Abstract

We use our recently developed beam-deflection technique to measure the dispersion of the nondegenerate nonlinear refraction (NLR) of direct-gap semiconductors. The magnitude and sign of the NLR coefficient n2(ωa; ωb) are determined over a broad spectral range for different values of nondegeneracy. In the extremely nondegenerate case, n2(ωa; ωb) is positively enhanced near the two-photon absorption (2PA) edge and is significantly larger than its degenerate counterpart, suggesting applications for nondegenerate all-optical switching. At higher photon energies within the 2PA regime, n2(ωa; ωb) switches sign to negative over a narrow wavelength range. This strong anomalous nonlinear dispersion provides large phase modulation of a femtosecond pulse with bandwidth centered near the zero-crossing frequency. The measured nondegenerate dispersion closely follows our earlier predictions based on nonlinear Kramers-Kronig relations [Sheik-Bahae et. al, IEEE J. Quant. Electron. 30, 249 (1994)].

© 2016 Optical Society of America

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2016 (5)

H. S. Pattanaik, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Three-dimensional IR imaging with uncooled GaN photodiodes using nondegenerate two-photon absorption,” Opt. Express 24(2), 1196–1205 (2016).
[Crossref] [PubMed]

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of Nondegenerate Two-Photon Gain in GaAs,” Phys. Rev. Lett. 117(7), 073602 (2016).
[Crossref] [PubMed]

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two- and three-photon nonlinearities in semiconductors,” in Ultrafast Bandgap Photonics, Proc. SPIE 9835, 98350A (2016).
[Crossref]

T. R. Ensley, H. Hu, M. Reichert, M. R. Ferdinandus, D. Peceli, J. M. Hales, J. W. Perry, Z. Li, S.-H. Jang, A. K. Y. Jen, S. R. Marder, D. J. Hagan, and E. W. Van Stryland, “Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules,” J. Opt. Soc. Am. B 33(4), 780–796 (2016).
[Crossref]

2015 (1)

2014 (2)

2013 (1)

2011 (2)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors [Invited],” Opt. Express 19(23), 22951–22960 (2011).
[Crossref] [PubMed]

2010 (1)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

2009 (1)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]

2008 (2)

2005 (1)

2004 (3)

M. Balu, J. Hales, D. Hagan, and E. Van Stryland, “White-light continuum Z-scan technique for nonlinear materials characterization,” Opt. Express 12(16), 3820–3826 (2004).
[Crossref] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref] [PubMed]

J. Chou, Y. Han, and B. Jalali, “Time-wavelength spectroscopy for chemical sensing,” IEEE Photonics Technol. Lett. 16(4), 1140–1142 (2004).
[Crossref]

2003 (1)

A. N. Naumov and A. M. Zheltikov, “Frequency–time and time–space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump–probe techniques,” Appl. Phys. B 77(2-3), 369–376 (2003).
[Crossref]

2002 (2)

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon absorption spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38(9), 1205–1216 (2002).
[Crossref]

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P. T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

1999 (2)

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[Crossref] [PubMed]

P. V. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. 35(19), 1661–1662 (1999).
[Crossref]

1998 (2)

D. Milam, “Review and Assessment of Measured Values of the Nonlinear Refractive-Index Coefficient of Fused Silica,” Appl. Opt. 37(3), 546–550 (1998).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

1994 (4)

S. Nakamura, K. Tajima, and Y. Sugimoto, “Experimental investigation on high‐speed switching characteristics of a novel symmetric Mach–Zehnder all‐optical switch,” Appl. Phys. Lett. 65(3), 283–285 (1994).
[Crossref]

M. Sheik-Bahae, J. Wang, and E. W. V. Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30(2), 249–255 (1994).
[Crossref]

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B Condens. Matter 50(7), 4622–4630 (1994).
[Crossref] [PubMed]

C. Aversa, J. E. Sipe, M. Sheik-Bahae, and E. W. Van Stryland, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

1993 (2)

J. A. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. 97(3-4), 203–209 (1993).
[Crossref]

D. C. Hutchings, J. S. Aitchison, and C. N. Ironside, “All-optical switching based on nondegenerate phase shifts from a cascaded second-order nonlinearity,” Opt. Lett. 18(10), 793–795 (1993).
[Crossref] [PubMed]

1992 (3)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krönig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9(11), 2065–2074 (1992).
[Crossref]

1991 (2)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16(1), 42–44 (1991).
[Crossref] [PubMed]

1990 (2)

G. I. Stegeman and E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22(2), 95–122 (1990).
[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(4), 760–769 (1990).
[Crossref]

