Abstract

The third order nonlinear optical property of Bi2Se3, a kind of topological insulator (TI), has been investigated under femto-second laser excitation. The open and closed aperture Z-scan measurements were used to unambiguously distinguish the real and imaginary part of the third order optical nonlinearity of the TI. When excited at 800 nm, the TI exhibits saturable absorption with a saturation intensity of 10.12 GW/cm2 and a modulation depth of 61.2%, and a giant nonlinear refractive index of 10−14 m2/W, almost six orders of magnitude larger than that of bulk dielectrics. This finding suggests that the TI: Bi2Se3 is indeed a promising nonlinear optical material and thus can find potential applications from passive laser mode locker to optical Kerr effect based photonic devices.

© 2013 OSA

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2012 (8)

J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett.37(11), 2166–2168 (2012).
[CrossRef] [PubMed]

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express20(21), 23201–23214 (2012).
[CrossRef] [PubMed]

H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett.37(11), 1856–1858 (2012).
[CrossRef] [PubMed]

S. Yamashita, “A tutorial on nonlinear photonic applications of carbon nanotube and graphene,” J. Lightwave Technol.30(4), 427–447 (2012).
[CrossRef]

C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with Topological Insulator: Bi2Se3 as a mode locker,” Opt. Express20(25), 27888–27895 (2012).
[CrossRef]

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

2011 (4)

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

J. Liu, S. Wu, Q. H. Yang, and P. Wang, “Stable nanosecond pulse generation from a graphene-based passively Q-switched Yb-doped fiber laser,” Opt. Lett.36(20), 4008–4010 (2011).
[CrossRef] [PubMed]

J. L. Xu, X. L. Li, Y. Z. Wu, X. P. Hao, J. L. He, and K. J. Yang, “Graphene saturable absorber mirror for ultra-fast-pulse solid-state laser,” Opt. Lett.36(10), 1948–1950 (2011).
[CrossRef] [PubMed]

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83(4), 1057–1110 (2011).
[CrossRef]

2010 (6)

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys.82(4), 3045–3067 (2010).
[CrossRef]

Z. Luo, M. Zhou, J. Weng, G. Huang, H. Xu, C. Ye, and Z. Cai, “Graphene-based passively Q-switched dual-wavelength erbium-doped fiber laser,” Opt. Lett.35(21), 3709–3711 (2010).
[CrossRef] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010).
[CrossRef]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express18(22), 23054–23061 (2010).
[CrossRef] [PubMed]

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[CrossRef]

2009 (5)

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]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express17(20), 17630–17635 (2009).
[CrossRef] [PubMed]

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

2006 (1)

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

2004 (2)

R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B21(3), 640–644 (2004).
[CrossRef]

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. B78(3–4), 433–438 (2004).
[CrossRef]

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[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(4), 760–769 (1990).
[CrossRef]

1988 (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

Abramski, K. M.

Analytis, J. G.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

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. B78(3–4), 433–438 (2004).
[CrossRef]

Bae, M. K.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[CrossRef]

Bao, Q.

Bao, Q. L.

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express17(20), 17630–17635 (2009).
[CrossRef] [PubMed]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010).
[CrossRef]

Boschetto, D.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Cai, Z.

Chatterjee, U.

Chattopadhyay, M.

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]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Chen, Y.

Chen, Y. L.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Chen, Y. P.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Dai, X.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

del Coso, R.

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Dresselhaus, M. S.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Fang, Z.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010).
[CrossRef]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

Fisher, I. R.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Fuse, K.

Ganeev, R. A.

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. B78(3–4), 433–438 (2004).
[CrossRef]

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Godbout, N.

Hagan, D. J.

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]

Hajlaoui, M.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Han, W. S.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[CrossRef]

Hao, X. P.

Hasan, M. Z.

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys.82(4), 3045–3067 (2010).
[CrossRef]

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010).
[CrossRef]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

He, J. L.

Hens, Z.

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

Huang, G.

Ishizawa, N.

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. B78(3–4), 433–438 (2004).
[CrossRef]

Jang, S. Y.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[CrossRef]

Jiang, Z.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Kane, C. L.

