Abstract

We explain reasons of oscillations frequently observed in total losses spectra (1 − RT) calculated on the basis of measurement spectral photometric data of thin film samples. The first reason of oscillations is related to difference in angles of incidence at which spectral transmittance and reflectance are measured. The second reason is an absorption in a thin film. The third reason is a slight thickness non-uniformity of the film. We observe a good agreement between theoretical models and corresponding measurements, which proves above statements on the origins of oscillations in total losses.

© 2012 OSA

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References

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  1. A. Duparré and D. Ristau, “2004 topical meeting on optical interference coatings: Measurement problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.
  2. A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Opt.47, C179–C184 (2008).
    [CrossRef] [PubMed]
  3. A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt.50, C172–C177 (2011).
    [CrossRef] [PubMed]
  4. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt.50, C75–C85 (2011).
    [CrossRef] [PubMed]
  5. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt.41, 2555–2560 (2002).
    [CrossRef] [PubMed]
  6. J. Woollam, “Ellipsometry, variable angle spectroscopic,” in “Wiley Encyclopedia of Electrical and Electronics Engineering,” J. Webster, ed. (Wiley, New York, 2000). Supplement 1.
  7. A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
    [CrossRef]
  8. T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.
  9. S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, 1992).
  10. Quartz Glass for Optics: Data and Properties, http://heraeus-quarzglas.com .
  11. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer thin film software, http://www.optilayer.com .
  12. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: 2-material technology versus rugate,” Appl. Opt.46, 1190–1193 (2007).
    [CrossRef] [PubMed]
  13. V. Pervak, F. Krausz, and A. Apolonski, “Hafnium oxide thin films deposited by reactive middle-frequency dual-magnetron sputtering,” Thin Solid Films515, 7984–7989 (2007).
    [CrossRef]
  14. A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
    [CrossRef]
  15. J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt.22, 3191–3200 (1983).
    [CrossRef] [PubMed]
  16. A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt.51, 245–254 (2012).
    [CrossRef] [PubMed]
  17. P. A. van Nijnatten, “An automated directional reflectance/transmittance analyser for coating analysis,” Thin Solid Films442, 74–79 (2003).
    [CrossRef]
  18. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
    [CrossRef]

2012

2011

2008

2007

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: 2-material technology versus rugate,” Appl. Opt.46, 1190–1193 (2007).
[CrossRef] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski, “Hafnium oxide thin films deposited by reactive middle-frequency dual-magnetron sputtering,” Thin Solid Films515, 7984–7989 (2007).
[CrossRef]

2003

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

P. A. van Nijnatten, “An automated directional reflectance/transmittance analyser for coating analysis,” Thin Solid Films442, 74–79 (2003).
[CrossRef]

2002

1983

Amotchkina, T.

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.

Amotchkina, T. V.

Apolonski, A.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: 2-material technology versus rugate,” Appl. Opt.46, 1190–1193 (2007).
[CrossRef] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski, “Hafnium oxide thin films deposited by reactive middle-frequency dual-magnetron sputtering,” Thin Solid Films515, 7984–7989 (2007).
[CrossRef]

DeBell, G.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt.50, C75–C85 (2011).
[CrossRef] [PubMed]

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
[CrossRef]

Dobrowolski, J. A.

Duparré, A.

Francis, R.

Furman, S.

S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, 1992).

Grilli, M. L.

Günster, S.

Ho, F. C.

Janicki, V.

Jupé, M.

T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.

Kokarev, M. A.

Krausz, F.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: 2-material technology versus rugate,” Appl. Opt.46, 1190–1193 (2007).
[CrossRef] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski, “Hafnium oxide thin films deposited by reactive middle-frequency dual-magnetron sputtering,” Thin Solid Films515, 7984–7989 (2007).
[CrossRef]

Lappschies, M.

T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
[CrossRef]

Pervak, V.

Pistner, J.

Quesnel, E.

Ristau, D.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt.50, C75–C85 (2011).
[CrossRef] [PubMed]

A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt.50, C172–C177 (2011).
[CrossRef] [PubMed]

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Opt.47, C179–C184 (2008).
[CrossRef] [PubMed]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt.41, 2555–2560 (2002).
[CrossRef] [PubMed]

T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.

A. Duparré and D. Ristau, “2004 topical meeting on optical interference coatings: Measurement problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.

Sancho-Parramon, J.

Sytchkova, A. K.

