Abstract

A new technique for determining absorbances of interferenceless (incoherent) layers based on measurements of the ratio of the front and the back reflectivities of a double-layer sample at the Brewster angles is proposed. A double-layer stack must have at least one absorbing layer, and the two layers should be interferenceless and should be thicker than the wavelength of the incident light. We found that under these conditions the ratio of the front and the back reflectivities at the Brewster angle of a sample surface is directly related to layer absorbance. For a layer with a known thickness this means finding the extinction coefficient of the layer material. In comparison with the conventional method for measuring transmittance, the advantage of this approach is that it affords an opportunity to get rid of the influence of surface effects on the measuring volume absorption coefficient. For a thick layer with known thickness, it makes possible the determination of a small bulk absorption on a background with even greater surface effects. We trust that this technique will prove to be powerful for measuring the extinction coefficients of weakly absorbing materials.

© 2002 Optical Society of America

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References

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  1. R. G. Buckley, D. Beaglehole, “Absorptance of thin films,” Appl. Opt. 16, 2495–2499 (1977).
    [CrossRef] [PubMed]
  2. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [CrossRef]
  3. R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
    [CrossRef]
  4. C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of system of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
    [CrossRef]
  5. D. B. Kushev, N. N. Zheleva, “Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness,” J. Phys. D 28, 1239–1243 (1995).
    [CrossRef]
  6. C. Deumié, O. Gilbert, C. Amra, “High-angle resolved scattering for detection and discrimination of bulk and surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuE4.
  7. C. K. Carniglia, D. G. Jensen, “The equivalence between surface roughness and an absorbing layer on the surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuB5.
  8. G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
    [CrossRef]
  9. R. Z. Vitlina, G. I. Surdutovich, “A blurred film model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D 34, 2593–2598 (2001).
    [CrossRef]
  10. C. Amra, “Light scattering from multiplayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  11. S. Jakobs, A. Duparré, H. Truckenbroadt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
    [CrossRef]
  12. D. E. Aspnes, “Optical response of microscopically rough surface,” Phys. Rev. B 41, 10334–10343 (1990).
    [CrossRef]
  13. R. Z. Vitlina, A. M. Dykhne, “Reflection of electromagnetic waves from a surface with a low relief,” Sov. Phys. JETP 72, 983–990 (1991).
  14. T. T. Greffet, “Theoretical model of the shift of the Brewster angle on a rough surface,” Opt. Lett. 17, 238–240 (1992).
    [CrossRef] [PubMed]
  15. D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
    [CrossRef]
  16. G. A. N. Connell, A. Lewis, “Comments on the evidence for sharp and gradual optical absorption edges in amorphous germanium,” Phys. Status Solid B 60, 291–298 (1973).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).
  18. G. I. Surdutovich, R. Z. Vitlina, A. V. Ghiner, S. F. Durrant, V. Baranauskas, “Three polarization reflectometry methods for determination of optical anisotropy,” Appl. Opt. 37, 65–78 (1998).
    [CrossRef]
  19. R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
    [CrossRef]
  20. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
    [CrossRef]

2001 (1)

R. Z. Vitlina, G. I. Surdutovich, “A blurred film model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D 34, 2593–2598 (2001).
[CrossRef]

1999 (2)

R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
[CrossRef]

1998 (2)

1995 (1)

D. B. Kushev, N. N. Zheleva, “Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness,” J. Phys. D 28, 1239–1243 (1995).
[CrossRef]

1994 (1)

1992 (1)

1991 (1)

R. Z. Vitlina, A. M. Dykhne, “Reflection of electromagnetic waves from a surface with a low relief,” Sov. Phys. JETP 72, 983–990 (1991).

1990 (1)

D. E. Aspnes, “Optical response of microscopically rough surface,” Phys. Rev. B 41, 10334–10343 (1990).
[CrossRef]

1989 (1)

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
[CrossRef]

1984 (1)

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

1977 (1)

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

1973 (1)

G. A. N. Connell, A. Lewis, “Comments on the evidence for sharp and gradual optical absorption edges in amorphous germanium,” Phys. Status Solid B 60, 291–298 (1973).
[CrossRef]

1971 (1)

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of system of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Amra, C.

C. Amra, “Light scattering from multiplayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

C. Deumié, O. Gilbert, C. Amra, “High-angle resolved scattering for detection and discrimination of bulk and surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuE4.