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys.82(4), 3045–3067 (2010).
[CrossRef]

Kian Ping, L.

Kirchmann, P. S.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Kobayashi, T.

Kockaert, P.

H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett.37(11), 1856–1858 (2012).
[CrossRef] [PubMed]

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

Kumbhakar, P.

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]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Kuroda, H.

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. B78(3–4), 433–438 (2004).
[CrossRef]

Lantz, G.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Li, X. L.

Li, Y.

Liu, C.-X.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

Liu, J.

Loh, K. P.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express17(20), 17630–17635 (2009).
[CrossRef] [PubMed]

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Loicq, J.

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

Lu, S.

Luo, Z.

Marsi, M.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Martinez, A.

Massar, S.

Mauchain, J.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Miotkowski, I.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Mitra, A. K.

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]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Moisan, N.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Moreels, I.

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

Ni, Z.

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Papalazarou, E.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Peng, B.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Peng, Z. P.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Perfetti, L.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Qi, X. L.

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83(4), 1057–1110 (2011).
[CrossRef]

Qi, X.-L.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Ryasnyansky, A. I.

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. B78(3–4), 433–438 (2004).
[CrossRef]

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(4), 760–769 (1990).
[CrossRef]

Sakakibara, S.

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. B78(3–4), 433–438 (2004).
[CrossRef]

Sarkar, R.

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

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(4), 760–769 (1990).
[CrossRef]

Shen, Z. X.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Sobon, G.

Sobota, J. A.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Solis, J.

Song, Y. W.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[CrossRef]

Soni, A.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Sotor, J.

Stegeman, G. I.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

Sun, Z.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010).
[CrossRef]

Suzuki, 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. B78(3–4), 433–438 (2004).
[CrossRef]

Taleb-Ibrahimi, A.

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

Tang, D.

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with Topological Insulator: Bi2Se3 as a mode locker,” Opt. Express20(25), 27888–27895 (2012).
[CrossRef]

Tang, D. Y.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express17(20), 17630–17635 (2009).
[CrossRef] [PubMed]

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Tiwary, C. S.

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

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. B78(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]

Van Thourhout, D.

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

Virally, S.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Wang, J. B.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Wang, P.

Wang, Y.

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Wang, Z.

C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with Topological Insulator: Bi2Se3 as a mode locker,” Opt. Express20(25), 27888–27895 (2012).
[CrossRef]

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

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]

Wen, S.

Weng, J.

Wright, E. M.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

Wu, S.

Wu, Y. Z.

Xiong, Q. H.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Xiong, Y.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Xu, B.

Xu, H.

Xu, J. L.

Yamashita, S.

Yan, Y.

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Yang, K. J.

Yang, Q. H.

Yang, S.

J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z. X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3.,” Phys. Rev. Lett.108(11), 117403 (2012).
[CrossRef] [PubMed]

Ye, C.

Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

Zhang, H.

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express20(21), 23201–23214 (2012).
[CrossRef] [PubMed]

H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett.37(11), 1856–1858 (2012).
[CrossRef] [PubMed]

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with Topological Insulator: Bi2Se3 as a mode locker,” Opt. Express20(25), 27888–27895 (2012).
[CrossRef]

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express17(20), 17630–17635 (2009).
[CrossRef] [PubMed]

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

Zhang, J.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Zhang, S. C.

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83(4), 1057–1110 (2011).
[CrossRef]

Zhang, S.-C.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys.5(6), 438–442 (2009).
[CrossRef]

Zhao, C.

Zhao, L. M.

Zhao, Y. Y.

J. Zhang, Z. P. Peng, A. Soni, Y. Y. Zhao, Y. Xiong, B. Peng, J. B. Wang, M. S. Dresselhaus, and Q. H. Xiong, “Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets,” Nano Lett.11(6), 2407–2414 (2011).
[CrossRef] [PubMed]

Zheng, Z.

Zhou, M.

Zou, Y.