Tikhonravov, A.

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
[CrossRef]

Tikhonravov, A. V.

Trubetskov, M.

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

Trubetskov, M. K.

van Nijnatten, P. A.

P. A. van Nijnatten, “An automated directional reflectance/transmittance analyser for coating analysis,” Thin Solid Films442, 74–79 (2003).
[CrossRef]

Waldorf, A.

Woollam, J.

J. Woollam, “Ellipsometry, variable angle spectroscopic,” in “Wiley Encyclopedia of Electrical and Electronics Engineering,” J. Webster, ed. (Wiley, New York, 2000). Supplement 1.

Zorc, H.

Appl. Opt.

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Opt.47, C179–C184 (2008).
[CrossRef] [PubMed]

A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt.50, C172–C177 (2011).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt.50, C75–C85 (2011).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt.41, 2555–2560 (2002).
[CrossRef] [PubMed]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: 2-material technology versus rugate,” Appl. Opt.46, 1190–1193 (2007).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt.22, 3191–3200 (1983).
[CrossRef] [PubMed]

A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt.51, 245–254 (2012).
[CrossRef] [PubMed]

Proc. SPIE

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Günster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE5188, 331–342 (2003).
[CrossRef]

Thin Solid Films

V. Pervak, F. Krausz, and A. Apolonski, “Hafnium oxide thin films deposited by reactive middle-frequency dual-magnetron sputtering,” Thin Solid Films515, 7984–7989 (2007).
[CrossRef]

P. A. van Nijnatten, “An automated directional reflectance/transmittance analyser for coating analysis,” Thin Solid Films442, 74–79 (2003).
[CrossRef]

Other

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
[CrossRef]

A. Duparré and D. Ristau, “2004 topical meeting on optical interference coatings: Measurement problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.

T. Amotchkina, D. Ristau, M. Lappschies, M. Jupé, A. V. Tikhonravov, and M. K. Trubetskov, “Optical properties of TiO2–SiO2 mixture thin films produced by ion-beam sputtering,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2007), paper TuA8.

S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, 1992).

Quartz Glass for Optics: Data and Properties, http://heraeus-quarzglas.com .

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer thin film software, http://www.optilayer.com .

J. Woollam, “Ellipsometry, variable angle spectroscopic,” in “Wiley Encyclopedia of Electrical and Electronics Engineering,” J. Webster, ed. (Wiley, New York, 2000). Supplement 1.

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Figures (12)

Fig. 1
Fig. 1

Comparison of theoretical TL(λ) Eq. (1) in a model sample with back side contribution, without back side contribution and approximate dependence TLAOI(λ) calculated by Eq. (2). AOI are θ1 = 0, θ2 = 7°.

Fig. 2
Fig. 2

Comparison of theoretical TL(χ, λ) Eq. (4) in a model sample with back side contribution, without back side contribution and approximate dependence TLAbs(λ) calculated by Eq. (5).

Fig. 3
Fig. 3

Comparison of theoretical TL(λ) Eq. (7) in a model sample with back side contribution, without back side contribution and approximate dependence TLΔd(λ) calculated by Eq. (8). AOI is θ = 7°.

Fig. 4
Fig. 4

Comparison of TL(λ) = 100% − R(7°, λ) − T(0°, λ) calculated from experimental data and TLAOI(λ) calculated by Eq. (2): (a) Ta2O5, (b) Nb2O5.

Fig. 5
Fig. 5

Total losses TL(λ) = 100% −T(0°, λ) − R(7°, λ) calculated from experimental data of SiO2 sample taken by Perkin Elmer Lambda 950.

Fig. 6
Fig. 6

Total losses TL(λ) = 100% − R(7°, λ) − T(7°, λ) calculated from experimental data taken by Perkin Elmer Lambda 950: (a) Ta2O5, (b) Nb2O5.

Fig. 7
Fig. 7

Comparison of TL(λ) = 100% − R(7°, λ) − T(7°, λ) calculated from experimental data and TLAbs(λj) calculated by Eq. (5): (a) TiO2, (b) HfO2.

Fig. 8
Fig. 8

Comparison of dependence TL(λ) = 100% − R(7°, λ) − T(7°, λ) calculated from experimental data measured using Perkin Elmer Lambda 950 and its approximation TLΔd(λ) calculated by Eq. (8): (a) Ta2O5, (b) Nb2O5.

