Abstract

We exploit efficient dispersion relations, which were developed for terahertz spectroscopy, to show their validity for testing linear and nonlinear optical spectra. As an example, we deal with the measured data for complex reflectivity of a KCl crystal and complex nonlinear susceptibility of a polysilane. It is suggested that the spectral data presented in the literature both for the KCl and the polysilane are consistent with the presented spectra analysis method.

© 2007 Optical Society of America

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References

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  1. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  2. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, Berlin, 2005).
  3. E. Gornov, E. M. Vartiainen, and K.-E. Peiponen, "Comparison of subtractive Kramers-Kronig analysis and maximum entropy model in resolving phase from finite spectral range reflectance data," Appl. Opt. 45, 6519-6524 (2006).
    [CrossRef] [PubMed]
  4. E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, "Numerical phase correction method for terahertz time-domain reflection spectroscopy," J. Appl. Phys. 96, 4171-4175 (2004).
    [CrossRef]
  5. V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
    [CrossRef]
  6. K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, "Testing the validity of terahertz reflection spectra by dispersion relations," Phys. Rev. B 72, 245109 (2005).
    [CrossRef]
  7. E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
    [CrossRef]
  8. H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, "Dispersion relation in the third-order electric susceptibility for polysilane film," Phys. Rev. Lett. 70, 3724-3727 (1993).
    [CrossRef] [PubMed]
  9. V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane," J. Chem. Phys. 119, 11095-11098 (2003).
    [CrossRef]
  10. K. F. Palmer, M. Z. Williams, and B. A. Budde, "Multiply subtractive Kramers-Kronig analysis of optical data," Appl. Opt. 37, 2660-2673 (1998).
    [CrossRef]

2006 (2)

2005 (2)

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, "Testing the validity of terahertz reflection spectra by dispersion relations," Phys. Rev. B 72, 245109 (2005).
[CrossRef]

2004 (1)

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, "Numerical phase correction method for terahertz time-domain reflection spectroscopy," J. Appl. Phys. 96, 4171-4175 (2004).
[CrossRef]

2003 (1)

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane," J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

1998 (1)

1993 (1)

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, "Dispersion relation in the third-order electric susceptibility for polysilane film," Phys. Rev. Lett. 70, 3724-3727 (1993).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

J. Appl. Phys. (1)

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, "Numerical phase correction method for terahertz time-domain reflection spectroscopy," J. Appl. Phys. 96, 4171-4175 (2004).
[CrossRef]

J. Chem. Phys. (1)

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane," J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

Phys. Rev. B (2)

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, "Testing the validity of terahertz reflection spectra by dispersion relations," Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, "Dispersion relation in the third-order electric susceptibility for polysilane film," Phys. Rev. Lett. 70, 3724-3727 (1993).
[CrossRef] [PubMed]

Other (2)

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, Berlin, 2005).

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Figures (3)

Fig. 1
Fig. 1

(a) Real and (b) imaginary parts of complex function f, and p is the complex reflectivity r of KCl: solid curve, experimental results; dashed curve, data inverted. The anchor point was 24   eV .

Fig. 2
Fig. 2

(a) Real and (b) imaginary parts of complex function f, and p is the complex reflectivity r of KCl for a narrow spectral range: solid curve, experimental results; dashed curve, data inverted. The anchor point was 15 .4   eV .

Fig. 3
Fig. 3

(a) Real and (b) imaginary parts of complex function f, and p is the complex third-order nonlinear susceptibility χ ( 3 ) : solid curve, experimental results; dashed curve, data inverted. The anchor point was 1.77   eV .

Equations (3)

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Re { f ( ω ) } Re { f ( ω 1 ) } + ( ω 2 ω 1 2 ) 2 π P × ω a ω b ω I m { f ( ω ) } ( ω 2 ω 2 ) ( ω 2 ω 1 2 ) d ω ,
I m { f ( ω ) } ω I m { f ( ω 1 ) } ω 1 + ( ω 2 ω 1 2 ) 2 π P × ω a ω b Re { f ( ω ) } ( ω 2 ω 2 ) ( ω 2 ω 1 2 ) d ω ,
f ( ω ) = [ p ( ω ) p ( ω a ) ] [ p ( ω ) p * ( ω a ) ] [ p ( ω ) p ( ω b ) ] × [ p ( ω ) p * ( ω b ) ] = [ p 2 ( ω ) 2 Re { p ( ω a ) } p ( ω ) + | p ( ω a ) | 2 ] × [ p 2 ( ω ) 2 Re { p ( ω b ) } p ( ω ) + | p ( ω b ) | 2 ] .

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