Abstract

The concept of a 2-beam action (2-BA) spectroscopy was recently introduced as a method for determining the order of effective nonlinear absorption in multiphoton photoresists. Here we demonstrate that the 2-BA approach can be extended to any measureable observable generated by linear and/or nonlinear absorption. As an example, 2-beam constant-amplitude photocurrent spectroscopy is used to study absorption of a tightly focused, mode-locked or continuous-wave, 800 nm laser by a GaAsP photodiode. The effective order of the absorption process can be measured at any desired value of the photocurrent or photovoltage. A self-consistent framework is presented for using non-integral 2-BA exponents to determine the relative contributions of two absorption mechanisms of different order. The dependence of the ratio of the quadratic and linear contributions on the average excitation power is used to verify that these are the dominant orders of absorption in the photodiode with 800 nm excitation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  28. J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22(17), 1344–1346 (1997).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  31. M. Garbugli, A. Gambetta, S. Schrader, T. Virgili, and G. Lanzani, “Multi-photon non-linear photocurrent in organic photodiodes,” J. Mater. Chem. 19(40), 7551–7560 (2009).
    [Crossref]
  32. R. Koeppe, J. G. Müller, J. M. Lupton, J. Feldmann, U. Scherf, and U. Lemmer, “One- and two-photon photocurrents from tunable organic microcavity photodiodes,” Appl. Phys. Lett. 82(16), 2601–2603 (2003).
    [Crossref]
  33. G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  36. E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, “Phase-controlled currents in semiconductors,” Phys. Rev. Lett. 74(18), 3596–3599 (1995).
    [Crossref] [PubMed]
  37. A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
    [Crossref]
  38. S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” IEEE J. Quantum Electron. 43(12), 1211–1217 (2007).
    [Crossref]
  39. P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
    [Crossref] [PubMed]
  40. D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
    [Crossref]
  41. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963).
    [Crossref]
  42. A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Rev. 51(4), 661–703 (2009).
    [Crossref]
  43. C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13(3), 481–491 (1996).
    [Crossref]
  44. D. Abbott, B. Davis, B. Gonzalez, A. Hernandez, and K. Eshraghian, “Modelling of low power CW laser beam heating effects on A GaAs substrate,” Solid-State Electron. 42(5), 809–816 (1998).
    [Crossref]
  45. S. R. Johnson and T. Tiedje, “Temperature dependence of the Urbach edge in GaAs,” J. Appl. Phys. 78(9), 5609–5613 (1995).
    [Crossref]

2017 (2)

N. Liaros and J. T. Fourkas, “The characterization of absorptive nonlinearities,” Laser Photonics Rev. 11(5), 1700106 (2017).
[Crossref]

F. Zhou and W. Ji, “Giant three-photon absorption in monolayer MoS2 and its application in near-infrared photodetection,” Laser Photonics Rev. 11(4), 1700021 (2017).
[Crossref]

2016 (1)

Z. Tomova, N. Liaros, S. A. Gutierrez Razo, S. M. Wolf, and J. T. Fourkas, “In situ measurement of the effective nonlinear absorption order in multiphoton photoresists,” Laser Photonics Rev. 10(5), 849–854 (2016).
[Crossref]

2015 (2)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: Towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

2013 (2)

P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
[Crossref] [PubMed]

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

2011 (2)

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: Invited review,” Semicond. Sci. Technol. 26(8), 083001 (2011).
[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-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

2010 (2)

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

K. Iliopoulos, O. Krupka, D. Gindre, and M. Sallé, “Reversible two-photon optical data storage in coumarin-based copolymers,” J. Am. Chem. Soc. 132(41), 14343–14345 (2010).
[Crossref] [PubMed]

2009 (2)

M. Garbugli, A. Gambetta, S. Schrader, T. Virgili, and G. Lanzani, “Multi-photon non-linear photocurrent in organic photodiodes,” J. Mater. Chem. 19(40), 7551–7560 (2009).
[Crossref]

A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Rev. 51(4), 661–703 (2009).
[Crossref]

2007 (3)

S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” IEEE J. Quantum Electron. 43(12), 1211–1217 (2007).
[Crossref]