Fig. 9
Fig. 9

(a) Comparison of two transmittance spectra of Ta2O5 sample taken at normal incidence using Perkin Elmer Lambda 950. (b) Comparison of δT(λ) = T(1)(λ) − T(2)(λ) calculated from experimental data and its approximation (Eqs. (9), (10)).

Fig. 10
Fig. 10

Comparison of TL(λ) = 100% − T(0°, λ) − R(7°, λ) calculated from experimental data, TLAOI(λ) calculated by Eq. (2) with n(λ) determined in the course of characterization process and TLAOI(λ) calculated by Eq. (2) with n(λ) + Δn: (a) Ta2O5, (b) Nb2O5.

Fig. 11
Fig. 11

(a) Comparison of TL(s)(λ) = 100% − T(s)(7°, λ) − R(s)(10°, λ) calculated from experimental data and T L AOI ( s ) ( λ ) calculated by Eq. (12). (b) Total losses TL(λ) = 100% − T(s)(7°, λ) − R(s)(7°, λ) calculated from experimental data.

Fig. 12
Fig. 12

(a) Comparison of two transmittance spectra taken by Cary 5000 spectrophotometer with two different accessories. The data are related to Ta2O5 sample described in Section 5, AOI=7°, s-polarization case. (b) Comparison of δ(s)(λ) = T(s,1)(7°, λ) − T(s,2)(7°, λ) calculated from experimental data and its approximation by Eqs. (10), (12).

Equations (12)

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T L ( λ j ) = 100 % T ( θ 1 , λ j ) R ( θ 2 , λ j ) , j = 1 , , L ,
T L AOI ( λ ) = 4 π d λ n s n sin 2 φ ( n 2 1 ) ( 1 ( n s / n ) 2 ) [ ( 1 + n s ) 2 cos 2 φ + ( n s / n + n ) 2 sin 2 φ ] 2 ( θ 2 2 θ 1 2 ) ,
n ( λ ) = A 0 + A 1 ( λ 0 / λ ) 2 + A 2 ( λ 0 / λ ) 4 ,
T L ( χ , λ ) = 100 % T ( χ , λ ) R ( χ , λ ) .
T L Abs = 4 π d χ λ { n s ( n s + 1 ) ( n s n + 1 ) + ( n s 2 1 ) cos 2 φ + [ n 2 ( n s / n ) 2 ] sin 2 φ [ ( 1 + n s ) 2 cos 2 φ + ( n s / n + n ) 2 sin 2 φ ] 2 } .
χ ( λ ) = B 0 exp { B 1 λ 0 / λ + B 2 λ / λ 0 } ,
T L ( d + Δ d , λ ) = 100 % T ( d , λ ) R ( d + Δ d , λ )
T L Δ d ( λ ) = π Δ d 4 λ q ( s ) sin 2 φ [ f ( s ) + f ( p ) ] , f ( s , p ) = T 2 [ ( q ( s , p ) ) 2 ( q a ( s , p ) ) 2 ] [ 1 ( q s ( s , p ) / q ( s , p ) ) 2 ] q s ( s , p ) ( q a ( s , p ) ) 2
T L Δ d ( λ ) = π Δ d 2 λ n sin 2 φ T 2 ( n 2 1 ) [ 1 ( n s / n ) 2 ] n s
δ T ( λ ) = T ( d , λ ) T ( d + Δ d , λ ) T ( λ ) Δ d | Δ d = 0 Δ d = R ( λ ) Δ d | Δ d = 0 Δ d = T L Δ d ( λ )
Δ n = ( n 2 + n s ) 3 8 n n s ( n s n 2 ) Δ T .
T L AOI = { 4 π d λ n s n sin 2 φ ( n 2 1 ) ( 1 ( n s / n ) 2 ) [ ( 1 + n s ) 2 cos 2 φ + ( n s / n + n ) 2 sin 2 φ ] 2 + + 2 n s a ( n , n s ) cos 2 φ + b ( n , n s ) sin 2 φ [ ( 1 + n s ) 2 cos 2 φ + ( n s / n + n ) 2 sin 2 φ ] 2 } ( θ 2 2 θ 1 2 ) , a ( n , n s ) = ( 1 / n s n s ) 2 , b ( n , n s ) = ( ( 1 + n s ) 2 + ( n s / n + n ) 2 + ( n s / n ) 2 ( n 2 / n s 2 ) 2 + n 2 n 4 ) / n 2

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