## Numerical evaluation of truncated Kramers–Kronig transforms

JOSA B, Vol. 24, Issue 7, pp. 1589-1595 (2007)

http://dx.doi.org/10.1364/JOSAB.24.001589

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### Abstract

The truncated Kramers–Kronig transform, used widely in the analysis of optical data, is recast into a form that avoids the need to evaluate a Cauchy principal-value integral. A specialized Gaussian quadrature involving the weight function

© 2007 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(160.4760) Materials : Optical properties

**ToC Category:**

Physical Optics

**History**

Original Manuscript: December 11, 2006

Revised Manuscript: March 5, 2007

Manuscript Accepted: March 22, 2007

Published: June 15, 2007

**Citation**

Frederick W. King, "Numerical evaluation of truncated Kramers-Kronig transforms," J. Opt. Soc. Am. B **24**, 1589-1595 (2007)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-7-1589

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### References

- K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1999).
- D. E. Aspnes, "The accurate determination of optical properties by ellipsometry," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 89-112.
- V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).
- V. Lucarini and K.-E. Peiponen, "Verification of generalized Kramers-Kronig relations and sum rules on experimental data of third harmonic generation susceptibility on polymer," J. Chem. Phys. 119, 620-627 (2003). [CrossRef]
- V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive Kramers-Krönig relations for arbitrary-order harmonic generation susceptibilities," Opt. Commun. 218, 409-414 (2003). [CrossRef]
- A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas (Prentice Hall, 1966).
- J. E. Bertie and S. L. Zhang, "Infrared intensities of liquids. IX. The Kramers-Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms," Can. J. Chem. 70, 520-531 (1992). [CrossRef]
- V. I. Krylov and A. A. Pal'cev, "Numerical integration of functions having logarithmic and power singularities," Vestsi Akad. Navuk BSSR, Ser. Fiz.-Tekh. Navuk 14-23 (1963).
- B. Danloy, "Numerical construction of Gaussian quadrature formulas for ∫01(−Logx)∙xα∙f(x)∙dx and ∫01Em(x)∙f(x)∙dx," Math. Comput. 27, 861-869 (1973).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77, 2nd ed. (Cambridge U. Press, 1992). [PubMed]
- R. A. Sack and A. F. Donovan, "An algorithm for Gaussian quadrature given modified moments," Numer. Math. 18, 465-478 (1972). [CrossRef]
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
- E. D. Palik, "Gallium arsenide (GaAs)," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 429.
- F. W. King, "Efficient numerical approach to the evaluation of Kramers-Kronig transforms," J. Opt. Soc. Am. B 19, 2427-2436 (2002). [CrossRef]

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