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

N. J. Durr, T. Larson, D. K. Smith, B. A. Korgel, K. Sokolov, and A. Ben-Yakar, “Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods,” Nano Lett. 7(4), 941–945 (2007).
[Crossref] [PubMed]

2006 (1)

C. N. LaFratta, L. Li, and J. T. Fourkas, “Rapid, in-line, non-interferometric auto- and cross-correlator for microscopy,” Opt. Express 14(23), 111215 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (1)

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-sensitivity two-photon absorption microcavity autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

2003 (2)

R. Koeppe, J. G. Müller, J. M. Lupton, J. Feldmann, U. Scherf, and U. Lemmer, “One- and two-photon photocurrents from tunable organic microcavity photodiodes,” Appl. Phys. Lett. 82(16), 2601–2603 (2003).
[Crossref]

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003).
[Crossref] [PubMed]

2002 (1)

C. E. Olson, M. J. Previte, and J. T. Fourkas, “Efficient and robust multiphoton data storage in molecular glasses and highly crosslinked polymers,” Nat. Mater. 1(4), 225–228 (2002).
[Crossref] [PubMed]

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

1999 (3)

A. C. Millard, D. N. Fittinghoff, J. A. Squier, M. Müller, and A. L. Gaeta, “Using GaAsP photodiodes to characterize ultrashort pulses under high numerical aperture focusing in microscopy,” J. Microsc. 193(3), 179–181 (1999).
[Crossref]

P. Langlois and E. P. Ippen, “Measurement of pulse asymmetry by three-photon-absorption autocorrelation in a GaAsP photodiode,” Opt. Lett. 24(24), 1868–1870 (1999).
[Crossref] [PubMed]

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75(24), 3778–3780 (1999).
[Crossref]

1998 (2)

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998).
[Crossref]

D. Abbott, B. Davis, B. Gonzalez, A. Hernandez, and K. Eshraghian, “Modelling of low power CW laser beam heating effects on A GaAs substrate,” Solid-State Electron. 42(5), 809–816 (1998).
[Crossref]

1997 (4)

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
[Crossref]

S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22(2), 132–134 (1997).
[Crossref] [PubMed]

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15(5), 201–204 (1997).
[PubMed]

J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22(17), 1344–1346 (1997).
[Crossref] [PubMed]

1996 (2)

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, “Coherent control of photocurrent generation in bulk semiconductors,” Phys. Rev. Lett. 76(10), 1703–1706 (1996).
[Crossref] [PubMed]

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13(3), 481–491 (1996).
[Crossref]

1995 (2)

S. R. Johnson and T. Tiedje, “Temperature dependence of the Urbach edge in GaAs,” J. Appl. Phys. 78(9), 5609–5613 (1995).
[Crossref]

E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, “Phase-controlled currents in semiconductors,” Phys. Rev. Lett. 74(18), 3596–3599 (1995).
[Crossref] [PubMed]

1994 (1)

F. R. Laughton, J. H. Marsh, D. A. Barrow, and E. L. Portnoi, “The two-photon absorption semiconductor waveguide autocorrelator,” IEEE J. Quantum Electron. 30(3), 838–845 (1994).
[Crossref]

1993 (1)

L. W. Tutt and T. F. Boggess, “A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials,” Prog. Quantum Electron. 17(4), 299–338 (1993).
[Crossref]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

1989 (1)

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989).
[Crossref] [PubMed]

1985 (1)

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963).
[Crossref]

Abbott, D.

D. Abbott, B. Davis, B. Gonzalez, A. Hernandez, and K. Eshraghian, “Modelling of low power CW laser beam heating effects on A GaAs substrate,” Solid-State Electron. 42(5), 809–816 (1998).
[Crossref]

Akundi, M. A.

Aloukos, P.

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

Atanasov, R.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
[Crossref]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, “Coherent control of photocurrent generation in bulk semiconductors,” Phys. Rev. Lett. 76(10), 1703–1706 (1996).
[Crossref] [PubMed]

Bakandritsos, A.

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

Bakr, O. M.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Baldacchini, T.

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

Baltuska, A.

Banfi, G.

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998).
[Crossref]

Barrow, D. A.

