Abstract

Two-photon absorption (2PA) spectra with pairs of extremely nondegenerate photons are measured in several direct-gap semiconductors (GaAs, CdTe, ZnO, ZnS and ZnSe) using picosecond or femtosecond pulses. In ZnSe, using photons with a ratio of energies of ~12, we obtain a 270-fold enhancement of 2PA when comparing to the corresponding degenerate 2PA coefficient at the average photon energy (ηω1 + ηω2)/2. This corresponds to a pump photon energy of 8% of the bandgap. 2PA coefficients as large as 1 cm/MW are measured. Thus, by using two widely different wavelengths we are able to access the large 2PA observed previously only in narrow gap semiconductors. We also calculate the corresponding enhancement of nonlinear refraction, consisting of two-photon, AC-Stark and Raman contributions. The net effect is a smaller enhancement, but exhibits very large dispersion within the 2PA regime.

© 2011 OSA

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    [CrossRef]
  3. 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).
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    [CrossRef] [PubMed]
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  23. R. A. Negres, J. M. Hales, 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]
  24. 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]
  25. 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]
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    [CrossRef]
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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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

2010 (1)

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (1)

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51(10), 1376–1380 (2007).
[CrossRef]

2006 (1)

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

2004 (1)

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

2002 (1)

R. A. Negres, J. M. Hales, 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]

2000 (1)

A. E. Rakhshani, “Study of Urbach tail, bandgap energy and grain-boundary characteristics in CdS by modulated photocurrent spectroscopy,” J. Phys. Condens. Matter 12(19), 4391–4400 (2000).
[CrossRef]

1994 (1)

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of 2-photon absorption in zincblende semiconductors,” Phys. Rev. B 49(4), 2418–2426 (1994).
[CrossRef]

1993 (1)

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]

1992 (4)

1991 (1)

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]

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]

1985 (1)

1984 (1)

1983 (1)

H. S. Brandi and C. B. Dearaujo, “Multiphoton absorption-coefficients in solids – a universal curve,” J. Phys. C Solid State Phys. 16(30), 5929–5936 (1983).
[CrossRef]

1977 (1)

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16(6), 2466–2473 (1977).
[CrossRef]

1965 (1)

L. V. Keldysh, “Ionization in field of a strong electromagnetic wave,” Sov. Phys. JETP 20(5), 1307 (1965).

1953 (1)

F. Urbach, “The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids,” Phys. Rev. 92(5), 1324 (1953).
[CrossRef]

Balu, M.

Barlow, S.

Belfield, K.

Belfield, K. D.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Bhaskar, A.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Bolger, J. A.

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]

Brajuskovic, V.

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

Brandi, H. S.

H. S. Brandi and C. B. Dearaujo, “Multiphoton absorption-coefficients in solids – a universal curve,” J. Phys. C Solid State Phys. 16(30), 5929–5936 (1983).
[CrossRef]

Bredas, J. L.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Cirloganu, C. M.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33(22), 2626–2628 (2008).
[CrossRef] [PubMed]

Dearaujo, C. B.

H. S. Brandi and C. B. Dearaujo, “Multiphoton absorption-coefficients in solids – a universal curve,” J. Phys. C Solid State Phys. 16(30), 5929–5936 (1983).
[CrossRef]

DeSalvo, R.

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]

Fainman, Y.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51(10), 1376–1380 (2007).
[CrossRef]

Fishman, D. A.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

Ginzburg, P.

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2(4), 238–241 (2008).
[CrossRef]

Gonzalez, L. P.

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

Goodson, T.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Guha, S.

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

Guyot-Sionnest, P.

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

Hagan, D.

Hagan, D. J.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[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]

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33(22), 2626–2628 (2008).
[CrossRef] [PubMed]

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

R. A. Negres, J. M. Hales, 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]

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]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig 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]

Hales, J. M.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

R. A. Negres, J. M. Hales, 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]

Hayat, A.

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2(4), 238–241 (2008).
[CrossRef]

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of 2-photon absorption in zincblende semiconductors,” Phys. Rev. B 49(4), 2418–2426 (1994).
[CrossRef]

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, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig Relations in Nonlinear Optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[CrossRef]

D. C. Hutchings and E. W. V. 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]

Ikeda, K.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51(10), 1376–1380 (2007).
[CrossRef]

Ironside, C. N.