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano4(2), 803–810 (2010).
[CrossRef] [PubMed]

Adv. Funct. Mater. (1)

Q. L. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009).
[CrossRef]

Appl. Phys. B (1)

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. B78(3–4), 433–438 (2004).
[CrossRef]

Appl. Phys. Lett. (5)

I. Moreels, Z. Hens, P. Kockaert, J. Loicq, and D. Van Thourhout, “Spectroscopy of the nonlinear refractive index of colloidal PbSe nanocrystals,” Appl. Phys. Lett.89(19), 193106 (2006).
[CrossRef]

C. Zhao and H. Zhang, X. QiY. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett.101(21), 211106 (2012).

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. K. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn 2+ doped ZnS quantum dots,” Appl. Phys. Lett.95(16), 163115 (2009).
[CrossRef]

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010).
[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(4), 760–769 (1990).
[CrossRef]

J. Lightwave Technol. (2)

S. Yamashita, “A tutorial on nonlinear photonic applications of carbon nanotube and graphene,” J. Lightwave Technol.30(4), 427–447 (2012).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol.6(6), 953–970 (1988).
[CrossRef]

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

Nano Lett. (2)

M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz, N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski, Y. P. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi, “Ultrafast surface carrier dynamics in the topological insulator Bi2Te3,” Nano Lett.12(7), 3532–3536 (2012).
[CrossRef] [PubMed]

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Nat. Phys. (1)

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Phys. Rev. Lett. (1)

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Other (2)

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Figures (8)

Fig. 1
Fig. 1

Characterization of TI sample on quartz plate for Z-scan measurement. (a) Raman spectra of the TI sample. (b) The AFM image of the TI sample, the height between the black line and the others indicates approximately 50 nm for this batch of synthesis.

Fig. 2
Fig. 2

Schematic diagram of the Z-scan experimental setup.

Fig. 3
Fig. 3

Z-scan traces for Bi2Se3 sample at an average power of 40 μW, corresponding to a peak power at focus of 10.4 GW/cm2. (a) Near field (open aperture). (b) Far field (closed aperture). Upon dividing by the near field curve one obtains the data of panel (c) which exhibits the typical shape of a Z-scan curve with positive nonlinear phase shift having an on-axis value of ΔΦ = 1.1 rad.

Fig. 4
Fig. 4

(a) Relation between normalized transmittance and input peak intensity for Bi2Se3. (b) Dependence of ΔΦ (right axis) and n2 (left axis) on peak intensity for Bi2Se3.

Fig. 5
Fig. 5

SEM images of as-grown Bi2Se3 nanoplatelets.

Fig. 6
Fig. 6

(a) The optical spectrum of 800 nm laser. (b) Beam intensity profile near the focus point. (c) Relation between the beam waist and the relative position with respect to the focus point. (d) Relation between laser beam intensity and the relative position of the focus point for an optical input power of about 40 μW.

Fig. 7
Fig. 7

Z-scan traces for 1 mm thickness CS2 sample at a peak intensity of 76 GW/cm2. (a) Near field (open aperture). (b) Far field (closed aperture). Upon dividing by the near field curve one obtains the data of panel (c) which exhibits the typical shape of a Z-scan curve with positive nonlinear phase shift having an on-axis value of ΔΦ = 1.35 rad. (d) The changes of ΔΦ and n2 with increasing peak intensity at the focus.

Fig. 8
Fig. 8

Z-scan traces for Bi2Se3 sample and pure quartz plate at an average power of 40 μW, corresponding to a peak power at focus of 10.4 GW/cm2. (a) Near field (open aperture). (b) Far field (closed aperture measurement/open aperture measurement).

Tables (1)

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Table 1 Nonlinear Refractive Index n2 of Different Materials

Equations (2)

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T(x)=1+ 4xΔΦ (1+ x 2 )(9+ x 2 ) + 4(3 x 2 5)Δ Φ 2 (1+ x 2 ) 2 (9+ x 2 )(25+ x 2 ) + 32(3 x 2 11)xΔ Φ 3 (1+ x 2 ) 3 (9+ x 2 )(25+ x 2 )(49+ x 2 )
T=1( α s 1+I/ I sat + α ns )

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