F. R. Laughton, J. H. Marsh, D. A. Barrow, and E. L. Portnoi, “The two-photon absorption semiconductor waveguide autocorrelator,” IEEE J. Quantum Electron. 30(3), 838–845 (1994).
[Crossref]

Barry, L. P.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-sensitivity two-photon absorption microcavity autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Ben-Yakar, A.

N. J. Durr, T. Larson, D. K. Smith, B. A. Korgel, K. Sokolov, and A. Ben-Yakar, “Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods,” Nano Lett. 7(4), 941–945 (2007).
[Crossref] [PubMed]

Bhawalkar, J. D.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15(5), 201–204 (1997).
[PubMed]

Boggess, T. F.

L. W. Tutt and T. F. Boggess, “A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials,” Prog. Quantum Electron. 17(4), 299–338 (1993).
[Crossref]

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

Bradley, A. L.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-sensitivity two-photon absorption microcavity autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Breuer, S.

P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
[Crossref] [PubMed]

Buchanan, M.

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Olson, C. E.

C. E. Olson, M. J. Previte, and J. T. Fourkas, “Efficient and robust multiphoton data storage in molecular glasses and highly crosslinked polymers,” Nat. Mater. 1(4), 225–228 (2002).
[Crossref] [PubMed]

Orenstein, M.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: Invited review,” Semicond. Sci. Technol. 26(8), 083001 (2011).
[Crossref]

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-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

Parkinson, P.

P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
[Crossref] [PubMed]

Parthenopoulos, D. A.

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989).
[Crossref] [PubMed]

Pogue, B. W.

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

Portnoi, E. L.

F. R. Laughton, J. H. Marsh, D. A. Barrow, and E. L. Portnoi, “The two-photon absorption semiconductor waveguide autocorrelator,” IEEE J. Quantum Electron. 30(3), 838–845 (1994).
[Crossref]

Prasad, P. N.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15(5), 201–204 (1997).
[PubMed]

Previte, M. J.

C. E. Olson, M. J. Previte, and J. T. Fourkas, “Efficient and robust multiphoton data storage in molecular glasses and highly crosslinked polymers,” Nat. Mater. 1(4), 225–228 (2002).
[Crossref] [PubMed]

Pshenichnikov, M. S.

Ranka, J. K.

Rao, D. N.

Razeghi, M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75(24), 3778–3780 (1999).
[Crossref]

Rentzepis, P. M.

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989).
[Crossref] [PubMed]

Ricard, D.

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998).
[Crossref]

Rizvi, I.

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

Roberts, J. S.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-sensitivity two-photon absorption microcavity autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Sallé, M.

K. Iliopoulos, O. Krupka, D. Gindre, and M. Sallé, “Reversible two-photon optical data storage in coumarin-based copolymers,” J. Am. Chem. Soc. 132(41), 14343–14345 (2010).
[Crossref] [PubMed]

Samkoe, K. S.

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

Sargent, E. H.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Scherf, U.

R. Koeppe, J. G. Müller, J. M. Lupton, J. Feldmann, U. Scherf, and U. Lemmer, “One- and two-photon photocurrents from tunable organic microcavity photodiodes,” Appl. Phys. Lett. 82(16), 2601–2603 (2003).
[Crossref]

Schrader, S.

M. Garbugli, A. Gambetta, S. Schrader, T. Virgili, and G. Lanzani, “Multi-photon non-linear photocurrent in organic photodiodes,” J. Mater. Chem. 19(40), 7551–7560 (2009).
[Crossref]

Sellan, D. P.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Shalizi, C. R.

A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Rev. 51(4), 661–703 (2009).
[Crossref]

Shi, D.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Sipe, J. E.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
[Crossref]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, “Coherent control of photocurrent generation in bulk semiconductors,” Phys. Rev. Lett. 76(10), 1703–1706 (1996).
[Crossref] [PubMed]

Smith, D. K.

N. J. Durr, T. Larson, D. K. Smith, B. A. Korgel, K. Sokolov, and A. Ben-Yakar, “Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods,” Nano Lett. 7(4), 941–945 (2007).
[Crossref] [PubMed]

Sokolov, K.

