Abstract

A succinct analysis of normal-incidence reflectometers for surface anisotropy, based on the Jones-matrix formalism, is performed. In particular, two relevant configurations with and without analyzers are compared and discussed. The latter is found to be more user friendly than the former, since most errors vanish to the first order of approximation. Therefore the optical alignment is greatly simplified. On the other hand, this configuration does not yield complete physical information. We discuss how this drawback can be circumvented in surface studies by use of the three-layer model and a Kramers–Kronig analysis.

© 2000 Optical Society of America

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References

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  1. P. Chiaradia, R. Del Sole, “Differential-reflectance spectroscopy and reflectance-anisotropy spectroscopy on semiconductor surfaces,” Surf. Rev. Lett. 6, 517–528 (1999), and references therein.
  2. J. F. McGilp, “Epioptics: linear and nonlinear optical spectroscopy of surfaces and interfaces,” J. Phys. Condens. Matter 2, 7985–8006 (1990).
    [CrossRef]
  3. See, for example, W. Ho, “High resolution energy loss spectroscopy,” in Physical Methods of Chemistry, 2nd. ed., B. W. Rossiter, R. C. Baetzold, eds., Vol. 9 of Investigations of Surfaces and Interfaces, Part A (Wiley, New York, 1993); also U. Del Pennino, M. G. Betti, C. Mariani, S. Nannarone, C. M. Bertoni, I. Abbati, L. Braicovich, A. Rizzi, “Azimuthal dependence of the vibrational excitation in Si(111)2 × 1,” Phys. Rev. B 39, 10380–10383 (1986).
  4. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).
  5. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998); M. Schubert, T. Hofmann, B. Rheinlaender, I. Pietzonka, T. Sass, V. Gottschalch, J. Woollam, “Near-band-gap CuPt-order-induced birefringence in Al0.48Ga0.52InP2,” Phys. Rev. B 60, 16618–16634 (1999).
  6. M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).
  7. D. E. Aspnes, A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 17, 1956–1959 (1985).
    [CrossRef]
  8. V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).
  9. D. E. Aspnes, J. P. Harbison, A. A. Studna, 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]
  10. J. C. Kemp, “Piezo-optical birefringence modulators: new use for a long-known effect,” J. Opt. Soc. Am. 59, 950–954 (1969).
  11. R. M. A. Azzam, “Perpendicular-incidence photometric ellipsometry,” J. Opt. (Paris) 12, 317–321 (1981).
    [CrossRef]
  12. J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
    [CrossRef]
  13. See, for example, R. Del Sole, “Reflectance spectroscopy: theory,” in Photonic Probes of Surfaces, Vol. 2 of Electromagnetic Waves: Recent Developments in Research, P. Halevi, ed. (North-Holland, Amsterdam, 1995).
  14. M. Rohlfing, S. G. Louie, “Excitons and optical spectrum of the Si(111) – 2 × 1 surface,” Phys. Rev. Lett. 83, 856–859 (1999).
    [CrossRef]
  15. D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
    [CrossRef]
  16. V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
    [CrossRef]

1999 (3)

P. Chiaradia, R. Del Sole, “Differential-reflectance spectroscopy and reflectance-anisotropy spectroscopy on semiconductor surfaces,” Surf. Rev. Lett. 6, 517–528 (1999), and references therein.

M. Rohlfing, S. G. Louie, “Excitons and optical spectrum of the Si(111) – 2 × 1 surface,” Phys. Rev. Lett. 83, 856–859 (1999).
[CrossRef]

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

1998 (1)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998); M. Schubert, T. Hofmann, B. Rheinlaender, I. Pietzonka, T. Sass, V. Gottschalch, J. Woollam, “Near-band-gap CuPt-order-induced birefringence in Al0.48Ga0.52InP2,” Phys. Rev. B 60, 16618–16634 (1999).

1990 (1)

J. F. McGilp, “Epioptics: linear and nonlinear optical spectroscopy of surfaces and interfaces,” J. Phys. Condens. Matter 2, 7985–8006 (1990).
[CrossRef]

1988 (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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]

1986 (1)

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

1985 (2)

D. E. Aspnes, A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 17, 1956–1959 (1985).
[CrossRef]

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

1981 (1)

R. M. A. Azzam, “Perpendicular-incidence photometric ellipsometry,” J. Opt. (Paris) 12, 317–321 (1981).
[CrossRef]

1971 (1)

J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
[CrossRef]

1969 (1)

1966 (1)

M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).

Aspnes, D. E.

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 17, 1956–1959 (1985).
[CrossRef]

J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Perpendicular-incidence photometric ellipsometry,” J. Opt. (Paris) 12, 317–321 (1981).
[CrossRef]

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

Bashara, N. M.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

Berkovits, V. L.

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

Bhat, R.

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Cardona, M.

M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).

Chiaradia, P.

P. Chiaradia, R. Del Sole, “Differential-reflectance spectroscopy and reflectance-anisotropy spectroscopy on semiconductor surfaces,” Surf. Rev. Lett. 6, 517–528 (1999), and references therein.

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

Del Sole, R.

