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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 3 — Jan. 20, 2012
  • pp: 306–315

Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses

L. García-Martínez, M. Rosete-Aguilar, and J. Garduño-Mejia  »View Author Affiliations

Applied Optics, Vol. 51, Issue 3, pp. 306-315 (2012)

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We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet.

© 2012 Optical Society of America

OCIS Codes
(220.1010) Optical design and fabrication : Aberrations (global)
(220.3630) Optical design and fabrication : Lenses
(320.0320) Ultrafast optics : Ultrafast optics
(320.1590) Ultrafast optics : Chirping
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5550) Ultrafast optics : Pulses

ToC Category:
Ultrafast Optics

Original Manuscript: July 6, 2011
Revised Manuscript: October 4, 2011
Manuscript Accepted: October 10, 2011
Published: January 16, 2012

L. García-Martínez, M. Rosete-Aguilar, and J. Garduño-Mejia, "Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses," Appl. Opt. 51, 306-315 (2012)

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