N. J. Durr, T. Larson, D. K. Smith, B. A. Korgel, K. Sokolov, and A. Ben-Yakar, “Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods,” Nano Lett. 7(4), 941–945 (2007).
[Crossref] [PubMed]

Spring, B. Q.

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

Squier, J. A.

A. C. Millard, D. N. Fittinghoff, J. A. Squier, M. Müller, and A. L. Gaeta, “Using GaAsP photodiodes to characterize ultrashort pulses under high numerical aperture focusing in microscopy,” J. Microsc. 193(3), 179–181 (1999).
[Crossref]

Streltsov, A. M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75(24), 3778–3780 (1999).
[Crossref]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Sutherland, B. R.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Szabo, T.

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

Tan, H. H.

P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
[Crossref] [PubMed]

Tanaka, K.

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
[Crossref]

Tiedje, T.

S. R. Johnson and T. Tiedje, “Temperature dependence of the Urbach edge in GaAs,” J. Appl. Phys. 78(9), 5609–5613 (1995).
[Crossref]

Tomova, Z.

Z. Tomova, N. Liaros, S. A. Gutierrez Razo, S. M. Wolf, and J. T. Fourkas, “In situ measurement of the effective nonlinear absorption order in multiphoton photoresists,” Laser Photonics Rev. 10(5), 849–854 (2016).
[Crossref]

Tsia, K. K.

S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” IEEE J. Quantum Electron. 43(12), 1211–1217 (2007).
[Crossref]

Tutt, L. W.

L. W. Tutt and T. F. Boggess, “A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials,” Prog. Quantum Electron. 17(4), 299–338 (1993).
[Crossref]

van Driel, H. M.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
[Crossref]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, “Coherent control of photocurrent generation in bulk semiconductors,” Phys. Rev. Lett. 76(10), 1703–1706 (1996).
[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-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

Venkatram, N.

Verma, S.

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

Virgili, T.

M. Garbugli, A. Gambetta, S. Schrader, T. Virgili, and G. Lanzani, “Multi-photon non-linear photocurrent in organic photodiodes,” J. Mater. Chem. 19(40), 7551–7560 (2009).
[Crossref]

Walker, D.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75(24), 3778–3780 (1999).
[Crossref]

Walters, G.

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Wasilewski, Z. R.

E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, “Phase-controlled currents in semiconductors,” Phys. Rev. Lett. 74(18), 3596–3599 (1995).
[Crossref] [PubMed]

Webb, W. W.

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-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011).
[Crossref]

Wiersma, D. A.

Wolf, S. M.

Z. Tomova, N. Liaros, S. A. Gutierrez Razo, S. M. Wolf, and J. T. Fourkas, “In situ measurement of the effective nonlinear absorption order in multiphoton photoresists,” Laser Photonics Rev. 10(5), 849–854 (2016).
[Crossref]

Xu, C.

Zboril, R.

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

Zhao, C. F.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15(5), 201–204 (1997).
[PubMed]

Zhou, F.

F. Zhou and W. Ji, “Giant three-photon absorption in monolayer MoS2 and its application in near-infrared photodetection,” Laser Photonics Rev. 11(4), 1700021 (2017).
[Crossref]

ACS Nano (1)

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9(9), 9340–9346 (2015).
[Crossref] [PubMed]

Adv. Phys. (1)

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998).
[Crossref]

Angew. Chem. Int. Ed. Engl. (1)

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75(24), 3778–3780 (1999).
[Crossref]

R. Koeppe, J. G. Müller, J. M. Lupton, J. Feldmann, U. Scherf, and U. Lemmer, “One- and two-photon photocurrents from tunable organic microcavity photodiodes,” Appl. Phys. Lett. 82(16), 2601–2603 (2003).
[Crossref]

Chem. Rev. (1)

J. P. Celli, B. Q. Spring, I. Rizvi, C. L. Evans, K. S. Samkoe, S. Verma, B. W. Pogue, and T. Hasan, “Imaging and photodynamic therapy: Mechanisms, monitoring, and optimization,” Chem. Rev. 110(5), 2795–2838 (2010).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (2)

