Gauss-Legendre quadrature method used to evaluate the electric field envelope of ultrashort pulses in the focal region of lenses

L. García-Martínez; M. Rosete-Aguilar; J. Garduño-Mejía

doi:10.1117/12.902177

25 October 2011 Gauss-Legendre quadrature method used to evaluate the electric field envelope of ultrashort pulses in the focal region of lenses

L. García-Martínez, M. Rosete-Aguilar, J. Garduño-Mejía

Author Affiliations +

Proceedings Volume 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World; 80113J (2011) https://doi.org/10.1117/12.902177
Event: International Commission for Optics (ICO 22), 2011, Puebla, Mexico

Abstract

We analyze the Gaussian temporal envelope of pulses with an initial duration of 10fs and a carrier wavelength of 810nm along the optical axis of an achromatic doublet designed in the IR region with numerical aperture 0.15 and focal length of 40mm. 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 GVD is not negligible for 10fs pulses @810nm propagating through the low numerical aperture doublet and its effect is more important than the propagation time difference, PTD. This last effect, however, is also significant.

Citation Download Citation

L. García-Martínez, M. Rosete-Aguilar, and J. Garduño-Mejía "Gauss-Legendre quadrature method used to evaluate the electric field envelope of ultrashort pulses in the focal region of lenses", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 80113J (25 October 2011); https://doi.org/10.1117/12.902177

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