C. N. Ironside, “2-Photon Gain Semiconductor Amplifier,” IEEE J. Quantum Electron. 28(4), 842–847 (1992).
[CrossRef]

Jones, H. D.

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16(6), 2466–2473 (1977).
[CrossRef]

Kar, A. K.

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]

Keldysh, L. V.

L. V. Keldysh, “Ionization in field of a strong electromagnetic wave,” Sov. Phys. JETP 20(5), 1307 (1965).

Keuleyan, S.

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

Krishnamurthy, S.

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

Kwon, O.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Lhuillier, E.

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

Lu, Z.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Marder, S.

Monroe, M.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

Morales, A. R.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Negres, R. A.

R. A. Negres, J. M. Hales, 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]

Olszak, P. D.

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33(22), 2626–2628 (2008).
[CrossRef] [PubMed]

Orenstein, M.

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2(4), 238–241 (2008).
[CrossRef]

Pacher, P.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Padilha, L.

Padilha, L. A.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33(22), 2626–2628 (2008).
[CrossRef] [PubMed]

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]

Rakhshani, A. E.

A. E. Rakhshani, “Study of Urbach tail, bandgap energy and grain-boundary characteristics in CdS by modulated photocurrent spectroscopy,” J. Phys. Condens. Matter 12(19), 4391–4400 (2000).
[CrossRef]

Ramakrishna, G.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Reiss, H. R.

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16(6), 2466–2473 (1977).
[CrossRef]

Said, A. A.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[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]

Schafer, K. J.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

Sheik-Bahae, M.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig Relations in Nonlinear Optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (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]

Soileau, M. J.

Stryland, E. W.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig Relations in Nonlinear Optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[CrossRef]

Stryland, E. W. V.

Twieg, R.

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Urbach, F.

F. Urbach, “The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids,” Phys. Rev. 92(5), 1324 (1953).
[CrossRef]

Van Stryland, E.

M. Balu, L. Padilha, D. Hagan, E. 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: erratum,” J. Opt. Soc. Am. B 26(8), 1663–1663 (2009).
[CrossRef]

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

Van Stryland, E. W.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[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]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

R. A. Negres, J. M. Hales, 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]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (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, 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.

Wang, J.

Webster, S.

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33(22), 2626–2628 (2008).
[CrossRef] [PubMed]

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[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]

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of 2-photon absorption in zincblende semiconductors,” Phys. Rev. B 49(4), 2418–2426 (1994).
[CrossRef]

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]

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
[CrossRef]

Woodall, M. A.

Yao, S.

Young, J.

Zheng, S.

Zojer, E.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (4)

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]

R. A. Negres, J. M. Hales, 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, 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]

C. N. Ironside, “2-Photon Gain Semiconductor Amplifier,” IEEE J. Quantum Electron. 28(4), 842–847 (1992).
[CrossRef]

J. Am. Chem. Soc. (1)

A. Bhaskar, G. Ramakrishna, Z. Lu, R. Twieg, J. M. Hales, D. J. Hagan, E. Van Stryland, and T. Goodson, “Investigation of two-photon absorption properties in branched alkene and alkyne chromophores,” J. Am. Chem. Soc. 128(36), 11840–11849 (2006).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121(7), 3152–3160 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (5)

J. Phys. C Solid State Phys. (1)

H. S. Brandi and C. B. Dearaujo, “Multiphoton absorption-coefficients in solids – a universal curve,” J. Phys. C Solid State Phys. 16(30), 5929–5936 (1983).
[CrossRef]

J. Phys. Condens. Matter (1)

A. E. Rakhshani, “Study of Urbach tail, bandgap energy and grain-boundary characteristics in CdS by modulated photocurrent spectroscopy,” J. Phys. Condens. Matter 12(19), 4391–4400 (2000).
[CrossRef]

Nat. Photonics (3)

