Abstract

This paper presents three-photon absorption (3PA) measurement results for nine direct-gap semiconductors, including full 3PA spectra for ZnSe, ZnS, and GaAs. These results, along with our theory of 3PA using an eight-band Kane model (four bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the eight-band model exhibits quantum interference between the various possible pathways that is not observed in previous two-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, ${E_g}$, scaling using -band tunneling and perturbation theories that show agreement with the predicted $E_g^{- 7}$ dependence; however, for those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both two-band theories. On the other hand, our eight-band model shows excellent agreement with the spectral data. We then use our eight-band theory to predict the 3PA spectra for 15 different semiconductors in their zinc-blende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. M. Chattopadhyay, P. Kumbhakar, R. Sarkar, and A. Mitra, “Enhanced three-photon absorption and nonlinear refraction in ZnS and Mn2+ doped ZnS quantum dots,” Appl. Phys. Lett. 95, 163115 (2009).
    [Crossref]
  2. G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
    [Crossref]
  3. G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
    [Crossref]
  4. G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
    [Crossref]
  5. J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235–9247 (2005).
    [Crossref]
  6. W. C. Hurlbut, Y.-S. Lee, K. Vodopyanov, P. Kuo, and M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. 32, 668–670 (2007).
    [Crossref]
  7. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
    [Crossref]
  8. P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
    [Crossref]
  9. G. Polónyi, B. Monoszlai, G. Gäumann, E. J. Rohwer, G. Andriukaitis, T. Balciunas, A. Pugzlys, A. Baltuska, T. Feurer, and J. Hebling, “High-energy terahertz pulses from semiconductors pumped beyond the three-photon absorption edge,” Opt. Express 24, 23872–23882 (2016).
    [Crossref]
  10. M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
    [Crossref]
  11. 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, 073602 (2016).
    [Crossref]
  12. M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two-and three-photon nonlinearities in semiconductors,” Proc. SPIE 9835, 98350A (2016).
    [Crossref]
  13. J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
    [Crossref]
  14. A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
    [Crossref]
  15. Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
    [Crossref]
  16. S. S. Mitra, N. Judell, A. Vaidyanathan, and A. H. Guenther, “Three-photon absorption in direct-gap crystals,” Opt. Lett. 7, 307–309 (1982).
    [Crossref]
  17. Z. Wang, H. Liu, N. Huang, Q. Sun, J. Wen, and X. Li, “Influence of three-photon absorption on mid-infrared cross-phase modulation in silicon-on-sapphire waveguides,” Opt. Express 21, 1840–1848 (2013).
    [Crossref]
  18. C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.
  19. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
    [Crossref]
  20. B. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67–72 (1984).
    [Crossref]
  21. E. W. Van Stryland, M. Woodall, H. Vanherzeele, and M. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
    [Crossref]
  22. J. H. Yee, “Three-photon absorption in semiconductors,” Phys. Rev. B 5, 449 (1972).
    [Crossref]
  23. A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
    [Crossref]
  24. A. Vaidyanathan, A. Guenther, and S. Mitra, “Two-photon absorption in direct-gap crystals—an addendum,” in Laser Induced Damage In Optical Materials: 1980 (ASTM International, 1981).
  25. J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.
  26. D. Hutchings and B. Wherrett, “Linear/circular dichroism of two-photon absorption in zinc-blende semiconductors,” Opt. Mater. 3, 53–60 (1994).
    [Crossref]
  27. D. Hutchings and B. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418 (1994).
    [Crossref]
  28. L. V. Keldysh, “Zh. É ksp. Teor. Fiz. 47, 1945 1964 Sov. Phys,” JETP 20, 1307 (1965).
  29. C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment,” Opt. Lett. 33, 2626–2628 (2008).
    [Crossref]
  30. C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment: erratum,” Opt. Lett. 45, 1025–1026 (2020).
    [Crossref]
  31. H. Brandi and C. De Araujos, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929 (1983).
    [Crossref]
  32. E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
    [Crossref]
  33. M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
    [Crossref]
  34. J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
    [Crossref]
  35. G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
    [Crossref]
  36. M. Sheik-Bahaei, P. Mukherjee, and H.-S. Kwok, “Two-photon and three-photon absorption coefficients of InSb,” J. Opt. Soc. Am. B 3, 379–385 (1986).
    [Crossref]
  37. J. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515 (1976).
    [Crossref]
  38. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [Crossref]
  39. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n 2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [Crossref]
  40. S. Shabahang, G. Tao, M. P. Marquez, H. Hu, T. R. Ensley, P. J. Delfyett, and A. F. Abouraddy, “Nonlinear characterization of robust multimaterial chalcogenide nanotapers for infrared supercontinuum generation,” J. Opt. Soc. Am. B 31, 450–457 (2014).
    [Crossref]
  41. M. A. Woodall, Nonlinear Absorption Techniques and Measurements in Semiconductors (1985).
  42. S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption: erratum,” Opt. Lett. 11, 59 (1986).
    [Crossref]
  43. S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285–287 (1985).
    [Crossref]
  44. 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, 235207 (2010).
    [Crossref]
  45. S. Z. Karazhanov and L. L. Y. Voon, “Ab initio studies of the band parameters of III–V and II–VI zinc-blende semiconductors,” Semiconductors 39, 161–173 (2005).
    [Crossref]
  46. S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (2011).
    [Crossref]
  47. I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
    [Crossref]
  48. B. V. Olson, M. P. Gehlsen, and T. F. Boggess, “Nondegenerate two-photon absorption in GaSb,” Opt. Commun. 304, 54–57 (2013).
    [Crossref]
  49. J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.
  50. M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
    [Crossref]
  51. P. Rochon and E. Fortin, “Photovoltaic effect and interband magneto-optical transitions in InP,” Phys. Rev. B 12, 5803 (1975).
    [Crossref]
  52. P. Zory, Quantum Well Lasers (Academic, 1993).
  53. M. Cardona and G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. 137, A1467 (1965).
    [Crossref]
  54. M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
    [Crossref]
  55. D. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065–2074 (1992).
    [Crossref]
  56. D. Thomas, “The exciton spectrum of zinc oxide,” J. Phys. Chem. Solids 15, 86–96 (1960).
    [Crossref]
  57. Y. S. Ang and C. Zhang, “Step-like multi-photon absorption in two-dimensional semiconductors with Rashba spin-orbit coupling in terahertz regime,” in 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (IEEE, 2014), p. 1.
  58. X. Feng, Y. L. Ang, J. He, C. W. Beh, H. Xu, W. S. Chin, and W. Ji, “Three-photon absorption in semiconductor quantum dots: experiment,” Opt. Express 16, 6999–7005 (2008).
    [Crossref]
  59. A. Mang and K. Reimann, “Band gaps, crystal-field splitting, spin-orbit coupling, and exciton binding energies in ZnO under hydrostatic pressure,” Solid State Commun. 94, 251–254 (1995).
    [Crossref]
  60. P. Lambropoulos and M. Teague, “Two-photon ionization with spin-orbit coupling,” J. Phys. B 9, 587 (1976).
    [Crossref]
  61. J. H. Davies, The Physics of Low-Dimensional Semiconductors: An Introduction (Cambridge University, 1998).
  62. S. L. Chuang and S. L. Chuang, Physics of Optoelectronic Devices (1995).
  63. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).
  64. M. Dinu, “Dispersion of phonon-assisted nonresonant third-order nonlinearities,” IEEE J. Quantum Electron. 39, 1498–1503 (2003).
    [Crossref]
  65. M. Reichert, Nonlinear Optical Response of Simple Molecules and Two-Photon Semiconductor Lasers (2015).
  66. S. L. Chuang, Physics of Photonic Devices (Wiley, 2012), Vol. 80.
  67. R. W. Boyd, Nonlinear optics (Elsevier, 2003).