1989 (2)

V. Mizrahi, M. A. Saifi, M. J. Andrejco, K. W. DeLong, and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14(20), 1140–1142 (1989).
[Crossref] [PubMed]

K. DeLong, K. Rochford, and G. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[Crossref]

1988 (2)

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]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5(9), 1980–1988 (1988).
[Crossref]

1985 (3)

1984 (1)

1969 (1)

A. E. Kaplan, “External self-focusing of light by a nonlinear layer,” Radiophys. Quantum Electron. 12(6), 692–696 (1969).
[Crossref]

1965 (2)

I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica*,†,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965).
[Crossref]

W. L. Bond, “Measurement of the Refractive Indices of Several Crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Absil, P. P.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P. T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Aitchison, J. S.

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M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of Nondegenerate Two-Photon Gain in GaAs,” Phys. Rev. Lett. 117(7), 073602 (2016).
[Crossref] [PubMed]

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two- and three-photon nonlinearities in semiconductors,” in Ultrafast Bandgap Photonics, Proc. SPIE 9835, 98350A (2016).
[Crossref]

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases,” Opt. Express 23(17), 22224–22237 (2015).
[Crossref] [PubMed]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1(6), 436–445 (2014).
[Crossref]

M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38(18), 3518–3521 (2013).
[Crossref] [PubMed]

Ritter, K.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P. T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Rivoire, K.

Rochford, K.

K. DeLong, K. Rochford, and G. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[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]

Saifi, M. A.

Salamo, G.

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of Nondegenerate Two-Photon Gain in GaAs,” Phys. Rev. Lett. 117(7), 073602 (2016).
[Crossref] [PubMed]

Santori, C.

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[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]

Segev, M.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[Crossref] [PubMed]

Seidel, M.

Sheik-Bahae, M.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, and E. W. Van Stryland, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

M. Sheik-Bahae, J. Wang, and E. W. V. Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30(2), 249–255 (1994).
[Crossref]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krönig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[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(4), 760–769 (1990).
[Crossref]

Shensky, W. M.

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

Sibbett, W.

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Sipe, J. E.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, and E. W. Van Stryland, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

Smirl, A. L.

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of Nondegenerate Two-Photon Gain in GaAs,” Phys. Rev. Lett. 117(7), 073602 (2016).
[Crossref] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two Photon Absorption, Nonlinear Refraction, And Optical Limiting In Semiconductors,” Opt. Eng. 24(4), 244613 (1985).
[Crossref]

Soileau, M. J.

Solli, D. R.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Spence, D. E.

Stegeman, G.

K. DeLong, K. Rochford, and G. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[Crossref]

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[Crossref] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

G. I. Stegeman and E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22(2), 95–122 (1990).
[Crossref]

V. Mizrahi, M. A. Saifi, M. J. Andrejco, K. W. DeLong, and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14(20), 1140–1142 (1989).
[Crossref] [PubMed]

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]

Stryland, E. W. V.

M. Sheik-Bahae, J. Wang, and E. W. V. Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30(2), 249–255 (1994).
[Crossref]

Sugimoto, Y.

S. Nakamura, K. Tajima, and Y. Sugimoto, “Experimental investigation on high‐speed switching characteristics of a novel symmetric Mach–Zehnder all‐optical switch,” Appl. Phys. Lett. 65(3), 283–285 (1994).
[Crossref]

Tajima, K.

S. Nakamura, K. Tajima, and Y. Sugimoto, “Experimental investigation on high‐speed switching characteristics of a novel symmetric Mach–Zehnder all‐optical switch,” Appl. Phys. Lett. 65(3), 283–285 (1994).
[Crossref]

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

Tatian, B.

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]

Van, V.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P. T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Van Stryland, E.

Van Stryland, E. W.

H. S. Pattanaik, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Three-dimensional IR imaging with uncooled GaN photodiodes using nondegenerate two-photon absorption,” Opt. Express 24(2), 1196–1205 (2016).
[Crossref] [PubMed]

T. R. Ensley, H. Hu, M. Reichert, M. R. Ferdinandus, D. Peceli, J. M. Hales, J. W. Perry, Z. Li, S.-H. Jang, A. K. Y. Jen, S. R. Marder, D. J. Hagan, and E. W. Van Stryland, “Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules,” J. Opt. Soc. Am. B 33(4), 780–796 (2016).
[Crossref]

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of Nondegenerate Two-Photon Gain in GaAs,” Phys. Rev. Lett. 117(7), 073602 (2016).
[Crossref] [PubMed]

