[Crossref]

1992 (2)

K. Watanabe, K. Inoue, and F. Minami, “Resonant phenomena of hyper-Raman-scattering of optic phonons in a TiO2 crystal,” Phys. Rev. B Condens. Matter 46(4), 2024–2033 (1992).
[Crossref] [PubMed]

M. Jinno and T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28(4), 875–882 (1992).
[Crossref]

1991 (1)

M. Higuchi, T. Hosokawa, and S. Kimura, “Growth of rutile single crystals by floating zone method,” J. Cryst. Growth 112(2-3), 354–358 (1991).
[Crossref]

1990 (3)

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(4), 760–769 (1990).
[Crossref]

K. Watanabe and K. Inoue, “Two-photon resonant effect of hyper-Raman scattering in the vicinity of the direct forbidden gap in a rutile crystal,” Phys. Rev. B Condens. Matter 41(11), 7957–7960 (1990).
[Crossref] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

1989 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

1985 (1)

1978 (1)

J. Pascual, J. Camassel, and H. Mathieu, “Fine structure in the intrinsic absorption edge of TiO2,” Phys. Rev. B 18(10), 5606–5614 (1978).
[Crossref]

1976 (1)

A. Penzkofer and W. Falkenstein, “Direct determination of the intensity of picosecond light pulses by two-photon absorption,” Opt. Commun. 17(1), 1–5 (1976).
[Crossref]

1970 (1)

H. S. Waff and K. Park, “Structure in the two-photon absorption spectrum of TiO2 (Rutile),” Phys. Lett. A 32(2), 109–110 (1970).
[Crossref]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Agrawal, G. P.

Anusha, P. T.

T. Sarma, P. K. Panda, P. T. Anusha, and S. V. Rao, “Dinaphthoporphycenes: synthesis and nonlinear optical studies,” Org. Lett. 13(2), 188–191 (2011).
[Crossref] [PubMed]

Arntzen, P.-O.

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[Crossref]

Baker, N. J.

Boudebs, G.

G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses,” Opt. Commun. 232(1-6), 417–423 (2004).
[Crossref]

Bulla, D. A.

Camassel, J.

J. Pascual, J. Camassel, and H. Mathieu, “Fine structure in the intrinsic absorption edge of TiO2,” Phys. Rev. B 18(10), 5606–5614 (1978).
[Crossref]

Castañeda, L.

Chapple, P. B.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay, and R. G. McDuff, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6(3), 251–293 (1997).
[Crossref]

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Chatterjee, U.

Chattopadhyay, M.

Chaux, R.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[Crossref]

Chen, A.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films 517(19), 5601–5604 (2009).
[Crossref]

H. Long, G. Yang, A. Chen, Y. Li, and P. Lu, “Femtosecond Z-scan measurement of third-order optical nonlinearities in anatase TiO2 thin films,” Opt. Commun. 282(9), 1815–1818 (2009).
[Crossref]

Chen, J.

Cherukulappurath, S.

G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses,” Opt. Commun. 232(1-6), 417–423 (2004).
[Crossref]

Choi, D. Y.

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(2), 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(2), 440–445 (2007).
[Crossref]

Couris, S.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[Crossref]

De Boni, L.

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J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
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P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93(9), 091114 (2008).
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M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
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B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B 95(2), 375–381 (2009).
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Torres-Martínez, R.

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M. Trejo-Valdez, R. Torres-Martínez, N. Peréa-López, P. Santiago-Jacinto, and C. Torres-Torres, “Contribution of the two-photon absorption to the third order nonlinearity of au nanoparticles embedded in TiO2 films and in ethanol suspension,” J. Phys. Chem. C 114(22), 10108–10113 (2010).
[Crossref]

D. Torres-Torres, M. Trejo-Valdez, L. Castañeda, C. Torres-Torres, L. Tamayo-Rivera, R. C. Fernández-Hernández, J. A. Reyes-Esqueda, J. Muñoz-Saldaña, R. Rangel-Rojo, and A. Oliver, “Inhibition of the two-photon absorption response exhibited by a bilayer TiO2 film with embedded Au nanoparticles,” Opt. Express 18(16), 16406–16417 (2010).
[Crossref] [PubMed]

Torres-Torres, D.