2020 (1)

2019 (1)

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

2016 (4)

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, 073602 (2016).
[Crossref]

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

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[Crossref]

G. Polónyi, B. Monoszlai, G. Gäumann, E. J. Rohwer, G. Andriukaitis, T. Balciunas, A. Pugzlys, A. Baltuska, T. Feurer, and J. Hebling, “High-energy terahertz pulses from semiconductors pumped beyond the three-photon absorption edge,” Opt. Express 24, 23872–23882 (2016).
[Crossref]

2014 (2)

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

S. Shabahang, G. Tao, M. P. Marquez, H. Hu, T. R. Ensley, P. J. Delfyett, and A. F. Abouraddy, “Nonlinear characterization of robust multimaterial chalcogenide nanotapers for infrared supercontinuum generation,” J. Opt. Soc. Am. B 31, 450–457 (2014).
[Crossref]

2013 (2)

2011 (1)

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (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, 235207 (2010).
[Crossref]

2009 (1)

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

2008 (4)

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

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

X. Feng, Y. L. Ang, J. He, C. W. Beh, H. Xu, W. S. Chin, and W. Ji, “Three-photon absorption in semiconductor quantum dots: experiment,” Opt. Express 16, 6999–7005 (2008).
[Crossref]

2007 (2)

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

W. C. Hurlbut, Y.-S. Lee, K. Vodopyanov, P. Kuo, and M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. 32, 668–670 (2007).
[Crossref]

2006 (1)

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

2005 (2)

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

S. Z. Karazhanov and L. L. Y. Voon, “Ab initio studies of the band parameters of III–V and II–VI zinc-blende semiconductors,” Semiconductors 39, 161–173 (2005).
[Crossref]

2003 (1)

M. Dinu, “Dispersion of phonon-assisted nonresonant third-order nonlinearities,” IEEE J. Quantum Electron. 39, 1498–1503 (2003).
[Crossref]

2002 (1)

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

2001 (1)

I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
[Crossref]

1998 (2)

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[Crossref]

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

1995 (3)

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
[Crossref]