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two- and three-photon nonlinearities in semiconductors,” in Ultrafast Bandgap Photonics, Proc. SPIE 9835, 98350A (2016).
[Crossref]

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases,” Opt. Express 23(17), 22224–22237 (2015).
[Crossref] [PubMed]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1(6), 436–445 (2014).
[Crossref]

M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38(18), 3518–3521 (2013).
[Crossref] [PubMed]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors [Invited],” Opt. Express 19(23), 22951–22960 (2011).
[Crossref] [PubMed]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

M. Balu, L. A. Padilha, D. J. Hagan, E. W. Van Stryland, S. Yao, K. Belfield, S. Zheng, S. Barlow, and S. Marder, “Broadband Z-scan characterization using a high-spectral-irradiance, high-quality supercontinuum,” J. Opt. Soc. Am. B 25(2), 159–165 (2008).
[Crossref]

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon absorption spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38(9), 1205–1216 (2002).
[Crossref]

C. Aversa, J. E. Sipe, M. Sheik-Bahae, and E. W. Van Stryland, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krönig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9(11), 2065–2074 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[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(4), 760–769 (1990).
[Crossref]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5(9), 1980–1988 (1988).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two Photon Absorption, Nonlinear Refraction, And Optical Limiting In Semiconductors,” Opt. Eng. 24(4), 244613 (1985).
[Crossref]

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.

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]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two Photon Absorption, Nonlinear Refraction, And Optical Limiting In Semiconductors,” Opt. Eng. 24(4), 244613 (1985).
[Crossref]

Vilches, F.

Villeneuve, A.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

Vo, S.

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]

Wang, J.

M. Sheik-Bahae, J. Wang, and E. W. V. Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30(2), 249–255 (1994).
[Crossref]

Webster, S.

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]

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B Condens. Matter 50(7), 4622–4630 (1994).
[Crossref] [PubMed]

J. A. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. 97(3-4), 203–209 (1993).
[Crossref]

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two Photon Absorption, Nonlinear Refraction, And Optical Limiting In Semiconductors,” Opt. Eng. 24(4), 244613 (1985).
[Crossref]

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]

Wright, E. M.

G. I. Stegeman and E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22(2), 95–122 (1990).
[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]

Wu, Y. Y.

Yang, C. C.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

Yao, S.

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]

Zhao, P.

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two- and three-photon nonlinearities in semiconductors,” in Ultrafast Bandgap Photonics, Proc. SPIE 9835, 98350A (2016).
[Crossref]

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases,” Opt. Express 23(17), 22224–22237 (2015).
[Crossref] [PubMed]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1(6), 436–445 (2014).
[Crossref]

Zheltikov, A. M.

A. N. Naumov and A. M. Zheltikov, “Frequency–time and time–space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump–probe techniques,” Appl. Phys. B 77(2-3), 369–376 (2003).
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Appl. Opt. (3)

Appl. Phys. B (1)

A. N. Naumov and A. M. Zheltikov, “Frequency–time and time–space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump–probe techniques,” Appl. Phys. B 77(2-3), 369–376 (2003).
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K. DeLong, K. Rochford, and G. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[Crossref]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61(2), 147–149 (1992).
[Crossref]

S. Nakamura, K. Tajima, and Y. Sugimoto, “Experimental investigation on high‐speed switching characteristics of a novel symmetric Mach–Zehnder all‐optical switch,” Appl. Phys. Lett. 65(3), 283–285 (1994).
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IEEE J. Quantum Electron. (4)

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon absorption spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38(9), 1205–1216 (2002).
[Crossref]

M. Sheik-Bahae, J. Wang, and E. W. V. Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30(2), 249–255 (1994).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[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(4), 760–769 (1990).
[Crossref]

IEEE Photonics Technol. Lett. (2)

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P. T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14(1), 74–76 (2002).
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J. Chou, Y. Han, and B. Jalali, “Time-wavelength spectroscopy for chemical sensing,” IEEE Photonics Technol. Lett. 16(4), 1140–1142 (2004).
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in Ultrafast Bandgap Photonics, Proc. SPIE (1)

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two- and three-photon nonlinearities in semiconductors,” in Ultrafast Bandgap Photonics, Proc. SPIE 9835, 98350A (2016).
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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. (1)

