## Wavelet transforms for optical pulse analysis

JOSA A, Vol. 22, Issue 12, pp. 2890-2899 (2005)

http://dx.doi.org/10.1364/JOSAA.22.002890

Acrobat PDF (968 KB)

### Abstract

An exploration of wavelet transforms for ultrashort optical pulse characterization is given. Some of the most common wavelets are examined to determine the advantages of using the causal quasi-wavelet suggested in Proceedings of the LEOS 15th Annual Meeting (IEEE, 2002), Vol. 2, p. 592, in terms of pulse analysis and, in particular, chirp extraction. Owing to its ability to distinguish between past and future pulse information, the causal quasi-wavelet is found to be highly suitable for optical pulse characterization.

© 2005 Optical Society of America

**OCIS Codes**

(100.7410) Image processing : Wavelets

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Holography

**Citation**

Javier Molina Vázquez, Michael Mazilu, Alan Miller, and Ian Galbraith, "Wavelet transforms for optical pulse analysis," J. Opt. Soc. Am. A **22**, 2890-2899 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-12-2890

Sort: Year | Journal | Reset

### References

- D. T. Reid, Ultrafast Photonics, A.Miller, D.T.Reid, and D.M.Finlayson, eds. (Institute of Physics, 2004), pp. 59-71.
- D. J. Kane and R. Trebino, "Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating," Opt. Lett. 18, 823-825 (1993).
- V. Wong and I. A. Walmsley, "Ultrashort-pulse characterization from dynamic spectrograms by iterative phase retrieval," J. Opt. Soc. Am. B 14, 944-949 (1997).
- C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
- L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, I. A. Walmsley, and U. Keller, "Spatially resolved amplitude and phase characterization of femtosecond optical pulses," Opt. Lett. 26, 96-98 (2001).
- P. Addison, "Beyond Fourier: wavelets make the most of data," Phys. World 3, 35-39 (2004).
- M. Farge, "Wavelet transforms and their applications to turbulence," Annu. Rev. Fluid Mech. 24, 395-457 (1992).
- P. S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance (Institute of Physics, 2002).
- M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (IEEE, 1994).
- J. Morlet, G. Arens, E. Fourgeau, and D. Giard, "Wave propagation and sampling theory--Part I: Complex signal and scattering in multilayered media," Geophysics 47, 203-221 (1982).
- J. Morlet, G. Arens, E. Fourgeau, and D. Giard, "Wave propagation and sampling theory--Part II: Sampling theory and complex waves," Geophysics 47, 222-236 (1982).
- I. Daubechies, A. Grossmann, and Y. Meyer, "Painless nonorthogonal expansions," J. Math. Phys. 27, 1271-1283 (1986).
- J. Molina Vázquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
- C. K. Chui, Wavelet Analysis and Its Applications Volume 1--An Introduction to Wavelets (Academic, 1992).
- C. Torrence and G. P. Compo, "A practical guide to wavelet analysis," Bull. Am. Meteorol. Soc. 79, 61-78 (1998).
- M. Mazilu and A. Miller, "Wavelet transformations for ultrashort pulse characterization," Proceedings of the LEOS 15th Annual Meeting (IEEE, 2002), Vol. 2, p. 592.
- J.-Z. Zhang, J. Molina Vázquez, M. Mazilu, A. Miller, and I. Galbraith, "Dispersion induced ultrafast pulse re-shaping in 1.55-µmInGaAs/InGaAsP optical amplifiers," IEEE J. Quantum Electron. 39, 1388-1393 (2003).
- J. S. Geronimo, D. P. Hardin, and P. R. Massopust, "Fractal functions and wavelet expansions based on several scaling functions," J. Approx. Theory 78, 373-401 (1994).
- It is sometimes desirable to use the phase of the wavelet transform. In our case, we found that this provided no further information and has therefore been omitted.
- Intel Pentium 4 processor with 3.0 GHz clock speed running on a Linux platform.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.