A. Mang and K. Reimann, “Band gaps, crystal-field splitting, spin-orbit coupling, and exciton binding energies in ZnO under hydrostatic pressure,” Solid State Commun. 94, 251–254 (1995).
[Crossref]

M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
[Crossref]

1994 (3)

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

D. Hutchings and B. Wherrett, “Linear/circular dichroism of two-photon absorption in zinc-blende semiconductors,” Opt. Mater. 3, 53–60 (1994).
[Crossref]

D. Hutchings and B. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418 (1994).
[Crossref]

1992 (1)

1990 (1)

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

1989 (1)

1986 (2)

1985 (3)

1984 (1)

1983 (1)

H. Brandi and C. De Araujos, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929 (1983).
[Crossref]

1982 (1)

1980 (1)

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

1976 (2)

J. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515 (1976).
[Crossref]

P. Lambropoulos and M. Teague, “Two-photon ionization with spin-orbit coupling,” J. Phys. B 9, 587 (1976).
[Crossref]

1975 (1)

P. Rochon and E. Fortin, “Photovoltaic effect and interband magneto-optical transitions in InP,” Phys. Rev. B 12, 5803 (1975).
[Crossref]

1972 (1)

J. H. Yee, “Three-photon absorption in semiconductors,” Phys. Rev. B 5, 449 (1972).
[Crossref]

1967 (1)

M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
[Crossref]

1965 (2)

M. Cardona and G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. 137, A1467 (1965).
[Crossref]

L. V. Keldysh, “Zh. É ksp. Teor. Fiz. 47, 1945 1964 Sov. Phys,” JETP 20, 1307 (1965).

1960 (1)

D. Thomas, “The exciton spectrum of zinc oxide,” J. Phys. Chem. Solids 15, 86–96 (1960).
[Crossref]

1957 (1)

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[Crossref]

Abouraddy, A. F.

Aitchison, J. S.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Al-Hemyari, K.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Allen, T.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Andriukaitis, G.

Ang, Y. L.

Ang, Y. S.

Y. S. Ang and C. Zhang, “Step-like multi-photon absorption in two-dimensional semiconductors with Rashba spin-orbit coupling in terahertz regime,” in 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (IEEE, 2014), p. 1.

Balciunas, T.

Baltuska, A.

Bechtel, J.

J. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515 (1976).
[Crossref]

Beh, C. W.

Benis, S.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Bhawalkar, J. D.

Boggess, T. F.

B. V. Olson, M. P. Gehlsen, and T. F. Boggess, “Nondegenerate two-photon absorption in GaSb,” Opt. Commun. 304, 54–57 (2013).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Brandi, H.

H. Brandi and C. De Araujos, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929 (1983).
[Crossref]

Cardona, M.

M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
[Crossref]

M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
[Crossref]

M. Cardona and G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. 137, A1467 (1965).
[Crossref]

Chattopadhyay, M.

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

Chen, R.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Chi, S.-H.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Chin, W. S.

Chowdhury, E.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Christensen, N.

M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
[Crossref]

Chuang, S. L.

S. L. Chuang and S. L. Chuang, Physics of Optoelectronic Devices (1995).

S. L. Chuang and S. L. Chuang, Physics of Optoelectronic Devices (1995).

S. L. Chuang, Physics of Photonic Devices (Wiley, 2012), Vol. 80.

Cirloganu, C. M.

Combrié, S.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Davies, J. H.

J. H. Davies, The Physics of Low-Dimensional Semiconductors: An Introduction (Cambridge University, 1998).

De Araujos, C.

H. Brandi and C. De Araujos, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929 (1983).
[Crossref]

De Rossi, A.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Delfyett, P. J.

Demir, H. V.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Dinu, M.

M. Dinu, “Dispersion of phonon-assisted nonresonant third-order nonlinearities,” IEEE J. Quantum Electron. 39, 1498–1503 (2003).
[Crossref]

Ensley, T. R.

Fan, Z.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Fejer, M.

Feng, X.

Feurer, T.

Fortin, E.

P. Rochon and E. Fortin, “Photovoltaic effect and interband magneto-optical transitions in InP,” Phys. Rev. B 12, 5803 (1975).
[Crossref]

Fox, A. M.

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

Gao, Y.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Gäumann, G.

Gehlsen, M. P.

B. V. Olson, M. P. Gehlsen, and T. F. Boggess, “Nondegenerate two-photon absorption in GaSb,” Opt. Commun. 304, 54–57 (2013).
[Crossref]

Gonzalez, L. P.

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (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, 235207 (2010).
[Crossref]

Guenther, A.

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

A. Vaidyanathan, A. Guenther, and S. Mitra, “Two-photon absorption in direct-gap crystals—an addendum,” in Laser Induced Damage In Optical Materials: 1980 (ASTM International, 1981).

Guenther, A. H.

Guha, S.

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (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, 235207 (2010).
[Crossref]

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption: erratum,” Opt. Lett. 11, 59 (1986).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285–287 (1985).
[Crossref]

J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.

Hagan, D. J.

