Abstract

The wavelength dependence of the retardation induced by a photoelastic modulator (PEM) is a central issue in multichannel modulator-based spectroscopic ellipsometry and reflectance difference spectroscopy (RDS), where the optical signal is detected simultaneously at different wavelengths. Here we present a refined analysis of the modulator crystal’s retardation and its effect on the signal quality. Two retardation correction schemes that take into account the actual wavelength dependence of the stress-optic coefficient are introduced. It is demonstrated experimentally that both methods provide a better correction than the procedure currently used in multichannel RDS. We define quality factors to evaluate the actual performance of the multichannel detection system as compared with a wavelength adaptive single-channel experiment. These quality factors thus provide a useful guideline for choosing the appropriate PEM retardation or reference wavelength in a multichannel experiment.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
    [Crossref]
  2. D. E. Aspnes and A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956-1959 (1985).
    [Crossref] [PubMed]
  3. D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible-near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498-1506 (1985).
    [Crossref]
  4. J. C. Kemp, “Piezo-optical birefringence modulators: new use for a long-known effect,” J. Opt. Soc. Am. 59, 950-954 (1969).
  5. D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
    [Crossref]
  6. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
    [Crossref]
  7. C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
    [Crossref]
  8. P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
    [Crossref]
  9. O. Acher and B. Drévillon, “A reflectance anisotropy spectrometer for real-time measurements,” Rev. Sci. Instrum. 63, 5332-5339 (1992).
    [Crossref]
  10. C. J. Canit and J. Badoz, “New design for a photoelastic modulator,” Appl. Opt. 22, 592-594 (1983).
    [Crossref] [PubMed]
  11. F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892-900 (1983).
    [Crossref]
  12. G. E. Jellison, Jr., and F. A. Modine, “Accurate calibration of a photo-elastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231-241 (1989).
  13. G. E. Jellison, Jr., and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959-974 (1990).
    [Crossref] [PubMed]
  14. G. E. Jellison, Jr., and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184-8189 (1997).
    [Crossref]
  15. J. Badoz, M. P. Silverman, and J. C. Canit, “A new method of a photoelastic modulator with distributed birefringence,” Proc. SPIE 1166, 478-488 (1989).
  16. J. Badoz, M. P. Silverman, and J. C. Canit, “Wave propagation through a medium with static and dynamic birefringence: theory of the photoelastic modulator,” J. Opt. Soc. Am. A 7, 672-682 (1990).
    [Crossref]
  17. F. A. Modine and G. E. Jellison, Jr., “Errors in polarization measurements due to static retardation in photoelastic modulators,” Appl. Phys. Commun. 12, 121-139 (1993).
  18. D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
    [Crossref]
  19. Dispersion equations, http://www.cvilaser.com/Common/PDFs/Index_of_Refraction.pdf.
  20. T. C. Oakberg, “Relative variation of stress-optic coefficient with wavelength in fused silica and calcium fluoride,” Proc. SPIE 3754, 226-234 (1999).
    [Crossref]
  21. J-K. Hansen, “Electronic and optical surface properties of noble metals studied by reflection anisotropy spectroscopy,” Ph.D. dissertation (University of Trondheim, 2000).
  22. M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
    [Crossref]

2005 (3)

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
[Crossref]

M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
[Crossref]

2001 (1)

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

1999 (1)

T. C. Oakberg, “Relative variation of stress-optic coefficient with wavelength in fused silica and calcium fluoride,” Proc. SPIE 3754, 226-234 (1999).
[Crossref]

1997 (1)

1995 (1)

D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
[Crossref]

1993 (1)

F. A. Modine and G. E. Jellison, Jr., “Errors in polarization measurements due to static retardation in photoelastic modulators,” Appl. Phys. Commun. 12, 121-139 (1993).

1992 (1)

O. Acher and B. Drévillon, “A reflectance anisotropy spectrometer for real-time measurements,” Rev. Sci. Instrum. 63, 5332-5339 (1992).
[Crossref]

1990 (2)

1989 (3)

G. E. Jellison, Jr., and F. A. Modine, “Accurate calibration of a photo-elastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231-241 (1989).

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
[Crossref]

J. Badoz, M. P. Silverman, and J. C. Canit, “A new method of a photoelastic modulator with distributed birefringence,” Proc. SPIE 1166, 478-488 (1989).

1988 (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

1985 (2)

D. E. Aspnes and A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956-1959 (1985).
[Crossref] [PubMed]

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible-near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498-1506 (1985).
[Crossref]

1983 (2)

1969 (1)

Acher, O.

O. Acher and B. Drévillon, “A reflectance anisotropy spectrometer for real-time measurements,” Rev. Sci. Instrum. 63, 5332-5339 (1992).
[Crossref]

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

D. E. Aspnes and A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956-1959 (1985).
[Crossref] [PubMed]

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible-near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498-1506 (1985).
[Crossref]

Badoz, J.

Bigan, E.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
[Crossref]

Canit, C. J.

Canit, J. C.