Aspnes, D. E.

D. E. Aspnes, “Optical response of microscopically rough surface,” Phys. Rev. B 41, 10334–10343 (1990).
[CrossRef]

Baranauskas, V.

G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
[CrossRef]

R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, A. V. Ghiner, S. F. Durrant, V. Baranauskas, “Three polarization reflectometry methods for determination of optical anisotropy,” Appl. Opt. 37, 65–78 (1998).
[CrossRef]

Beaglehole, D.

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Buckley, R. G.

Carniglia, C. K.

C. K. Carniglia, D. G. Jensen, “The equivalence between surface roughness and an absorbing layer on the surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuB5.

Connell, G. A. N.

G. A. N. Connell, A. Lewis, “Comments on the evidence for sharp and gradual optical absorption edges in amorphous germanium,” Phys. Status Solid B 60, 291–298 (1973).
[CrossRef]

Deumié, C.

C. Deumié, O. Gilbert, C. Amra, “High-angle resolved scattering for detection and discrimination of bulk and surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuE4.

Duparré, A.

Durrant, S. F.

Dykhne, A. M.

R. Z. Vitlina, A. M. Dykhne, “Reflection of electromagnetic waves from a surface with a low relief,” Sov. Phys. JETP 72, 983–990 (1991).

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Gabriel, C. J.

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of system of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Ghiner, A. V.

Gilbert, O.

C. Deumié, O. Gilbert, C. Amra, “High-angle resolved scattering for detection and discrimination of bulk and surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuE4.

Greffet, T. T.

Jakobs, S.

Jensen, D. G.

C. K. Carniglia, D. G. Jensen, “The equivalence between surface roughness and an absorbing layer on the surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuB5.

Kushev, D. B.

D. B. Kushev, N. N. Zheleva, “Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness,” J. Phys. D 28, 1239–1243 (1995).
[CrossRef]

Lewis, A.

G. A. N. Connell, A. Lewis, “Comments on the evidence for sharp and gradual optical absorption edges in amorphous germanium,” Phys. Status Solid B 60, 291–298 (1973).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Minkov, D. A.

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
[CrossRef]

Nedoluha, A.

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of system of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Surdutovich, G. I.

R. Z. Vitlina, G. I. Surdutovich, “A blurred film model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D 34, 2593–2598 (2001).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
[CrossRef]

R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, A. V. Ghiner, S. F. Durrant, V. Baranauskas, “Three polarization reflectometry methods for determination of optical anisotropy,” Appl. Opt. 37, 65–78 (1998).
[CrossRef]

Swanepoel, R.

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

Truckenbroadt, H.

Vitlina, R. Z.

R. Z. Vitlina, G. I. Surdutovich, “A blurred film model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D 34, 2593–2598 (2001).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
[CrossRef]

R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, A. V. Ghiner, S. F. Durrant, V. Baranauskas, “Three polarization reflectometry methods for determination of optical anisotropy,” Appl. Opt. 37, 65–78 (1998).
[CrossRef]

R. Z. Vitlina, A. M. Dykhne, “Reflection of electromagnetic waves from a surface with a low relief,” Sov. Phys. JETP 72, 983–990 (1991).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Zheleva, N. N.

D. B. Kushev, N. N. Zheleva, “Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness,” J. Phys. D 28, 1239–1243 (1995).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am A (1)

R. Z. Vitlina, G. I. Surdutovich, V. Baranauskas, “Combined grazing-angle and normal-incidence reflectometry of absorbing media,” J. Opt. Soc. Am A 16, 371–377 (1999).
[CrossRef]

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

J. Phys. D (3)

D. B. Kushev, N. N. Zheleva, “Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness,” J. Phys. D 28, 1239–1243 (1995).
[CrossRef]

R. Z. Vitlina, G. I. Surdutovich, “A blurred film model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D 34, 2593–2598 (2001).
[CrossRef]

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
[CrossRef]

J. Phys. E (3)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constant n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Opt. Acta (1)

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of system of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

D. E. Aspnes, “Optical response of microscopically rough surface,” Phys. Rev. B 41, 10334–10343 (1990).
[CrossRef]

Phys. Status Solid B (1)

G. A. N. Connell, A. Lewis, “Comments on the evidence for sharp and gradual optical absorption edges in amorphous germanium,” Phys. Status Solid B 60, 291–298 (1973).
[CrossRef]

Sov. Phys. JETP (1)

R. Z. Vitlina, A. M. Dykhne, “Reflection of electromagnetic waves from a surface with a low relief,” Sov. Phys. JETP 72, 983–990 (1991).