P. Chiaradia, R. Del Sole, “Differential-reflectance spectroscopy and reflectance-anisotropy spectroscopy on semiconductor surfaces,” Surf. Rev. Lett. 6, 517–528 (1999), and references therein.

See, for example, R. Del Sole, “Reflectance spectroscopy: theory,” in Photonic Probes of Surfaces, Vol. 2 of Electromagnetic Waves: Recent Developments in Research, P. Halevi, ed. (North-Holland, Amsterdam, 1995).

Florez, L. T.

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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]

Goletti, C.

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

Gordeeva, A. B.

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

Harbison, J. P.

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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]

Ho, W.

See, for example, W. Ho, “High resolution energy loss spectroscopy,” in Physical Methods of Chemistry, 2nd. ed., B. W. Rossiter, R. C. Baetzold, eds., Vol. 9 of Investigations of Surfaces and Interfaces, Part A (Wiley, New York, 1993); also U. Del Pennino, M. G. Betti, C. Mariani, S. Nannarone, C. M. Bertoni, I. Abbati, L. Braicovich, A. Rizzi, “Azimuthal dependence of the vibrational excitation in Si(111)2 × 1,” Phys. Rev. B 39, 10380–10383 (1986).

Kelso, S. M.

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Kemp, J. C.

Logan, R. A.

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Louie, S. G.

M. Rohlfing, S. G. Louie, “Excitons and optical spectrum of the Si(111) – 2 × 1 surface,” Phys. Rev. Lett. 83, 856–859 (1999).
[CrossRef]

Makarenko, I. V.

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

McGilp, J. F.

J. F. McGilp, “Epioptics: linear and nonlinear optical spectroscopy of surfaces and interfaces,” J. Phys. Condens. Matter 2, 7985–8006 (1990).
[CrossRef]

McIntyre, J. D. E.

J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
[CrossRef]

Minashvili, T. A.

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

Paget, D.

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

Pollak, F. H.

M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).

Rohlfing, M.

M. Rohlfing, S. G. Louie, “Excitons and optical spectrum of the Si(111) – 2 × 1 surface,” Phys. Rev. Lett. 83, 856–859 (1999).
[CrossRef]

Safarov, V. I.

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

Schubert, M.

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998); M. Schubert, T. Hofmann, B. Rheinlaender, I. Pietzonka, T. Sass, V. Gottschalch, J. Woollam, “Near-band-gap CuPt-order-induced birefringence in Al0.48Ga0.52InP2,” Phys. Rev. B 60, 16618–16634 (1999).

Shaklee, K. L.

M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).

Studna, A. A.

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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, A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 17, 1956–1959 (1985).
[CrossRef]

J. Appl. Phys. (1)

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlGaAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

J. Opt. (Paris) (1)

R. M. A. Azzam, “Perpendicular-incidence photometric ellipsometry,” J. Opt. (Paris) 12, 317–321 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Condens. Matter (1)

J. F. McGilp, “Epioptics: linear and nonlinear optical spectroscopy of surfaces and interfaces,” J. Phys. Condens. Matter 2, 7985–8006 (1990).
[CrossRef]

J. Phys. Soc. Jpn (1)

M. Cardona, F. H. Pollak, K. L. Shaklee, “Electroreflectance in semiconductors,” J. Phys. Soc. Jpn, Suppl. 21, 89–94 (1966).

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

D. E. Aspnes, J. P. Harbison, A. A. Studna, 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]

Phys. Rev. Lett. (2)

D. E. Aspnes, A. A. Studna, “Anisotropies in the above-band-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 17, 1956–1959 (1985).
[CrossRef]

M. Rohlfing, S. G. Louie, “Excitons and optical spectrum of the Si(111) – 2 × 1 surface,” Phys. Rev. Lett. 83, 856–859 (1999).
[CrossRef]

Solid State Commun. (1)

V. L. Berkovits, I. V. Makarenko, T. A. Minashvili, V. I. Safarov, “Optical transitions on GaAs(110) surface,” Solid State Commun. 56, 449–450 (1985); V. L. Berkovits, V. A. Kiselev, V. I. Safarov, “Optical spectroscopy of (110) surfaces of III–V semiconductors,” Surf. Sci. 211/212, 489–502 (1989).

Surf. Rev. Lett. (1)

P. Chiaradia, R. Del Sole, “Differential-reflectance spectroscopy and reflectance-anisotropy spectroscopy on semiconductor surfaces,” Surf. Rev. Lett. 6, 517–528 (1999), and references therein.

Surf. Sci. (2)

J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
[CrossRef]

V. L. Berkovits, P. Chiaradia, D. Paget, A. B. Gordeeva, C. Goletti, “Origin of the optical anisotropy of GaAs(001),” Surf. Sci. 441, 26–32 (1999).
[CrossRef]

Thin Solid Films (1)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998); M. Schubert, T. Hofmann, B. Rheinlaender, I. Pietzonka, T. Sass, V. Gottschalch, J. Woollam, “Near-band-gap CuPt-order-induced birefringence in Al0.48Ga0.52InP2,” Phys. Rev. B 60, 16618–16634 (1999).

