Abstract

We have obtained the complete polarization dependence of the two-photon absorption coefficient β by measuring the orientational dependence and the contrast ratio of the photocurrent in an Al0.2 Ga0.8 As waveguide autocorrelator at an optical frequency far above the half-bandgap. The measured polarization dependence is consistent with theory and previous picosecond nonlinear transmission experiments. The cubic symmetry of the nonlinearity provides a contrast ratio that exceeds 2, which is larger than would be obtained assuming an isotropic medium and Kleinmann symmetry. This device was used to obtain an autocorrelation of a mode-locked Nd:YLF laser.

© 1997 Optical Society of America

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References

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  1. H. P. Weber, “Method for pulse width measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967);J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10, 16–18 (1967).
    [CrossRef]
  2. J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
    [CrossRef]
  3. W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
    [CrossRef]
  4. Y. Takagi, T. Kobayashi, K. Yoshihara, “Multiple-and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett. 17, 658–660 (1992).
    [CrossRef] [PubMed]
  5. F. R. Laughton, J. H. Marsh, D. A. Barrow, E. L. Portnoi, “The two-photon absorption semiconductor waveguide autocorrelator,” IEEE J. Quantum Electron. 30, 838–845 (1994).
    [CrossRef]
  6. M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
    [CrossRef]
  7. D. C. Hutchings, B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
    [CrossRef]
  8. M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
    [CrossRef]
  9. M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
    [CrossRef]
  10. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
    [CrossRef]
  11. R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18, 194–196 (1993).
    [CrossRef] [PubMed]
  12. S. J. Bepko, “Anisotropy of two-photon absorption in GaAs and CdTe,” Phys. Rev. B 12, 669–672 (1975).
    [CrossRef]
  13. J. P. van der Ziel, “Two-photon absorption spectra of GaAs with 2ℏω1 near the direct band gap,” Phys. Rev. B 16, 2775–2780 (1977).
    [CrossRef]
  14. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
    [CrossRef]
  15. N. Bélanger, A. Villeneuve, J. S. Aitchison, “Soliton-like pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B (to be published).
  16. Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
    [CrossRef]

1997 (3)

M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
[CrossRef]

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

1995 (1)

1994 (3)

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

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

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

1993 (1)

1992 (1)

1988 (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

1977 (1)

J. P. van der Ziel, “Two-photon absorption spectra of GaAs with 2ℏω1 near the direct band gap,” Phys. Rev. B 16, 2775–2780 (1977).
[CrossRef]

1975 (1)

S. J. Bepko, “Anisotropy of two-photon absorption in GaAs and CdTe,” Phys. Rev. B 12, 669–672 (1975).
[CrossRef]

1974 (1)

W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
[CrossRef]

1967 (2)

H. P. Weber, “Method for pulse width measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967);J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10, 16–18 (1967).
[CrossRef]

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Aitchison, J. S.

N. Bélanger, A. Villeneuve, J. S. Aitchison, “Soliton-like pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B (to be published).

Andersen, D. R.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Barrow, D. A.

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

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

Bélanger, N.

N. Bélanger, A. Villeneuve, J. S. Aitchison, “Soliton-like pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B (to be published).

Bennett, W. R.

W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
[CrossRef]

Bepko, S. J.

S. J. Bepko, “Anisotropy of two-photon absorption in GaAs and CdTe,” Phys. Rev. B 12, 669–672 (1975).
[CrossRef]

Bryce, A. C.

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

Carlin, D. B.

W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
[CrossRef]

Collins, G. J.

W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
[CrossRef]

DeSalvo, R.

Dvorak, M. D.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Hagan, D. J.

Hamilton, C. J.

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
[CrossRef]

Harken, D. R.

Hutchings, D. C.

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

Karkhanehchi, M. M.

M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
[CrossRef]

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

Kobayashi, T.

Laughton, F. R.

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

Marsh, J. H.

M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
[CrossRef]

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

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

McCallum, D. S.