Torruellas, W. E.

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. Lond. A 354(1708), 745–756 (1996).
[Crossref]

Trejo-Valdez, M.

D. Torres-Torres, M. Trejo-Valdez, L. Castañeda, C. Torres-Torres, L. Tamayo-Rivera, R. C. Fernández-Hernández, J. A. Reyes-Esqueda, J. Muñoz-Saldaña, R. Rangel-Rojo, and A. Oliver, “Inhibition of the two-photon absorption response exhibited by a bilayer TiO2 film with embedded Au nanoparticles,” Opt. Express 18(16), 16406–16417 (2010).
[Crossref] [PubMed]

M. Trejo-Valdez, R. Torres-Martínez, N. Peréa-López, P. Santiago-Jacinto, and C. Torres-Torres, “Contribution of the two-photon absorption to the third order nonlinearity of au nanoparticles embedded in TiO2 films and in ethanol suspension,” J. Phys. Chem. C 114(22), 10108–10113 (2010).
[Crossref]

Troles, J.

G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses,” Opt. Commun. 232(1-6), 417–423 (2004).
[Crossref]

Tsuchiya, T.

Y. Watanabe, M. Ohnishi, and T. Tsuchiya, “Measurement of nonlinear absorption and refraction in titanium dioxide single crystal by using a phase distortion method,” Appl. Phys. Lett. 66(25), 3431–3432 (1995).
[Crossref]

Turner, A. C.

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[Crossref]

Van Stryland, E. W.

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(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10(10), 490–492 (1985).
[Crossref] [PubMed]

Vanherzeele, H.

Vivas, M. G.

Voss, T.

Waff, H. S.

H. S. Waff and K. Park, “Structure in the two-photon absorption spectrum of TiO2 (Rutile),” Phys. Lett. A 32(2), 109–110 (1970).
[Crossref]

Wang, H.-T.

J. Wang, B. Gu, X.-W. Ni, and H.-T. Wang, “Z-scan theory with simultaneous two- and three-photon absorption saturation,” Opt. Laser Technol. 44(2), 390–393 (2012).
[Crossref]

B. Gu, J. Wang, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, “Z-scan theory for material with two- and three-photon absorption,” Opt. Express 13(23), 9230–9234 (2005).
[Crossref] [PubMed]

Wang, J.

J. Wang, B. Gu, X.-W. Ni, and H.-T. Wang, “Z-scan theory with simultaneous two- and three-photon absorption saturation,” Opt. Laser Technol. 44(2), 390–393 (2012).
[Crossref]

B. Gu, J. Wang, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, “Z-scan theory for material with two- and three-photon absorption,” Opt. Express 13(23), 9230–9234 (2005).
[Crossref] [PubMed]

A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
[Crossref]

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, “Ultrafast optical nonlinearity in poly(methylmethacrylate)-TiO2 nanocomposites,” Appl. Phys. Lett. 82(16), 2691–2693 (2003).
[Crossref]

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 95(2), 375–381 (2009).
[Crossref]

Watanabe, K.

K. Watanabe, K. Inoue, and F. Minami, “Resonant phenomena of hyper-Raman-scattering of optic phonons in a TiO2 crystal,” Phys. Rev. B Condens. Matter 46(4), 2024–2033 (1992).
[Crossref] [PubMed]

K. Watanabe and K. Inoue, “Two-photon resonant effect of hyper-Raman scattering in the vicinity of the direct forbidden gap in a rutile crystal,” Phys. Rev. B Condens. Matter 41(11), 7957–7960 (1990).
[Crossref] [PubMed]

Watanabe, Y.

