Abstract

We report an extension of the spectrally resolved two-beam coupling technique to measure the nonlinear intensity index of refraction (n2I) and the two-photon absorption coefficient (β) by use of chirped laser pulses. The linear chirp parameter b is incorporated into the derivation of a more general model than the previous one [Opt. Lett. 22, 1077 (1997)]. We have also analyzed the validity of this linear chirp model through a comparison of the experimental results for fused silica with the numerically accurate calculation that considers higher-order chirps obtained by second-harmonic generation frequency-resolved optical gating. The results show that this method potentially can be used to extract the chirp. Finally, we applied this transient spectrally resolved nonlinear transmittance spectroscopy to semiconductor-doped glasses to extract their n2I and β.

© 1999 Optical Society of America

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  1. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York 1996), and references therein.
  2. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.
  3. X. Kang, T. Krauss, and F. Wise, Opt. Lett. 22, 1077 (1997).
  4. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif. 1995).
  5. G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).
  6. D. Milam, Appl. Opt. 37, 546 (1998).
  7. In the calculation of the simulated nonlinear transmittance signals we used the complete phase derived from the FROG measurement. The best Gaussian fit to the intensity data was adopted in the calculation. A calculation with the actual intensity data was also performed, which resulted in a worse match with the experimental nonlinear transmittance data, perhaps because of an error in the intensity retrieved from the FROG measurement.
  8. We also performed the calculation by using different orders of polynomials to fit the extracted phase from the FROG measurement. We found that the amplitude of the simulated transient when only the linear chirp was used did not agree with the experimental data. When the higher-order chirps were included in the calculation, the whole body of experimental data could be reproduced. A close comparison of the experimental and the simulation results has shown that there are still slight differences between them. Furthermore, the sample length is one hundredth of the dispersion length LD. The effect of GVD is normally regarded to be negligible [G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif. 1989), Chapter 4]. It is thus conceivable that this discrepancy is due to errors in intensity and phase of the laser pulses extracted from the FROG measurement. This fact has further demonstrated that the transient nonlinear transmittance technique is more sensitive to the chirp than is FROG.
  9. A. J. Taylor, G. Rodriguez, and T. S. Clement, Opt. Lett. 21, 1812 (1996).
  10. G. Rodriguez and A. J. Taylor, Opt. Lett. 23, 858 (1998).
  11. G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
  12. M. G. Bawendi, M. L. Steigerwald, and L. E. Brus, Annu. Rev. Phys. Chem. 41, 477 (1990); Y. Wang and N. Herron, J. Phys. Chem. 95, 525 (1991); A. P. Alivisatos, J. Phys. Chem. JPCHAX 100, 13, 226 (1996); A. Tomasulo and M. C. Ramakrishna, J. Chem. Phys. JCPSA6 105, 3612 (1996).
  13. G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

1998 (3)

D. Milam, Appl. Opt. 37, 546 (1998).

G. Rodriguez and A. J. Taylor, Opt. Lett. 23, 858 (1998).

G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).

1997 (1)

1996 (2)

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

A. J. Taylor, G. Rodriguez, and T. S. Clement, Opt. Lett. 21, 1812 (1996).

1995 (1)

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Banfi, G. P.

G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

Christov, I. P.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Clement, T. S.

Degiorgio, V.

G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

DeLong, K. W.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Fittinghoff, D. N.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Fortusini, D.

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Kang, X.

Kapteyn, H. C.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Krauss, T.

Krumbügel, M. A.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Milam, D.

Murnane, M.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Ricard, D.

G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).

Rodriguez, G.

Rundquist, A.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Sweetser, J. N.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Taft, G.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Tan, H. M.

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

Taylor, A. J.

Trebino, R.

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

Wise, F.

Adv. Phys. (1)

G. P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. P. Banfi, V. Degiorgio, D. Fortusini, and H. M. Tan, Appl. Phys. Lett. 67, 13 (1995).

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-6, 760 (1990), and references therein.

IEEE J. Sel. Top. Quantum Electron. (1)

G. Taft, A. Rundquist, M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).

Opt. Lett. (3)

Other (5)

In the calculation of the simulated nonlinear transmittance signals we used the complete phase derived from the FROG measurement. The best Gaussian fit to the intensity data was adopted in the calculation. A calculation with the actual intensity data was also performed, which resulted in a worse match with the experimental nonlinear transmittance data, perhaps because of an error in the intensity retrieved from the FROG measurement.

We also performed the calculation by using different orders of polynomials to fit the extracted phase from the FROG measurement. We found that the amplitude of the simulated transient when only the linear chirp was used did not agree with the experimental data. When the higher-order chirps were included in the calculation, the whole body of experimental data could be reproduced. A close comparison of the experimental and the simulation results has shown that there are still slight differences between them. Furthermore, the sample length is one hundredth of the dispersion length LD. The effect of GVD is normally regarded to be negligible [G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif. 1989), Chapter 4]. It is thus conceivable that this discrepancy is due to errors in intensity and phase of the laser pulses extracted from the FROG measurement. This fact has further demonstrated that the transient nonlinear transmittance technique is more sensitive to the chirp than is FROG.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif. 1995).

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York 1996), and references therein.

M. G. Bawendi, M. L. Steigerwald, and L. E. Brus, Annu. Rev. Phys. Chem. 41, 477 (1990); Y. Wang and N. Herron, J. Phys. Chem. 95, 525 (1991); A. P. Alivisatos, J. Phys. Chem. JPCHAX 100, 13, 226 (1996); A. Tomasulo and M. C. Ramakrishna, J. Chem. Phys. JCPSA6 105, 3612 (1996).

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