Portnoi, E. L.

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

Rentzepis, P. M.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Said, A. A.

Schroeder, W. A.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Shapiro, S. L.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Sheik-Bahae, M.

Smirl, A. L.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Takagi, Y.

van der Ziel, J. P.

J. P. van der Ziel, “Two-photon absorption spectra of GaAs with 2ℏω1 near the direct band gap,” Phys. Rev. B 16, 2775–2780 (1977).
[CrossRef]

Van Stryland, E. W.

Villeneuve, A.

N. Bélanger, A. Villeneuve, J. S. Aitchison, “Soliton-like pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B (to be published).

Weber, H. P.

H. P. Weber, “Method for pulse width measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967);J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10, 16–18 (1967).
[CrossRef]

Wecht, K. W.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Weiner, A. M.

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

Wherrett, B. S.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

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

Wright, E. M.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Yoshihara, K.

Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Zheng, Z.

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

IEEE J. Quantum Electron. (4)

W. R. Bennett, D. B. Carlin, G. J. Collins, “Picosecond time-interval measurement and intensity correlations using the two-quantum photoelectric effect,” IEEE J. Quantum Electron. 10, 97–99 (1974).
[CrossRef]

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

M. M. Karkhanehchi, D. A. Barrow, A. C. Bryce, C. J. Hamilton, J. H. Marsh, “The influence of single photon absorption on the performance of the two photon waveguide autocorrelator,” IEEE J. Quantum Electron. 33, 933–937 (1997).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

J. Appl. Phys. (1)

H. P. Weber, “Method for pulse width measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967);J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10, 16–18 (1967).
[CrossRef]

J. Lightwave Technol. (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, , “3rd-order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

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

Opt. Lett. (2)

Photonics Technol. Lett. (2)

M. M. Karkhanehchi, C. J. Hamilton, J. H. Marsh, “Autocorrelation measurements of mode-locked Nd:YLF pulses using two-photon absorption waveguide autocorrelator,” Photonics Technol. Lett. 9, 645–647 (1997).
[CrossRef]

Z. Zheng, A. M. Weiner, J. H. Marsh, M. M. Karkhanehchi, “Ultrafast optical thresholding based on two-photon absorption waveguide photodetectors,” Photonics Technol. Lett. 9, 493–495 (1997).
[CrossRef]

Phys. Rev. B (3)

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

S. J. Bepko, “Anisotropy of two-photon absorption in GaAs and CdTe,” Phys. Rev. B 12, 669–672 (1975).
[CrossRef]

J. P. van der Ziel, “Two-photon absorption spectra of GaAs with 2ℏω1 near the direct band gap,” Phys. Rev. B 16, 2775–2780 (1977).
[CrossRef]

Other (1)

N. Bélanger, A. Villeneuve, J. S. Aitchison, “Soliton-like pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B (to be published).

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Figures (2)

Fig. 1
Fig. 1

Optical power (immediately before coupling into the waveguide) dependence of the photocurrent response in the AlGaAs waveguide photodiode for both TE and TM modes. The solid curves are a best fit to the data. From the quadratic dependence, the two-photon absorption coefficient can be determined.

Fig. 2
Fig. 2

Intensity autocorrelation trace of a mode-locked Nd:YLF laser pulse train. The solid curve is the theoretical fit assuming a Gaussian pulse shape.

Equations (4)

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dITMdz=-αITM-βL001ITM2+1-δ-σ/2ITMITE,dITEdz=-αITE-βL0011-σ/2ITE2+1-δ-σ/2ITMITE,
dNdt=αBωITE+ITM+βL0012ωITM2+1-σ/2×ITE2+21-δ-σ/2ITMITE,
IpheLvL=αBωETM+ETE+βL0012πωTAeff×ETM2+1-σ/2ETE2+2×1-δ-σ/2ETMETE exp-td2/T2, 
C=a+4-2δ-3σ/2a+2-σ/2,

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