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment: erratum,” Opt. Lett. 45, 1025–1026 (2020).
[Crossref]

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two-and three-photon nonlinearities in semiconductors,” Proc. SPIE 9835, 98350A (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, 073602 (2016).
[Crossref]

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[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, 235207 (2010).
[Crossref]

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

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

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Hales, J. M.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Harbeke, G.

M. Cardona and G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. 137, A1467 (1965).
[Crossref]

Hasselbeck, M.

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[Crossref]

He, G. S.

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
[Crossref]

He, J.

He, T. C.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Hebling, J.

Hu, H.

Huang, N.

Hurlbut, W. C.

Husko, C.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Hutchings, D.

D. Hutchings and B. Wherrett, “Linear/circular dichroism of two-photon absorption in zinc-blende semiconductors,” Opt. Mater. 3, 53–60 (1994).
[Crossref]

D. Hutchings and B. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418 (1994).
[Crossref]

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

Ironside, C. N.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Ispasoiu, R. G.

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

Ji, W.

Judell, N.

Kane, E. O.

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[Crossref]

Kang, J. U.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Karazhanov, S. Z.

S. Z. Karazhanov and L. L. Y. Voon, “Ab initio studies of the band parameters of III–V and II–VI zinc-blende semiconductors,” Semiconductors 39, 161–173 (2005).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, “Zh. É ksp. Teor. Fiz. 47, 1945 1964 Sov. Phys,” JETP 20, 1307 (1965).

Krishnamurthy, S.

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (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, 235207 (2010).
[Crossref]

Kumbhakar, P.

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

Kuo, P.

Kwok, H.-S.

Lad, A. D.

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Lambropoulos, P.

P. Lambropoulos and M. Teague, “Two-photon ionization with spin-orbit coupling,” J. Phys. B 9, 587 (1976).
[Crossref]

Lee, Y.-S.

Li, H.

Li, X.

Lin, T.-C.

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

Liu, H.

Mahamuni, S.

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Mang, A.

A. Mang and K. Reimann, “Band gaps, crystal-field splitting, spin-orbit coupling, and exciton binding energies in ZnO under hydrostatic pressure,” Solid State Commun. 94, 251–254 (1995).
[Crossref]

Markowicz, P. P.

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

Marquez, M. P.

McMorrow, D.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Meyer, J.

I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
[Crossref]

Mi, J.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

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

Mitra, A.

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

Mitra, S.

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

A. Vaidyanathan, A. Guenther, and S. Mitra, “Two-photon absorption in direct-gap crystals—an addendum,” in Laser Induced Damage In Optical Materials: 1980 (ASTM International, 1981).

Mitra, S. S.

Monoszlai, B.

Mukherjee, P.

Munera, N.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Murray, J.

J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.

Mutlugun, E.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Narducci, L.

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

Ng, K. K.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

Olson, B. V.

B. V. Olson, M. P. Gehlsen, and T. F. Boggess, “Nondegenerate two-photon absorption in GaSb,” Opt. Commun. 304, 54–57 (2013).
[Crossref]

Olszak, P. D.

Padilha, L. A.

Pattanaik, H. S.

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

Pearl, S.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

Perry, J. W.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Pollak, F. H.

M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
[Crossref]

Polónyi, G.

Prasad, P. N.

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
[Crossref]

Prem Kiran, P.

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Pugzlys, A.

Qu, Y.

Raineri, F.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Ram-Mohan, L.

I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
[Crossref]

Ravindra Kumar, G.

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Reichert, M.

M. Reichert, P. Zhao, H. S. Pattanaik, D. J. Hagan, and E. W. Van Stryland, “Nondegenerate two-and three-photon nonlinearities in semiconductors,” Proc. SPIE 9835, 98350A (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, 073602 (2016).
[Crossref]

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[Crossref]

M. Reichert, Nonlinear Optical Response of Simple Molecules and Two-Photon Semiconductor Lasers (2015).

Reimann, K.

A. Mang and K. Reimann, “Band gaps, crystal-field splitting, spin-orbit coupling, and exciton binding energies in ZnO under hydrostatic pressure,” Solid State Commun. 94, 251–254 (1995).
[Crossref]

Reinhardt, B. A.

Reyner, C.

J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.

Rochon, P.

P. Rochon and E. Fortin, “Photovoltaic effect and interband magneto-optical transitions in InP,” Phys. Rev. B 12, 5803 (1975).
[Crossref]

Rohwer, E. J.

Rotenberg, N.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

Ryan, J. F.

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

Said, A.

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[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, 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n 2 measurements,” Opt. Lett. 14, 955–957 (1989).
[Crossref]

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, 073602 (2016).
[Crossref]

Sarkar, R.

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

Schucan, G.-M.

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

Shabahang, S.

Shaklee, K. L.

M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
[Crossref]

Shcherbakov, M. R.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Sheik-Bahae, M.

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[Crossref]

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

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

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n 2 measurements,” Opt. Lett. 14, 955–957 (1989).
[Crossref]

Sheik-Bahaei, M.

Shvets, G.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

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, 073602 (2016).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

Smith, W. L.

J. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515 (1976).
[Crossref]

Soileau, M.

Stegeman, G. I.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Sun, H. D.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Sun, Q.

Sze, S. M.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

Ta, V. D.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Talisa, N.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Tan, L.-S.

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

Tao, G.

Teague, M.

P. Lambropoulos and M. Teague, “Two-photon ionization with spin-orbit coupling,” J. Phys. B 9, 587 (1976).
[Crossref]

Thomas, D.

D. Thomas, “The exciton spectrum of zinc oxide,” J. Phys. Chem. Solids 15, 86–96 (1960).
[Crossref]

Tran, Q.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Vaidyanathan, A.

S. S. Mitra, N. Judell, A. Vaidyanathan, and A. H. Guenther, “Three-photon absorption in direct-gap crystals,” Opt. Lett. 7, 307–309 (1982).
[Crossref]

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

A. Vaidyanathan, A. Guenther, and S. Mitra, “Two-photon absorption in direct-gap crystals—an addendum,” in Laser Induced Damage In Optical Materials: 1980 (ASTM International, 1981).

van Driel, H. M.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

Van Stryland, E.

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[Crossref]

Van Stryland, E. W.

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment: erratum,” Opt. Lett. 45, 1025–1026 (2020).
[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, 073602 (2016).
[Crossref]

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

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[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, 235207 (2010).
[Crossref]

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

D. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065–2074 (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, 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n 2 measurements,” Opt. Lett. 14, 955–957 (1989).
[Crossref]

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption: erratum,” Opt. Lett. 11, 59 (1986).
[Crossref]

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

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285–287 (1985).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

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

Villeneuve, A.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Vodopyanov, K.

Voon, L. L. Y.

S. Z. Karazhanov and L. L. Y. Voon, “Ab initio studies of the band parameters of III–V and II–VI zinc-blende semiconductors,” Semiconductors 39, 161–173 (2005).
[Crossref]

Vurgaftman, I.

I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
[Crossref]

Walker, T.

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

Wang, Y.

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Wang, Z.

Webster, S.

Wei, J.

J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.

Wei, T.-H.

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

Wen, J.

Werner, K.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Wherrett, B.

D. Hutchings and B. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418 (1994).
[Crossref]

D. Hutchings and B. Wherrett, “Linear/circular dichroism of two-photon absorption in zinc-blende semiconductors,” Opt. Mater. 3, 53–60 (1994).
[Crossref]

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

Willatzen, M.

M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
[Crossref]

Wong, C.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

Woodall, M.

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

M. A. Woodall, Nonlinear Absorption Techniques and Measurements in Semiconductors (1985).

Xu, H.

Yee, J. H.

J. H. Yee, “Three-photon absorption in semiconductors,” Phys. Rev. B 5, 449 (1972).
[Crossref]

Ying, J. Y.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

Yu, Z. G.

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (2011).
[Crossref]

Zhang, C.

Y. S. Ang and C. Zhang, “Step-like multi-photon absorption in two-dimensional semiconductors with Rashba spin-orbit coupling in terahertz regime,” in 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (IEEE, 2014), p. 1.

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,” Proc. SPIE 9835, 98350A (2016).
[Crossref]

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[Crossref]

Zheng, Q.

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

Zheng, Y.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

Zory, P.

P. Zory, Quantum Well Lasers (Academic, 1993).

Adv. Mater. (1)

Y. Wang, V. D. Ta, Y. Gao, T. C. He, R. Chen, E. Mutlugun, H. V. Demir, and H. D. Sun, “Stimulated emission and lasing from CdSe/CdS/ZnS core-multi-shell quantum dots by simultaneous three-photon absorption,” Adv. Mater. 26, 2954–2961 (2014).
[Crossref]

Appl. Phys. Lett. (5)

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

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300–3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

A. D. Lad, P. Prem Kiran, G. Ravindra Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and Zn Se/Zn S quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-Hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65, 147–149 (1994).
[Crossref]

Chem. Rev. (1)

G. S. He, L.-S. Tan, Q. Zheng, and P. N. Prasad, “Multiphoton absorbing materials: molecular designs, characterizations, and applications,” Chem. Rev. 108, 1245–1330 (2008).
[Crossref]

IEEE J. Quantum Electron. (3)

G.-M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, “Ultrafast two-photon nonlinearities in CdSe near 1.5/spl mu/m studied by interferometric autocorrelation,” IEEE J. Quantum Electron. 34, 1374–1379 (1998).
[Crossref]

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

M. Dinu, “Dispersion of phonon-assisted nonresonant third-order nonlinearities,” IEEE J. Quantum Electron. 39, 1498–1503 (2003).
[Crossref]

J. Appl. Phys. (2)

S. Krishnamurthy, Z. G. Yu, L. P. Gonzalez, and S. Guha, “Temperature-and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP,” J. Appl. Phys. 109, 033102 (2011).
[Crossref]