Other (3)

See, for example, W. Ho, “High resolution energy loss spectroscopy,” in Physical Methods of Chemistry, 2nd. ed., B. W. Rossiter, R. C. Baetzold, eds., Vol. 9 of Investigations of Surfaces and Interfaces, Part A (Wiley, New York, 1993); also U. Del Pennino, M. G. Betti, C. Mariani, S. Nannarone, C. M. Bertoni, I. Abbati, L. Braicovich, A. Rizzi, “Azimuthal dependence of the vibrational excitation in Si(111)2 × 1,” Phys. Rev. B 39, 10380–10383 (1986).

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

See, for example, R. Del Sole, “Reflectance spectroscopy: theory,” in Photonic Probes of Surfaces, Vol. 2 of Electromagnetic Waves: Recent Developments in Research, P. Halevi, ed. (North-Holland, Amsterdam, 1995).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the first RAS configuration (see the text). The second configuration is obtained by omitting the analyzer. Standard instruments, such as the source, monochromator, and detector, are not shown.

Fig. 2
Fig. 2

Reflectance anisotropy spectra of a test sample [oxidized Si(110) surface] recorded with the experimental setup including the analyzer (configuration A) and with the same setup in which the analyzer has been omitted (configuration B). In the first case both the real and the imaginary parts of Δr/ r [see Eqs. (28)] are measured. It is seen that the spectrum labeled Re of configuration A is essentially the same as the spectrum recorded with configuration B.

Equations (29)

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E=Ex expjδxEy expjδy
T=T11T12T21T22,
E0xE0y=T11T12T21T22EixEiy.
cos α-sin αsin αcos αT100T2cos αsin α-sin αcos α.
E=1i,
100ap,
cos ΔPsin ΔP-sin ΔPcos ΔP,
E=1iap-ΔP.
exp-2πiλ nsd00exp-2πiλ n0d=exp-iϕ100exp-iϕ2=exp-iϕ1100exp-iϕ=exp-iϕ1exp-i ϕ2expi ϕ200exp-i ϕ2,
φt=2πλ dnst-n0=2πλ dφm sin ωt.
φt=π sin ωt.
cosφ2+i cos 2ϑ sinφ2i sin 2ϑ sinφ2i sin 2ϑ sinφ2cosφ2-i cos 2ϑ sinφ2.
cosφ2+icos 2ϑ-2ΔM sin 2ϑsinφ2isin 2ϑ+2ΔM cos 2ϑsinφ2isin 2ϑ+2ΔM cos 2ϑsinφ2cosφ2-icos 2ϑ-2ΔM sin 2ϑsinφ2.
r100r2,
r1+Δr2r001-Δr2r.
r1+Δr2rcos 2γsin 2γ Δr2rsin 2γ Δr2r1-Δr2rcos 2γ.
r1+Δr2rcos 2γ-2Δγ sin 2γsin 2γ+2Δγ cos 2γΔr2rsin 2γ+2Δγ cos 2γΔr2r1-Δr2rcos 2γ-2Δγ sin 2γ.
100apcos αsin α-sin αcos α=100ap121-ΔA1+ΔA-1-ΔA1-ΔA=121-ΔA1+ΔA-iapiap,
expi δ200exp-i δ21+i δ2001-i δ2,
cos ϑ-sin ϑsin ϑcos ϑ1+i δ2001-i δ2cos ϑsin ϑ-sin ϑcos ϑ=1+FcFsFs1-Fc,
E=121-ΔA1+ΔA-iapiap1+Fc2Fs2Fs21-Fc2×1+Δr2r001-Δr2r1+Fc1Fs1Fs11-Fc1×cosφ2-2iΔM sinφ2i sinφ2i sinφ2cosφ2+2iΔM sinφ2×1iap-ΔP,
Ex=12cosφ21+Δr2r+Fc1+Fc2-ΔA+Fs2+Fs1+iap-ΔP+i sinφ2-2ΔM+iap-ΔP+1-Δr2r-Fc1-Fc2+Fs2+Fs1+ΔA,
Ey=12 iap-cosφ2+i sinφ2.
I  121-2ΔM+ΔP+cos φReΔrr+2ΔM-ΔA+sin φImΔrr-i2Fc1-i2Fc2.
I  121+2ΔM-ΔA+cos φReΔrr-2ΔM+ΔP+sin φImΔrr+2ap-i2Fs1-i2Fs2.
E=1+Fc2Fs2Fs21-Fc21+Δr2r001-Δr2r1+Fc1Fs1Fs11-Fc1×cosφ2-2iΔM sinφ2i sinφ2i sinφ2cosφ2+2iΔM sinφ21iap-ΔP=cosφ2-2iΔM sinφ2+i sinφ2iap-ΔP+Δr2rcosφ2i sinφ2+cosφ2iap-ΔP-i Δr2r sinφ2,
I  1+cos φ ReΔrr.
Δrr=-4πidnaλΔεs1-εb,
ReΔrr=4πdnaλΔεs1-εb+Δεsεb1-εb2+εb2, ImΔrr=4πdnaλΔεsεb+Δεs1-εb1-εb2+εb2.

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