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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1563–1572

High-resolution femtosecond pulse shaping

A. M. Weiner, J. P. Heritage, and E. M. Kirschner  »View Author Affiliations

JOSA B, Vol. 5, Issue 8, pp. 1563-1572 (1988)

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The synthesis of arbitrarily shaped femtosecond pulses by spectral filtering in a temporally nondispersive grating apparatus is demonstrated. Spectral filtering is accomplished by utilizing spatially patterned masks to modify the amplitude and the phase of the optical frequency components that are spatially dispersed within the apparatus. We are able to pattern spectra over a large dynamic range (approaching 104) and with unprecedented resolution. We illustrate the power of this technique by synthesizing a number of femtosecond waveforms, including femtosecond tone bursts with terahertz repetition rates, picosecond square pulses with 100-fsec rise times, and highly complex pseudonoise bursts produced by spectral phase encoding.

© 1988 Optical Society of America

Original Manuscript: February 8, 1988
Manuscript Accepted: April 25, 1988
Published: August 1, 1988

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, "High-resolution femtosecond pulse shaping," J. Opt. Soc. Am. B 5, 1563-1572 (1988)

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  28. The relations Bδt≃ 0.44 and δfT≃ 0.44 are derived assuming Gaussian line shapes for the power spectrum and for the finest achievable spectral feature, with B, δf, T,and δt all referring to FWHM intensity widths. If, instead, the power spectrum is rectangular, then Bδt≃ 0.886, and we obtain T/δt≃ 0.5B/δf= 0.5η.
  29. In Ref. 8 a slightly different complexity measure m was introduced, defined in terms of spatial factors, such as the laser spot size at the mask, and the physical width of the spatially dispersed spectrum. The complexity measure used here, η,is defined in Eq. (4) in terms of spectral features. The relationship is η= m/(ln 2)1/2.
  30. In the present setup, encoding and decoding masks are placed adjacent to each other; in a real CDMA system the two masks would be located apart from each other at separate pulse-shaping stations. As a result, the contrast between correctly and incorrectly addressed information will be somewhat different in a real system than in the present data. The difference arises because of scattering from the edges of individual pixels on the phase masks. In a real system, frequency components impinging upon the edges of pixels will be attenuated by scattering, and decoded pulses will have narrow holes in their frequency spectra. The primary effect of these holes is to diminish the intensity of decoded pulses. When an encoding and a matching decoding mask are adjacent, however, much of the scattering is eliminated. Under the present circumstances, with length 127 M sequences and with a resolving power η= 250, we calculate that the intensity of decoded pulses would be diminished by ≃50% in a real system. The contrast in second-harmonic intensity generated by correctly and incorrectly decoded pulses would be ≃67:1, as opposed to the ratio of ≃130:1 evident in Fig. 12. For the case of high resolving power (η/P≫ 1), the distinction discussed above disappears.
  31. E. P. Ippen, C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), pp. 85–88.

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