D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
[Crossref]

J. Badoz, M. P. Silverman, and J. C. Canit, “Wave propagation through a medium with static and dynamic birefringence: theory of the photoelastic modulator,” J. Opt. Soc. Am. A 7, 672-682 (1990).
[Crossref]

J. Badoz, M. P. Silverman, and J. C. Canit, “A new method of a photoelastic modulator with distributed birefringence,” Proc. SPIE 1166, 478-488 (1989).

Cole, R. J.

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

Drévillon, B.

O. Acher and B. Drévillon, “A reflectance anisotropy spectrometer for real-time measurements,” Rev. Sci. Instrum. 63, 5332-5339 (1992).
[Crossref]

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
[Crossref]

Farrell, T.

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Ferrell, T.

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

Florez, L. T.

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

Gaignebet, E.

D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
[Crossref]

Gruzalski, G. R.

Hansen, J-K.

J-K. Hansen, “Electronic and optical surface properties of noble metals studied by reflection anisotropy spectroscopy,” Ph.D. dissertation (University of Trondheim, 2000).

Harbison, J. P.

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

Harrison, P.

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Hohage, M.

M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
[Crossref]

Jellison, G. E.

G. E. Jellison, Jr., and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184-8189 (1997).
[Crossref]

F. A. Modine and G. E. Jellison, Jr., “Errors in polarization measurements due to static retardation in photoelastic modulators,” Appl. Phys. Commun. 12, 121-139 (1993).

G. E. Jellison, Jr., and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959-974 (1990).
[Crossref] [PubMed]

G. E. Jellison, Jr., and F. A. Modine, “Accurate calibration of a photo-elastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231-241 (1989).

F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892-900 (1983).
[Crossref]

Kaspari, C.

C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
[Crossref]

Kemp, J. C.

Martin, D. S.

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

Maunder, A.

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Modine, F. A.

G. E. Jellison, Jr., and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184-8189 (1997).
[Crossref]

F. A. Modine and G. E. Jellison, Jr., “Errors in polarization measurements due to static retardation in photoelastic modulators,” Appl. Phys. Commun. 12, 121-139 (1993).

G. E. Jellison, Jr., and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959-974 (1990).
[Crossref] [PubMed]

G. E. Jellison, Jr., and F. A. Modine, “Accurate calibration of a photo-elastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231-241 (1989).

F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892-900 (1983).
[Crossref]

Oakberg, T. C.

T. C. Oakberg, “Relative variation of stress-optic coefficient with wavelength in fused silica and calcium fluoride,” Proc. SPIE 3754, 226-234 (1999).
[Crossref]

Pristovsek, M.

C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
[Crossref]

Richter, W.

C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
[Crossref]

Silverman, M. P.

J. Badoz, M. P. Silverman, and J. C. Canit, “Wave propagation through a medium with static and dynamic birefringence: theory of the photoelastic modulator,” J. Opt. Soc. Am. A 7, 672-682 (1990).
[Crossref]

J. Badoz, M. P. Silverman, and J. C. Canit, “A new method of a photoelastic modulator with distributed birefringence,” Proc. SPIE 1166, 478-488 (1989).

Smith, C. I.

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Studna, A. A.

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

D. E. Aspnes and A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956-1959 (1985).
[Crossref] [PubMed]

Sun, L. D.

M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
[Crossref]

Weightman, P.

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Yang, D.

D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
[Crossref]

Zeppenfeld, P.

M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
[Crossref]

Appl. Opt. (3)

Appl. Phys. A (1)

M. Hohage, L. D. Sun, and P. Zeppenfeld, “Reflectance difference spectroscopy--a powerful tool to study adsorption and growth,” Appl. Phys. A 80, 1005-1010 (2005).
[Crossref]

Appl. Phys. Commun. (1)

F. A. Modine and G. E. Jellison, Jr., “Errors in polarization measurements due to static retardation in photoelastic modulators,” Appl. Phys. Commun. 12, 121-139 (1993).

J. Opt. (Paris) (1)

D. Yang, J. C. Canit, and E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. (Paris) 26, 151-159 (1995).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. A (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327-1332 (1988).
[Crossref]

J. Vac. Sci. Technol. B (1)

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible-near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498-1506 (1985).
[Crossref]

Meas. Sci. Technol. (1)

P. Harrison, T. Farrell, A. Maunder, C. I. Smith, and P. Weightman, “A rapid reflectance anisotropy spectrometer,” Meas. Sci. Technol. 12, 2185-2191 (2001).
[Crossref]

Phys. Rev. Lett. (1)

D. E. Aspnes and A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956-1959 (1985).
[Crossref] [PubMed]

Phys. Status Solidi B (1)

C. Kaspari, M. Pristovsek, and W. Richter, “A fast reflectance anisotropy spectrometer for in situ growth monitoring,” Phys. Status Solidi B 242, 2561-2569 (2005).
[Crossref]

Proc. SPIE (3)

G. E. Jellison, Jr., and F. A. Modine, “Accurate calibration of a photo-elastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231-241 (1989).

J. Badoz, M. P. Silverman, and J. C. Canit, “A new method of a photoelastic modulator with distributed birefringence,” Proc. SPIE 1166, 478-488 (1989).