I. Vurgaftman, J. Meyer, and L. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815–5875 (2001).
[Crossref]

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

J. Phys. B (1)

P. Lambropoulos and M. Teague, “Two-photon ionization with spin-orbit coupling,” J. Phys. B 9, 587 (1976).
[Crossref]

J. Phys. C (1)

H. Brandi and C. De Araujos, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929 (1983).
[Crossref]

J. Phys. Chem. Solids (2)

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[Crossref]

D. Thomas, “The exciton spectrum of zinc oxide,” J. Phys. Chem. Solids 15, 86–96 (1960).
[Crossref]

JETP (1)

L. V. Keldysh, “Zh. É ksp. Teor. Fiz. 47, 1945 1964 Sov. Phys,” JETP 20, 1307 (1965).

Nat. Commun. (1)

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1345 (2019).
[Crossref]

Nature (1)

G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415, 767–770 (2002).
[Crossref]

Opt. Commun. (1)

B. V. Olson, M. P. Gehlsen, and T. F. Boggess, “Nondegenerate two-photon absorption in GaSb,” Opt. Commun. 304, 54–57 (2013).
[Crossref]

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 244613 (1985).
[Crossref]

Opt. Express (5)

Opt. Lett. (9)

C. M. Cirloganu, P. D. Olszak, L. A. Padilha, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Three-photon absorption spectra of zinc blende semiconductors: theory and experiment: erratum,” Opt. Lett. 45, 1025–1026 (2020).
[Crossref]

W. C. Hurlbut, Y.-S. Lee, K. Vodopyanov, P. Kuo, and M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. 32, 668–670 (2007).
[Crossref]

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

S. S. Mitra, N. Judell, A. Vaidyanathan, and A. H. Guenther, “Three-photon absorption in direct-gap crystals,” Opt. Lett. 7, 307–309 (1982).
[Crossref]

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285–287 (1985).
[Crossref]

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

S. Guha, E. W. Van Stryland, and M. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption: erratum,” Opt. Lett. 11, 59 (1986).
[Crossref]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n 2 measurements,” Opt. Lett. 14, 955–957 (1989).
[Crossref]

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
[Crossref]

Opt. Mater. (1)

D. Hutchings and B. Wherrett, “Linear/circular dichroism of two-photon absorption in zinc-blende semiconductors,” Opt. Mater. 3, 53–60 (1994).
[Crossref]

Opt. Quantum Electron. (1)

M. Hasselbeck, A. Said, E. Van Stryland, and M. Sheik-Bahae, “Three-photon absorption in InAs,” Opt. Quantum Electron. 30, 193–200 (1998).
[Crossref]

Phys. Rev. (2)

M. Cardona, K. L. Shaklee, and F. H. Pollak, “Electroreflectance at a semiconductor-electrolyte interface,” Phys. Rev. 154, 696 (1967).
[Crossref]

M. Cardona and G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. 137, A1467 (1965).
[Crossref]

Phys. Rev. B (7)

M. Willatzen, M. Cardona, and N. Christensen, “Spin-orbit coupling parameters and electron g factor of II-VI zinc-blende materials,” Phys. Rev. B 51, 17992 (1995).
[Crossref]

P. Rochon and E. Fortin, “Photovoltaic effect and interband magneto-optical transitions in InP,” Phys. Rev. B 12, 5803 (1975).
[Crossref]

J. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515 (1976).
[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, 235207 (2010).
[Crossref]

D. Hutchings and B. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418 (1994).
[Crossref]

J. H. Yee, “Three-photon absorption in semiconductors,” Phys. Rev. B 5, 449 (1972).
[Crossref]

A. Vaidyanathan, T. Walker, A. Guenther, S. Mitra, and L. Narducci, “Two-photon absorption in several direct-gap crystals,” Phys. Rev. B 21, 743 (1980).
[Crossref]

Phys. Rev. Lett. (1)

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, 073602 (2016).
[Crossref]

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,” Proc. SPIE 9835, 98350A (2016).
[Crossref]

Semiconductors (1)

S. Z. Karazhanov and L. L. Y. Voon, “Ab initio studies of the band parameters of III–V and II–VI zinc-blende semiconductors,” Semiconductors 39, 161–173 (2005).
[Crossref]

Solid State Commun. (1)

A. Mang and K. Reimann, “Band gaps, crystal-field splitting, spin-orbit coupling, and exciton binding energies in ZnO under hydrostatic pressure,” Solid State Commun. 94, 251–254 (1995).
[Crossref]

Other (13)

P. Zory, Quantum Well Lasers (Academic, 1993).

J. Wei, J. Murray, C. Reyner, and S. Guha, “Measurement of Wavelength and Temperature Dependent Refractive Index of GaSb,” in Novel Optical Materials and Applications (Optical Society of America, 2019), paper NoM3B. 3.

M. A. Woodall, Nonlinear Absorption Techniques and Measurements in Semiconductors (1985).

A. Vaidyanathan, A. Guenther, and S. Mitra, “Two-photon absorption in direct-gap crystals—an addendum,” in Laser Induced Damage In Optical Materials: 1980 (ASTM International, 1981).