Y. Watanabe, M. Ohnishi, and T. Tsuchiya, “Measurement of nonlinear absorption and refraction in titanium dioxide single crystal by using a phase distortion method,” Appl. Phys. Lett. 66(25), 3431–3432 (1995).
[Crossref]

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(4), 760–769 (1990).
[Crossref]

White, T. J.

A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
[Crossref]

White, W. R.

Wicksted, J. P.

Woodall, M. A.

Xue, J.

A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
[Crossref]

Xue, J. M.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, “Ultrafast optical nonlinearity in poly(methylmethacrylate)-TiO2 nanocomposites,” Appl. Phys. Lett. 82(16), 2691–2693 (2003).
[Crossref]

Yang, G.

H. Long, G. Yang, A. Chen, Y. Li, and P. Lu, “Femtosecond Z-scan measurement of third-order optical nonlinearities in anatase TiO2 thin films,” Opt. Commun. 282(9), 1815–1818 (2009).
[Crossref]

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films 517(19), 5601–5604 (2009).
[Crossref]

Yao, J.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[Crossref]

Yao, X.

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Yoko, T.

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn. 67(3), 653–660 (1994).
[Crossref]

Yuwono, A. H.

A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
[Crossref]

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, “Ultrafast optical nonlinearity in poly(methylmethacrylate)-TiO2 nanocomposites,” Appl. Phys. Lett. 82(16), 2691–2693 (2003).
[Crossref]

Zhang, J. X.

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Zhang, L. Y.

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Zhang, Q. Q.

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Zhao, Y.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[Crossref]

Zhou, Q. F.

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (4)

P. Sathy and A. Penzkofer, “Three-photon absorption and its limitation of third-order nonlinear optical effects in rutile,” Appl. Phys. B 61(2), 127–134 (1995).
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R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
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M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
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B. Gu, X. Q. Huang, S. Q. Tan, M. Wang, and W. Ji, “Z-scan analytical theories for characterizing multiphoton absorbers,” Appl. Phys. B 95(2), 375–381 (2009).
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Appl. Phys. Lett. (3)

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93(9), 091114 (2008).
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Y. Watanabe, M. Ohnishi, and T. Tsuchiya, “Measurement of nonlinear absorption and refraction in titanium dioxide single crystal by using a phase distortion method,” Appl. Phys. Lett. 66(25), 3431–3432 (1995).
[Crossref]

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, “Ultrafast optical nonlinearity in poly(methylmethacrylate)-TiO2 nanocomposites,” Appl. Phys. Lett. 82(16), 2691–2693 (2003).
[Crossref]

Bull. Chem. Soc. Jpn. (1)

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn. 67(3), 653–660 (1994).
[Crossref]

Bull. Korean Chem. Soc. (1)

M. Kyoung and M. Lee, “Z-scan studies on the third-order optical nonlinearity of Au nanoparticles embedded in TiO2,” Bull. Korean Chem. Soc. 21, 26–28 (2000).

Chem. Phys. Lett. (1)

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
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IEEE J. Quantum Electron. (2)

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(4), 760–769 (1990).
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M. Jinno and T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28(4), 875–882 (1992).
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J. Colloid Interface Sci. (1)

L. Irimpan, B. Krishnan, V. P. N. Nampoori, and P. Radhakrishnan, “Luminescence tuning and enhanced nonlinear optical properties of nanocomposites of ZnO-TiO2.,” J. Colloid Interface Sci. 324(1-2), 99–104 (2008).
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A. H. Yuwono, B. Liu, J. Xue, J. Wang, H. I. Elim, W. Ji, Y. Li, and T. J. White, “Controlling the crystallinity and nonlinear optical properties of transparent TiO2-PMMA nanohybrids,” J. Mater. Chem. 14(20), 2978–2987 (2004).
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J. Nonlinear Opt. Phys. Mater. (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay, and R. G. McDuff, “Single-beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater. 6(3), 251–293 (1997).
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J. Opt. Soc. Am. B (2)