T. C. Oakberg, “Relative variation of stress-optic coefficient with wavelength in fused silica and calcium fluoride,” Proc. SPIE 3754, 226-234 (1999).
[Crossref]

Rep. Prog. Phys. (1)

P. Weightman, D. S. Martin, R. J. Cole, and T. Ferrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251-1341 (2005).
[Crossref]

Rev. Sci. Instrum. (2)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65-77 (1989).
[Crossref]

O. Acher and B. Drévillon, “A reflectance anisotropy spectrometer for real-time measurements,” Rev. Sci. Instrum. 63, 5332-5339 (1992).
[Crossref]

Other (2)

J-K. Hansen, “Electronic and optical surface properties of noble metals studied by reflection anisotropy spectroscopy,” Ph.D. dissertation (University of Trondheim, 2000).

Dispersion equations, http://www.cvilaser.com/Common/PDFs/Index_of_Refraction.pdf.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Index of refraction n of fused silica as a function of wavelength. (b) Wavelength dependence of the refractive index n 3 ( λ ) n 633 3 (open circles) and the stress optic coefficient C ( λ ) C 633 (solid curve), both normalized to a reference wavelength λ 0 = 633 nm .

Fig. 2
Fig. 2

Relationship between the retardation amplitude A and the ratio J 1 ( A ) J 3 ( A ) . The circle marks the usual set point A = A 0 = 137.8 ° for which J 0 ( A ) = 0 .

Fig. 3
Fig. 3

Quality factors f 1 (solid curves) and f 2 (dashed curves) as defined in Eq. (17), (a) as a function of the detected wavelength λ for two reference wavelengths λ 0 = 300 and 700 nm , respectively, and (b) as a function of the reference wavelength λ 0 for two fixed detected wavelengths λ = 300 and 700 nm , respectively.

Fig. 4
Fig. 4

Correction of the PEM retardation amplitude according to the wavelength correction [Eq. (9), open squares], improved wavelength correction [Eq. (12), open circles], and voltage correction [Eq. (15), open triangles] for a reference wavelength λ 0 = 250 nm .

Fig. 5
Fig. 5

Schematic of the two-channel RDS setup.

Fig. 6
Fig. 6

(a) RD signals recorded with the two-channel setup. The sample is a clean Cu ( 110 ) surface. Channel one (open squares) is the RD spectrum obtained by linearly scanning the photon energy between 1.5 and 5 eV and adapting the PEM control voltage accordingly. Channel two (open circles) is the RD signal obtained at a fixed photon energy of 2.06 eV but with a varying PEM control voltage as adjusted for channel one. (b) RDS data of channel two before (open circles) and after simple wavelength or voltage correction (open squares and dotted curve, respectively). The smooth solid curves through the data points are calculated on the basis of Eqs. (17, 9) assuming a constant RD intensity Δ r r (horizontal line through the voltage corrected data).

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

Δ r r = 2 r x r y r x + r y .
I ( t ) = I 0 [ 1 + I s sin δ ( t ) + I c cos δ ( t ) ] .
sin δ ( t ) = 2 J 1 ( A ) sin ω t + 2 J 3 ( A ) sin 3 ω t +
cos δ ( t ) = J 0 ( A ) + 2 J 2 ( A ) cos 2 ω t + 2 J 4 ( A ) cos 4 ω t + ,
I ( t ) = I 0 [ 1 + I c J 0 ( A ) + 2 I s J 1 ( A ) sin ω t + 2 I c J 2 ( A ) cos 2 ω t + 2 I s J 3 ( A ) sin 3 ω t + ] .
S 0 = I 0 [ 1 + I c J 0 ( A ) ] ,
S 1 = 2 I 0 I s J 1 ( A ) ,
S 2 = 2 I 0 I c J 2 ( A ) ,
S 3 = 2 I 0 I s J 3 ( A ) .
I s = 1 2 J 1 ( A ) S 1 S 0 ,
I c = 1 2 J 2 ( A ) S 2 S 0 .
A = 2 π d λ Δ n = 2 π d λ C P ( V ) = 2 π d λ n 3 2 ( q 12 q 11 ) P ( V ) ,
A ( λ ) 2 π d λ P ( V ) .
A ( λ , λ 0 ) = λ 0 λ A 0 .
C λ C 633 = λ 1.1056 λ 66.76 .
A ( λ ) 2 π d λ C ( λ ) V .
A ( λ , λ 0 ) = λ 0 C ( λ ) λ C ( λ 0 ) A 0 .
A 0 2 π d λ C ( λ ) V 0 ( λ ) .
A ( λ ) 2 π d λ C ( λ ) V 0 ( λ 0 ) ,
A ( λ , λ 0 ) = V 0 ( λ 0 ) V 0 ( λ ) A 0 .
S 1 S 3 = J 1 ( A ) J 3 ( A ) .
f 1 ( λ , λ 0 ) = J 1 [ A ( λ , λ 0 ) ] J 1 ( A 0 ) ,
f 2 ( λ , λ 0 ) = J 2 [ A ( λ , λ 0 ) ] J 2 ( A 0 )

Metrics