S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” IEEE J. Quantum Electron. 43(12), 1211–1217 (2007).
[Crossref]

F. R. Laughton, J. H. Marsh, D. A. Barrow, and E. L. Portnoi, “The two-photon absorption semiconductor waveguide autocorrelator,” IEEE J. Quantum Electron. 30(3), 838–845 (1994).
[Crossref]

IEEE Photonics Technol. Lett. (1)

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-sensitivity two-photon absorption microcavity autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

J. Am. Chem. Soc. (1)

K. Iliopoulos, O. Krupka, D. Gindre, and M. Sallé, “Reversible two-photon optical data storage in coumarin-based copolymers,” J. Am. Chem. Soc. 132(41), 14343–14345 (2010).
[Crossref] [PubMed]

J. Appl. Phys. (1)

S. R. Johnson and T. Tiedje, “Temperature dependence of the Urbach edge in GaAs,” J. Appl. Phys. 78(9), 5609–5613 (1995).
[Crossref]

J. Clin. Laser Med. Surg. (1)

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15(5), 201–204 (1997).
[PubMed]

J. Mater. Chem. (1)

M. Garbugli, A. Gambetta, S. Schrader, T. Virgili, and G. Lanzani, “Multi-photon non-linear photocurrent in organic photodiodes,” J. Mater. Chem. 19(40), 7551–7560 (2009).
[Crossref]

J. Mater. Sci. Mater. Electron. (1)

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
[Crossref]

J. Microsc. (1)

A. C. Millard, D. N. Fittinghoff, J. A. Squier, M. Müller, and A. L. Gaeta, “Using GaAsP photodiodes to characterize ultrashort pulses under high numerical aperture focusing in microscopy,” J. Microsc. 193(3), 179–181 (1999).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. C (1)

N. Liaros, P. Aloukos, A. Kolokithas-Ntoukas, A. Bakandritsos, T. Szabo, R. Zboril, and S. Couris, “Nonlinear Optical Properties and Broadband Optical Power Limiting Action of Graphene Oxide Colloids,” J. Phys. Chem. C 117(13), 6842–6850 (2013).
[Crossref]

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963).
[Crossref]

Laser Photonics Rev. (4)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: Towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

N. Liaros and J. T. Fourkas, “The characterization of absorptive nonlinearities,” Laser Photonics Rev. 11(5), 1700106 (2017).
[Crossref]

Z. Tomova, N. Liaros, S. A. Gutierrez Razo, S. M. Wolf, and J. T. Fourkas, “In situ measurement of the effective nonlinear absorption order in multiphoton photoresists,” Laser Photonics Rev. 10(5), 849–854 (2016).
[Crossref]

F. Zhou and W. Ji, “Giant three-photon absorption in monolayer MoS2 and its application in near-infrared photodetection,” Laser Photonics Rev. 11(4), 1700021 (2017).
[Crossref]

Nano Lett. (2)

P. Parkinson, Y.-H. Lee, L. Fu, S. Breuer, H. H. Tan, and C. Jagadish, “Three-dimensional in situ photocurrent mapping for nanowire photovoltaics,” Nano Lett. 13(4), 1405–1409 (2013).
[Crossref] [PubMed]

N. J. Durr, T. Larson, D. K. Smith, B. A. Korgel, K. Sokolov, and A. Ben-Yakar, “Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods,” Nano Lett. 7(4), 941–945 (2007).
[Crossref] [PubMed]

Nat. Mater. (1)

C. E. Olson, M. J. Previte, and J. T. Fourkas, “Efficient and robust multiphoton data storage in molecular glasses and highly crosslinked polymers,” Nat. Mater. 1(4), 225–228 (2002).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Nature (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003).
[Crossref] [PubMed]

Opt. Express (2)

N. Venkatram, D. N. Rao, and M. A. Akundi, “Nonlinear absorption, scattering and optical limiting studies of CdS nanoparticles,” Opt. Express 13(3), 867–872 (2005).
[Crossref] [PubMed]

C. N. LaFratta, L. Li, and J. T. Fourkas, “Rapid, in-line, non-interferometric auto- and cross-correlator for microscopy,” Opt. Express 14(23), 111215 (2006).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. Lett. (3)