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-order nonlinear optical coefficients of Si and GaAs in the near-infrared spectral region,” in Applications and Technology (CLEO) (Optical Society of America, 2018), paper JTu2A. 59.

C. Husko, S. Combrié, Q. Tran, F. Raineri, A. De Rossi, and C. Wong, “Slow-light enhanced self-phase modulation, three-photon absorption and free-carriers in photonic crystals: experiment and theory,” in Laser Science to Photonic Applications (CLEO/QELS) (IEEE, 2010), pp. 1–2.

J. H. Davies, The Physics of Low-Dimensional Semiconductors: An Introduction (Cambridge University, 1998).

S. L. Chuang and S. L. Chuang, Physics of Optoelectronic Devices (1995).

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

M. Reichert, Nonlinear Optical Response of Simple Molecules and Two-Photon Semiconductor Lasers (2015).

S. L. Chuang, Physics of Photonic Devices (Wiley, 2012), Vol. 80.

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Y. S. Ang and C. Zhang, “Step-like multi-photon absorption in two-dimensional semiconductors with Rashba spin-orbit coupling in terahertz regime,” in 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (IEEE, 2014), p. 1.

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Figures (8)

Fig. 1.
Fig. 1. (a) Z-scans at several peak irradiances in ZnSe at 1050 nm ($29\;\text{GW} / \text{cm}^2$ pink, $41\;\text{GW} / \text{cm}^2$ blue, $60\;\text{GW} / \text{cm}^2$ red, and $72\;\text{GW} / \text{cm}^2$ black) along with fits (solid lines) using the values for ${\alpha _3}$ shown in (b). (b) ${\alpha _3}$ values obtained from the data in (a). The error bars (blue) are absolute, while the errors (red) relative to the lowest irradiance Z-scan are considerably smaller. The average ${\alpha _3} = ({7.8 \pm 3}) \times {10^{- 3}}\;{\text{cm}^3}/{\text{GW}^2}$ while considering there is no free-carrier absorption.
Fig. 2.
Fig. 2. Scaled 3PA ($\alpha _3^{\text{scaled}}$) data from literature in Table 1 (stars), picosecond measurements (${\Delta}$’s) [41] and ${\Delta}$ for InSb at 80 K, and femtosecond data (circles) compared to Wherrett’s theory (solid line). Values taken from Table 1, and femtosecond spectra for ZnSe and ZnS (every other datum graphed), and GaAs (all fs data graphed) see Figs. 35.
Fig. 3.
Fig. 3. Measured data (circles) for 3PA in (a) ZnSe (taken from [29,30]) and (b) ZnS obtained from Z-scans, compared to calculated spectra from the eight-band model (black dotted line). Scaling the calculated spectra by factors of 1.9 and 2.3, respectively (solid black curves), provides the best agreement with experimental data. Band parameters used for theoretical calculation are provided in Table 2.
Fig. 4.
Fig. 4. (a) Measured data for 3PA in GaAs obtained from Z-scans compared to the calculated spectrum from the eight-band model (black dotted line). Scaling the calculated spectrum by a factor of 4.2 (solid black curve), provides the best agreement with experimental data. Band parameters used for the theoretical calculation are provided in Table 2. Red circles are experimental data taken with ${\sim} 150\;\text{ps}$ pulses. Blue circles are data for the ${\sim} 15\;\text{ps}$ pulses. (b) The FCA cross section from the two-parameter fit for 3PA and the FCA.
Fig. 5.
Fig. 5. Theoretical contributions of starting in the HH (red), LH (blue), and SO bands (green) to the total (black) 3PA in several zinc-blende semiconductors using the eight-band model (see the appendices). These are ordered from small to large $\Delta /{E_g}$ to show the continuous evolution of the 3PA spectral shape, and the 3PA energy sum starts just below the onset of 3PA and goes to where 2PA turns on. No scaling is applied. Band parameters are summarized in Table 2.
Fig. 6.
Fig. 6. Dependence of ${\alpha _{3,\text{norm}}}$ on the normalized three-photon energy sum and $\Delta / E_g$. ${\alpha _{3, \text{norm}}}$ is normalized to the value of 3PA when $\Delta = 0$. The range of $\Delta /{E_g}$ is limited to $\Delta /{E_g} \lt 0.3$ to better represent the effects of the SO band on the 3PA spectra.
Fig. 7.
Fig. 7. Expansion coefficients for the light hole unit cell function versus three-photon energy sum for simulated values of (a) $\Delta /{E_g} = 0.08$ and (b) $\Delta /{E_g} = 0.008$. The horizontal axis is related to $k$ by ${E_{\textit{cv}}}(k) = 3\hbar \omega$ for $v = \textit{LH}$.
Fig. 8.
Fig. 8. Energy bands of InP calculated from parameters given in Table 2 with horizontal axes chosen to be (a) $k$ and (b) three-photon energy sum resonant with the conduction (C) to LH gap at a given $k$ (${E_{\textit{cv}}}(k) = 3\hbar \omega$ with $v = \textit{LH}$). The ranges of $k$ values in (a) and (b) are identical.