J. Phys. Chem. C (1)

M. Trejo-Valdez, R. Torres-Martínez, N. Peréa-López, P. Santiago-Jacinto, and C. Torres-Torres, “Contribution of the two-photon absorption to the third order nonlinearity of au nanoparticles embedded in TiO2 films and in ethanol suspension,” J. Phys. Chem. C 114(22), 10108–10113 (2010).
[Crossref]

Mater. Lett. (1)

Q. F. Zhou, Q. Q. Zhang, J. X. Zhang, L. Y. Zhang, and X. Yao, “Preparation and optical properties of TiO2 nanocrystalline particles dispersed in SiO2 nano-composites,” Mater. Lett. 31(1-2), 39–42 (1997).
[Crossref]

Opt. Commun. (5)

H. Long, G. Yang, A. Chen, Y. Li, and P. Lu, “Femtosecond Z-scan measurement of third-order optical nonlinearities in anatase TiO2 thin films,” Opt. Commun. 282(9), 1815–1818 (2009).
[Crossref]

A. Penzkofer and W. Falkenstein, “Direct determination of the intensity of picosecond light pulses by two-photon absorption,” Opt. Commun. 17(1), 1–5 (1976).
[Crossref]

G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses,” Opt. Commun. 232(1-6), 417–423 (2004).
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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(2), 440–445 (2007).
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Opt. Express (7)

M. G. Vivas, T. Shih, T. Voss, E. Mazur, and C. R. Mendonca, “Nonlinear spectra of ZnO: reverse saturable, two- and three-photon absorption,” Opt. Express 18(9), 9628–9633 (2010).
[Crossref] [PubMed]

D. Torres-Torres, M. Trejo-Valdez, L. Castañeda, C. Torres-Torres, L. Tamayo-Rivera, R. C. Fernández-Hernández, J. A. Reyes-Esqueda, J. Muñoz-Saldaña, R. Rangel-Rojo, and A. Oliver, “Inhibition of the two-photon absorption response exhibited by a bilayer TiO2 film with embedded Au nanoparticles,” Opt. Express 18(16), 16406–16417 (2010).
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A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13(20), 7976–7981 (2005).
[Crossref] [PubMed]

B. Gu, J. Wang, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, “Z-scan theory for material with two- and three-photon absorption,” Opt. Express 13(23), 9230–9234 (2005).
[Crossref] [PubMed]

V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
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M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
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S. J. Madden, D. Y. Choi, D. A. Bulla, A. V. Rode, B. Luther-Davies, V. G. Ta’eed, M. D. Pelusi, and B. J. Eggleton, “Long, low loss etched As(2)S(3) chalcogenide waveguides for all-optical signal regeneration,” Opt. Express 15(22), 14414–14421 (2007).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

J. Wang, B. Gu, X.-W. Ni, and H.-T. Wang, “Z-scan theory with simultaneous two- and three-photon absorption saturation,” Opt. Laser Technol. 44(2), 390–393 (2012).
[Crossref]

Opt. Lett. (3)

Org. Lett. (1)

T. Sarma, P. K. Panda, P. T. Anusha, and S. V. Rao, “Dinaphthoporphycenes: synthesis and nonlinear optical studies,” Org. Lett. 13(2), 188–191 (2011).
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Philos. Trans. R. Soc. Lond. A (1)

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. Lond. A 354(1708), 745–756 (1996).
[Crossref]

Phys. Lett. A (1)

H. S. Waff and K. Park, “Structure in the two-photon absorption spectrum of TiO2 (Rutile),” Phys. Lett. A 32(2), 109–110 (1970).
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Phys. Rev. B (2)

J. Pascual, J. Camassel, and H. Mathieu, “Fine structure in the intrinsic absorption edge of TiO2,” Phys. Rev. B 18(10), 5606–5614 (1978).
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[Crossref] [PubMed]