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, “Coherent control of photocurrent generation in bulk semiconductors,” Phys. Rev. Lett. 76(10), 1703–1706 (1996).
[Crossref] [PubMed]

E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, “Phase-controlled currents in semiconductors,” Phys. Rev. Lett. 74(18), 3596–3599 (1995).
[Crossref] [PubMed]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78(2), 306–309 (1997).
[Crossref]

Prog. Quantum Electron. (1)

L. W. Tutt and T. F. Boggess, “A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials,” Prog. Quantum Electron. 17(4), 299–338 (1993).
[Crossref]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

Science (2)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: Invited review,” Semicond. Sci. Technol. 26(8), 083001 (2011).
[Crossref]

SIAM Rev. (1)

A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Rev. 51(4), 661–703 (2009).
[Crossref]

Solid-State Electron. (1)

D. Abbott, B. Davis, B. Gonzalez, A. Hernandez, and K. Eshraghian, “Modelling of low power CW laser beam heating effects on A GaAs substrate,” Solid-State Electron. 42(5), 809–816 (1998).
[Crossref]

Other (2)

T. Baldacchini, ed., Three-Dimensional Microfabrication Using Two-Photon Polymerization (Elsevier, 2016).

J. Stampfl, R. Liska, and A. Ovsianikov, eds., Multiphoton Lithography: Techniques, Materials and Applications (Wiley-VCH, 2017).

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Figures (6)

Fig. 1
Fig. 1 Schematic depiction of a 2-beam constant-amplitude photocurrent experiment. Two trains of pulses whose amplitudes can be adjusted independently are interleaved and focused onto a photodiode. Multiple sets of average powers for the two pulse trains that generate the same photocurrent (or photovoltage) are determined, allowing for the measurement of the effective order of the absorption process in the photodiode.
Fig. 2
Fig. 2 (a) Logarithmic photocurrent excitation plots for a GaAsP photodiode for 800 nm excitation with a ML laser (at the focal plane) and a CW laser (out of the focal plane). The solid lines are free fits and the dashed line is a fit with the slope constrained to 1. (b) 2-BCAmP data collected under the same conditions. The error bars are smaller than the symbols in all cases.
Fig. 3
Fig. 3 (a) Logarithmic PE plots for ML 800 nm excitation, with the GaAsP photodiode different distances from the focal plane. (b) 2-BCAmP data collected under the same conditions.
Fig. 4
Fig. 4 (a) A representative linearized plot used to extract the fractional contribution of linear absorption from a 2-BCAmP data set. The line is a linear least-squares fit constrained to pass through the origin. (b) Fraction of photocurrent arising from 2-photon absorption at a fixed average laser power as a function of the distance of the photodiode from the focal plane.
Fig. 5
Fig. 5 (a) 2-BCAmP data for a GaAsP photodiode 1.28 mm from the focal plane of the objective for mode-locked 800 nm excitation at three different average powers. (b) Ratio of 2-photon to linear absorption as a function of average power from the three 2-BCAmP data sets (red symbols). The solid line is a linear least-squares fit, constrained to pass through the origin. The blue symbols are the values of b/a for fits to a linear absorption process and a 3-photon absorption process, in which case the ratio should depend on the square of the average power.
Fig. 6
Fig. 6 (a) A logarithmic PE plot for a GaAsP photodiode for 800 nm CW excitation at the focal plane of the objective. The solid line is a fit to a linear term and a quadratic term. (b) 2-BCAmP data for different CW laser powers. (c) Ratio of 2-photon to linear absorption as a function of power from the three 2-BCAmP data sets. The solid line in the plot is a linear least-squares fit, constrained to pass through the origin.

Equations (6)

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P ¯ 1 n + P ¯ 2 n =1
S(I)=A I n +B I n+1 .
B I n+1 A I n = BI A = 1 9 .
B I n+1 A I n = BI A =9 .
a( P ¯ 1 + P ¯ 2 )+b( P ¯ 1 2 + P ¯ 2 2 )=1.
1 P ¯ 1 2 P ¯ 2 2 =a( P ¯ 1 + P ¯ 2 P ¯ 1 2 P ¯ 2 2 ).

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