OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.51.000306


View Full Text Article

Enhanced HTML    Acrobat PDF (1591 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-3-306


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Kempe and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9, 1158–1165 (1992). [CrossRef]
  2. M. Rosete-Aguilar, “Analytical method for calculating the electric field envelope of ultrashort pulses by approximating the wavenumber up to third order,” Appl. Opt. 49, 2463–2468 (2010). [CrossRef]
  3. F. C. Estrada-Silva, J. Garduño-Mejía, and M. Rosete-Aguilar, “Third-order dispersion effects generated by non-ideal achromatic doublets on sub-20 femtosecond pulses,” J. Mod. Opt. 58, 825–834 (2011). [CrossRef]
  4. J. L. Rayces and M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum. I: Tolerance conditions for secondary spectrum, spherochromatism and fifth-order spherical aberration,” Appl. Opt. 40, 5663–5676 (2001). [CrossRef]
  5. M. Rosete-Aguilar and J. L. Rayces, “Selection of glasses for achromatic doublets with reduced secondary spectrum. II. Application of the method for selecting pairs of glasses with reduced secondary spectrum,” Appl. Opt. 40, 5677–5692 (2001). [CrossRef]
  6. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1970).
  7. John H. Mathews and Kurtis D. Fink, “Integración numérica,” in Métodos Numéricos con MATLAB (Prentice Hall, 1999), pp. 371–432.
  8. J. C. Diels and W. Rudolph, “Femtosecond optics,” in Ultrashort Pulse Phenomena (Elsevier, 2006), pp. 61–142.
  9. Zs. Bor and Z. L. Horváth, “Distortion of a 6 fs pulse in the focus of a BK7 lens,” in Ultrafast Phenomena VIII, Vol. 55 of Springer Series in Chemical PhysicsJ. L. Martin, A. Migus, G. A. Mourous, and A. H. Zewail, eds. (Springer-Verlag, 1993).
  10. V. V. Lozovoy, Y. Andegeko, X. Zhu, and M. Dantus, “Applications of ultrashort shaped pulses in microscopy and for controlling chemical reactions,” Chem. Phys. 350, 118–124 (2008). [CrossRef]
  11. J. M. Gunn, B. W. Xu, B. W. J. M. De la Cruz, V. V. Lozovoy, and M. Dantus, “The MIIPS method for simultaneous phase measurement and compensation of femtosecond laser pulses and its role in two-photon microscopy and imaging,” Proc. SPIE 6108, 61080C (2006).
  12. Z. L. Horváth and Zs. Bor, “Behaviour of femtosecond pulses on the optical axis of a lens. Analytical description,” Opt. Commun. 108, 333–342 (1994). [CrossRef]
  13. Z. L. Horváth and Zs. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601 (2001). [CrossRef]
  14. Z. L. Horváth, J. Klebniczki, G. Kurdi, and A. P. Kovács, “Experimental investigation of the boundary wave pulse,” Opt. Commun. 239, 243–250 (2004). [CrossRef]
  15. J. L. Rayces and M. Rosete-Aguilar, “Differential equation for normal glass dispersion and evaluation of the secondary spectrum,” Appl. Opt. 38, 2028–2039 (1999). [CrossRef]
  16. J. Garduño-Mejía, A. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics,” Opt. Express 11, 2030–2040 (2003). [CrossRef]

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.

CrossCheck Deposited