K. Watanabe and K. Inoue, “Two-photon resonant effect of hyper-Raman scattering in the vicinity of the direct forbidden gap in a rutile crystal,” Phys. Rev. B Condens. Matter 41(11), 7957–7960 (1990).
[Crossref] [PubMed]

K. Watanabe, K. Inoue, and F. Minami, “Resonant phenomena of hyper-Raman-scattering of optic phonons in a TiO2 crystal,” Phys. Rev. B Condens. Matter 46(4), 2024–2033 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

Thin Solid Films (2)

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[Crossref]

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films 517(19), 5601–5604 (2009).
[Crossref]

Other (3)

E. W. V. Stryland and M. Sheik-Bahae, “Z-Scan measurements of optical nonlinearities,” in Characterization techniques and tabulations for organic nonlinear optical materials, M. G. Kuzyk and C. W. Dirk, eds. (Marcel Dekker, 1998).

C. C. Evans, J. D. B. Bradley, F. Parsy, K. C. Phillips, R. Senaratne, E. A. Martí-Panameño, and E. Mazur, “Thermally managed Z-scan measurements of titanium dioxide thin films,” presented at Photonics West, San Francisco, CA, USA, 27 Jan. 2011.

I. O. f. Standardization, ISO 11146–1:2005 Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios (Geneva, Switzerland, 2005).

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Figures (4)

Fig. 1
Fig. 1 The left plot shows open-aperture Z-scan measurements of bulk rutile (open circles) using a 50-fs pulse with λ0 = 800 nm for the extraordinary (E | | c) polarization (peak on-axis irradiance of 0.95 GW/mm2). Theoretical fits for pure two-photon [23], three-photon [31], and our mixed multi-photon absorption models are shown in dashed, dotted, and solid lines, respectively. The right plot shows the change in transmittance (ΔT = 1 – T) at the focus as a function of peak on-axis irradiance for the same sample, wavelength, and pulse duration. Data is shown in open circles with error bars. Theoretical fits for pure two-photon, three-photon and mixed two- and three-photon absorption are shown in dashed, dotted, and solid lines, respectively.

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Fig. 4
Fig. 4 Open-aperture Z-scan measurements of bulk rutile using a 50-fs pulse with λ0 = 800 nm for ordinary (E ⊥ c) and extraordinary (E | | c) polarizations (left and right, respectively). Solid lines are a fit across all intensities shown. Fit parameters are α2, α3, average z0 and the astigmatism.

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Fig. 2
Fig. 2 Open-aperture Z-scan measurements of bulk rutile using a 290-fs pulse with λ0 = 774 nm for ordinary (E ⊥ c) and extraordinary (E | | c) polarizations (left and right, respectively). Solid lines are a fit across all irradiances shown. Fit parameters are α2, α3, average z0 and the astigmatism.

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Fig. 3
Fig. 3 Open-aperture Z-scan measurements of bulk rutile using a 174-fs pulse with λ0 = 813 nm for ordinary (E ⊥ c) and extraordinary (E | | c) polarizations (left and right, respectively). Solid lines are a fit across all intensities shown. Fit parameters are α2, α3, average z0 and the astigmatism.

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Tables (2)

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Table 1 Measured Laser Parameters*

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Table 2 Nonlinear Absorption Coefficients, 2PA Figures of Merit and Maximum Intensities from 3PA*

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Equations (4)

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

I in [ x,y,z,P( t ) ]= 2P( t ) π​​​​​  w x ( z )  w y ( z ) exp[ − 2 x 2 w x 2 ( z ) − 2 y 2 w y 2 ( z ) ].
w x ( z )= w x0 2 + ( M x 2 λ 0 π w x0 ) 2 ( z− z x0 ) 2 .
dI dz' =−α( I )I.
T( z )= ∫ P( t ) T[ z,P( t )  ]dt ∫ P( t )  dt = E out ( z ) E in .

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