Tables (2)

Tables Icon

Table 1. 3PA Coefficients [Experimental Data, α 3 exp , and Values from Eq. (2), Wherrett] with Relevant Material Parametersa

Tables Icon

Table 2. Band-Structure Parameters for Semiconductors in Their Zinc-Blende Form at 300 K (Except ZnO, at 4.2 K) Used for Modeling of 3PAa

Equations (30)

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dI dz = α 3 I 3 σ FCA N I and dN dt = α 3 I 3 3 ω ,
α 3 ( ω ) = K 3 E p 3 / 2 n 3 E g 7 F 3 ( ω E G ) where F 3 ( x ) = ( 3 x 1 ) 1 / 2 ( 3 x ) 9 ,
α 3 scaled ( E g ) α 3 exp . n 3 E p 3 / 2 F ( x ) .
H 0 Ψ n ( r ) = E n Ψ ( r ) ,
Ψ n k ( r ) = exp ( i k r ) u n k ( r ) ,
H 0 u n k ( r ) + ( m ) k p u n k ( r ) = E n u n k ( r ) ,
E n = E n 2 k 2 2 m 0 .
u n k = m c mn ( k ) u m 0 ( r ) .
H SO = 4 m 0 2 c 2 ( V × p ) σ ,
[ H 0 + ( m ) k p + ( 4 m 2 c 2 ) ( V × p ) σ ] | u n k ( r ) ; s = E n | u n k ( r ) ; s ,
| i S , | ( X i Y ) 2 | ( X i Y ) 2 | , | Z , | ( X + i Y ) 2 ( X i Y ) 2 , | i S , | ( X + i Y ) 2 ( X i Y ) 2 , | Z , | ( X i Y ) 2 ( X i Y ) 2 .
[ H 0 0 H ] where H = [ E s 0 k P 0 0 E p Δ 3 2 Δ 3 0 k P 2 Δ 3 E p 0 0 0 0 E p + Δ 3 ] .
P = i ( / m ) S | p z | Z = i ( / m ) S | p y | Y = i ( / m ) S | p x | X ,
Δ = 3 i 4 m 2 c 2 X | V x p y V y p x | Y
[ X Y Z ] = [ cos θ cos ϕ cos θ sin ϕ sin θ sin ϕ cos ϕ 0 sin θ cos ϕ sin θ sin ϕ cos θ ] [ X Y Z ] .
[ ] = [ e ϕ / 2 cos ( θ / 2 ) e ϕ / 2 sin ( θ / 2 ) e ϕ / 2 sin ( θ / 2 ) e ϕ / 2 cos ( θ / 2 ) ] [ ] ,
E = 0 E ( E E G ) ( E + Δ ) k 2 P 2 ( E + 2 Δ / 3 ) = 0 ,
u i α = a i [ i S ] + b i [ ( X i Y ) / 2 ] + c i [ Z ] u i β = a i [ i S ] + b i [ ( X + i Y ) / 2 ] + c i [ Z ] u HH α = [ ( X + i Y ) / 2 ] u HH β = [ ( X i Y ) / 2 ] ,
a i = kP ( E i + 2 Δ / 3 ) / N b i = ( 2 Δ / 3 ) ( E i E G ) / N c i = ( E i E G ) ( E i + 2 Δ / 3 ) / N
H p = e i ω m 0 ( I 2 ε 0 n 0 c ) 1 / 2 a ^ p ^ ,
W 3 = 2 π V c , v k | i , j c | H p | j j | H p | i I | H p | v ( E jv ( k ) 2 ω ) ( E iv ( k ) ω ) | 2 × δ [ E cv ( k ) 3 ω ] ,
α 3 ( ω ) = 3 ω W 3 I 3 .
α 3 = 3 ω ( 2 π ) 5 ( n 0 c ) 3 ( e P ω ) 6 c , v 0 π ( | i , j M cj z ( k r , θ ) M ji z ( k r , θ ) M iv z ( k r , θ ) ( E iv ( k r ) ω ) ( E jv ( k r ) 2 ω ) | 2 ) k r 2 sin θ d θ | E cv ( k ) k | k = k r ,
M ij z ( k r , θ ) = 3 m 0 P u i ( k r , θ ) | p z | u j ( k r , θ ) ,
E cv ( k r ) 3 ω = 0 ,
u C = a c ( k ) | iS + b B ( k ) | Z u SO = a z ( k ) | iS + b z ( k ) | Z u HH = 1 2 | X iY u LH = 1 2 | X + iY .
M C HH z = u c | p z | u HH = 3 2 a c sin θ M C LH z = u c | p z | u LH = 3 2 a c sin θ .
α 3 1 x 5 | A x 2 + B x 2 ( 3 x 1 ) | 2 ( 3 x 1 ) 1 2 ,
E cv ( k r ) 3 ω E g + 2 k r 2 2 μ cv 3 ω = 0 ,
k r = 2 μ cv ( 3 x 1 ) 1 / 2 .