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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 1 — Jan. 1, 2000
  • pp: 146–150

Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics

Evgeni Sorokin, Gabriel Tempea, and Thomas Brabec  »View Author Affiliations

JOSA B, Vol. 17, Issue 1, pp. 146-150 (2000)

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Based on two theorems, the importance of the root-mean-square (rms) width for the characterization of ultrashort optical pulses is demonstrated. First, it is shown that one can directly determine the rms width from the autocorrelation without making any assumptions about the specific form of the pulse envelope. Second, it is shown that a bandwidth-limited (unchirped) wave packet has the smallest possible rms time–bandwidth product. This reveals a natural definition for a rms chirp that is easily accessible to experimental measurement and that presents a useful measure for the quality of pulse compression techniques.

© 2000 Optical Society of America

OCIS Codes
(320.5520) Ultrafast optics : Pulse compression
(320.7100) Ultrafast optics : Ultrafast measurements

Evgeni Sorokin, Gabriel Tempea, and Thomas Brabec, "Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics," J. Opt. Soc. Am. B 17, 146-150 (2000)

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  1. K. L. Sala, G. A. Kenney-Wallace, and G. E. Hall, IEEE J. Quantum Electron. 16, 990–996 (1980). [CrossRef]
  2. For a review, see the feature issue on ultrashort-laser-pulse intensity and phase measurement and applications, IEEE J. Quantum Electron. 35, 418–523 (1999), and references therein.
  3. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, Opt. Lett. 24, 411–413 (1999); D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, Opt. Lett. 24, 631–633 (1999). [CrossRef]
  4. A. Baltuska, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102–104 (1997). [CrossRef] [PubMed]
  5. S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 22, 1562–1564 (1997). [CrossRef]
  6. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997). [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  8. K. Naganuma, K. Mogi, and H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989). [CrossRef]
  9. For the derivation, we need to make the following assumptions. We require that the complex envelopes U and tU are absolutely integrable; that is, ∫−∞|tnU(t)|dt for n=0, 1 is finite. The absolute integrability ensures that the Fourier transform of U and its first derivative, Ũ(ω), dŨ/dω→ 0 for ω→±∞.
  10. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995).
  11. A. H. Liang and H. K. Tsang, IEEE J. Quantum Electron. 32, 2064 (1996); A. H. Liang, H. K. Tsang, and L. Y. Chan, J. Opt. Soc. Am. B 13, 2464 (1996). [CrossRef]
  12. D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793–1795 (1997); T. Baumert, T. Brixner, V. Setfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997); A. Efimov, M. D. Moores, N. M. Beach, J. L. Krause, and D. H. Reitze, Opt. Lett. OPLEDP 23, 1915–1917 (1998). [CrossRef]
  13. R. N. Bracewell, Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, New York, 1986), p. 172.
  14. If the operator L does not contain explicit functions of time and the boundary conditions are defined at t=±∞, then the Green’s function G(t, t) has the form G(t−t). Most, if not all, physical processes of interest satisfy these conditions.

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