S. Keuleyan, E. Lhuillier, V. Brajuskovic, and P. Guyot-Sionnest, “Mid-infrared HgTe colloidal quantum dot photodetectors,” Nat. Photonics 5(8), 489–493 (2011).
[CrossRef]

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2(4), 238–241 (2008).
[CrossRef]

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-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig Relations in Nonlinear Optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[CrossRef]

Phys. Rev. (1)

F. Urbach, “The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids,” Phys. Rev. 92(5), 1324 (1953).
[CrossRef]

Phys. Rev. B (3)

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16(6), 2466–2473 (1977).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of 2-photon absorption in zincblende semiconductors,” Phys. Rev. B 49(4), 2418–2426 (1994).
[CrossRef]

P. D. Olszak, C. M. Cirloganu, S. Webster, L. A. Padilha, S. Guha, L. P. Gonzalez, S. Krishnamurthy, D. J. Hagan, and E. W. Van Stryland, “Spectral and temperature dependence of two-photon and free-carrier absorption in InSb,” Phys. Rev. B 82(23), 235207 (2010).
[CrossRef]

Solid-State Electron. (1)

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51(10), 1376–1380 (2007).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in field of a strong electromagnetic wave,” Sov. Phys. JETP 20(5), 1307 (1965).

Other (1)

F. T. Arecchi, E. O. Schulz-Dubois, M. L. Stitch, W. B. Colson, C. Pellegrini, and A. Renieri, Laser handbook. 1972, Amsterdam, New York: North-Holland Pub. Co.; American Elsevier Pub. Co. v. <1–6 >.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic representation of transitions involved in a 2PA process for photons having various energy ratios, with ND-2PA and END-2PA characterized by a small detuning energy as compared to the bandgap. (b) The equivalent representation within the perturbative framework showing the possible transitions for two-band structure consisting of direct (“allowed”) and self (“forbidden”) transitions.

Fig. 2
Fig. 2

Typical experimental pump-probe data in CdTe (a) using picoseconds pulses and ZnO (b) using femtosecond pulses along with theoretical fits (solid lines).

Fig. 3
Fig. 3

Non-degenerate 2PA spectra of CdTe and GaAs measured with picosecond pulses (a) and of ZnS measured with femtosecond pulses (b). The theoretically calculated non-degenerate spectra are shown with straight lines, while the dashed lines denote the respective degenerate spectra, along with measured degenerate data. The non-degenerate data in GaAs was taken from [7].

Fig. 4
Fig. 4

Non-degenerate 2PA spectra of ZnSe (a) and ZnO (b) measured with femtosecond pulses. The theoretically calculated non-degenerate spectra are shown with straight lines, while the dashed lines denote the respective degenerate spectra, along with measured degenerate data. The 2PA data in (a) was taken from [7] and the degenerate data in (b) was taken from [24].

Fig. 5
Fig. 5

Calculated nondegenerate induced refraction index (solid lines) and nondegenerate 2PA (dotted lines) of GaAs for pump energies equal to (1) 20% (4.32 μm), (2) 15% (5.81 μm) and (3) 10% (8.84 μm) of the bandgap.

Equations (5)

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

W 2 ND = 2π vc | i [ c| H 2 |i i| H 1 |v E iv (k) ω 1 + c| H 1 |i i| H 2 |v E iv (k) ω 2 ] | 2 δ[ E cv (k) ω 1 ω 2 ] 
W 2 ND ~ | M vc 2 M vv 1 ω 1 + M vc 1 M vv 2 ω 2 + M cc 2 M vc 1 ω 2 + M cc 1 M vc 2 ω 1 | 2 ,
α 2 ( ω 1 ; ω 2 )=K E p n 1 n 2 E g 3 F 2 ( ω 1 E g ; ω 2 E g ), where   F 2 ( x 1 ; x 2 )= ( x 1 + x 2 1 ) 3/2 2 7 x 1 x 2 2 ( 1 x 1 + 1 x 2 ) 2 ,
d I p ( ω p ) dz =2 α 2 ( ω p ; ω e ) I e ( ω e ) I p ( ω p ).
W 2 D | M vc (2) M vv (2) ω 2 + M cc (2) M vc (2) ω 2 | 2 .

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