J. Opt. Soc. Am. B (4)

Nat. Photonics (4)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Illustrations of nondegenerate NLA processes contributing to NLR in the sub-gap regime; (b) calculated degenerate NLR dispersion function G2 with total contribution (solid line) decomposed into 2PA, Raman and AC Stark contributions (dashed lines) [22]; (c) calculated ND-NLR (solid lines) and ND-2PA (dashed lines) coefficients of ZnO with excitation photon energy ћωb of 20% (2), 15% (3) and 10% (4) of the bandgap, as compared to the degenerate case (1).
Fig. 2
Fig. 2 (a) Illustration of the nondegenerate BD experiment [35]; (b) spatial irradiance distribution of the excitation beam (red) and overlapping geometry with the probe beam (blue) at the sample plane.
Fig. 3
Fig. 3 (a) Examples of measured BD signals (circles) from ZnO, ZnSe, CdS, and fused silica, along with fits (lines) using Eqs. (3-5) considering GVM; Measured n2(ωa; ωb) dispersion (red circles) of (b) ZnO, (c) ZnSe, and (d) CdS, compared to theoretical calculations for nondegenerate (solid lines) and degenerate (dashed lines) n2 using Eq. (2); Shaded region represents errors from the bandwidth of the excitation pulse; degenerate n2 data is from [23] (open squares) and [51] (black squares).
Fig. 4
Fig. 4 (a) Converted n2(T) assuming linear chirp at the front (black) and back (red) surface of the sample compared to the initial probe pulsewidth (blue dashed). Inset is the theoretical n2(ωa; ωb) dispersion (black solid) of ZnO (same as Fig. 3(b)) relative to the probe bandwidth (blue solid) at λa = 430 nm. (b) measured ΔE/E (black circles), compared to theoretical predictions based on chirping conditions at the front (red dashed) and back (red solid) surface of the sample along with the averaged curve (blue solid).
Fig. 5
Fig. 5 Measured FOM of ZnSe in the presence of 2PA for degenerate (black squares) and nondegenerate (red circles) NLR, as compared to theory (solid lines) [22,23]; FOM in the presence of ND-3PA are based on Isw = 10 GW/cm2 (green triangles) and Isw = 1 GW/cm2 (blue stars). The degenerate data is from [51]. The minimum requirements for AOS geometries of a Mach-Zehnder (MZ) interferometer, nonlinear directional coupler (NLDC) and Fabry-Perot (FP) filter are included for comparison.

Tables (2)

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Table 1 Measured nondegenerate NLR and NLA coefficients for semiconductors with λb = 2.3 μma

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Table 2 Measured nondegenerate FOM in 2PA and 3PA spectral region a, b

Equations (9)

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n 2 ( ω a ; ω b )= c π P 0 α NL ( ω ; ω b ) ω 2 ω a 2 d ω ,
n 2 ( ω a ; ω b )= cK 2 E p n a n b E g 4 G 2 ( ω a E g ; ω b E g ),
i( E a z + n g,a c E a t )={ 2 k 0,a n 2 ( ω a ; ω b )+i α 2 ( ω a ; ω b )+i 3 2 α 3 ( ω a ; ω b , ω b ) I b ( t ) } I b ( t ) E a ,
E a = E 0,a exp( (T T d ρ) 2 2 ( τ a / τ b ) 2 + i ρ Tρ T { 2 k a n 2 ( ω a ; ω b )+i α 2 ( ω a ; ω b )+i 3 2 α 3 ( ω a ; ω b , ω b ) I b ( T ) }L I b ( T )dT ),
E a = E 0,a exp( (T T d ρ) 2 2 ( τ a / τ b ) 2 + i π 2ρ { 2 k a n 2 ( ω a ; ω b )+i α 2 ( ω a ; ω b ) }L I b,0 [ erf( T )erf( Tρ ) ] 3 2π 8ρ α 3 L I b,0 2 [ erf( 2 T )erf( 2 (Tρ) ) ] ).
ω a ( t )= ω 0,a 2at τ G 2 ,
E a = E 0,a exp( (T T d ρ) 2 2 ( τ a / τ b ) 2 + i π 2ρ ( 2 k a n 2,0 +i α 2 )L I b,0 [ erf( T )erf( Tρ ) ] + i 2ρ 2 k a n 2,1 L I b,0 ( e ( Tρ ) 2 e T 2 ) )
FO M 2PA =2| Δϕ 2 α 2 ( ω a ; ω b ) I sw L |= 4π λ a | n 2 ( ω a ; ω b ) α 2 ( ω a ; ω b ) |
FO M 3PA =2| Δϕ 3 α 3 ( ω a ; ω b , ω b ) I sw 2 L |= 8π 3 λ a | n 2 ( ω a ; ω b ) α 3 ( ω a ; ω b , ω b ) I sw |

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