Thin Solid Films (1)

G. I. Surdutovich, R. Z. Vitlina, V. Baranauskas, “Unique Brewster-angle window transparent to both polarizations,” Thin Solid Films 355–356, 60–63 (1999).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

C. Deumié, O. Gilbert, C. Amra, “High-angle resolved scattering for detection and discrimination of bulk and surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuE4.

C. K. Carniglia, D. G. Jensen, “The equivalence between surface roughness and an absorbing layer on the surface,” in Optics in Computing, Alexander A. Sawchuk, ed., Vol. 48 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper TuB5.

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Figures (2)

Fig. 1
Fig. 1

Stack of an absorbing film with absorbance A and a finite blurred absorbing substrate with absorbance B; r 1, r 2, and r 3 are the Fresnel reflection coefficients of the interfaces and n 1,2 and d 1,2 are the refractive index and the metrical thickness of the film and the substrate, respectively. θ and θ′ are the front and back angles of incidence, respectively.

Fig. 2
Fig. 2

For sufficiently wide aperture a of the incident beam, the nonparallelism of the film’s planes (angle α) leads to the effect of blurring for 4Δd 1 n 1/λ ≫ 1.

Equations (35)

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δ=4πdλN2-sin2 θ1/2,
r=r1+r2 exp-ix+r1r2+exp-ixr3 exp-iy1+r1r2 exp-ix+r1 exp-ix+r2r3 exp-iy, r=-r3+r2 exp-iy+r2r3+exp-iyr1 exp-ix1+r1r2 exp-ix+r1 exp-ix+r2r3 exp-iy,
x=4π d1λn1-ik12-sin2 θ1/2=x-ix4π d1λn12-sin2 θ1/2-i n1k1n12-sin2 θ1/2,
y=4π d2λn2-ik22-sin2 θ1/2=y-iy4π d2λn22-sin2 θ1/2-i n2k2n22-sin2 θ1/2,
rθB1=-r3 exp-ix1-exp-iy1-r32 exp-iyθB1, rθB1=r31-exp-iy1-r32 exp-iyθB1, rθB2=r11-exp-ix1-r12 exp-ixθB2, rθB2=-r1 exp-iy1-exp-ix1-r12 exp-ixθB2.
A2θB1=exp-2x=exp-8π d1λn1k1n12-sin2 θB11/2,
B2θB2=exp-2y=exp-8π d2λn2k2n22-sin2 θB21/2.
A2θB1=RθB1RθB1,
B2θB2=RθB2RθB2.
1+2 δr3r3cot an y2,
1+2δr11+r22sin x-r22 sinx-y-sinx+y2r2 sin2 y/2,
R0=R 1+B2-2RB21-R2B2, T0=B 1-R21-R2B2,
R=1-1-r121-r22A21+2r1r2A cos x+r12r22A2+r32A2B21-r1221-r2221+2r1r2A cos x+r12r22A21-r22r32B2+r12A2r22-r32B2+2r1r2A1-r32B2cos x,
R=1-1-r321-r22B2-r12A2B2-r22+2r1r2A1-B2cos x1-r22r32B2+r12A2r22-r32B2+2r1r2A1-r32B2cos x.
T=T=AB1-r121-r221-r321-r22r32B2+r12A2r22-r32B2+2r1r2A1-r32B2cos x.
4 d1Δωn1c  1, 4 d2Δωn2c  1,c4d2n2  Δω  c4d1n1.
R=R1+A21-R121-R1A21-1-R21-R3B2F;
R=R3+B21-R321-R3B21-1-R21-R1A2F;
T=1-R11-R21-R3ABF,
F=1-R2R3B2+R1A2R2-R3B22-4R1R2A21-R3B221/2.
R=A2R21+B2-2R2B21-R2B2,R=R21+B2-2R2B21-R2B2.
R=Rsi+R3Tsi2,
R=Rsi+R3Tsi21+R1R2A21-R1R2A2,
Rsi=R1+R2A2-2R1R2A21-R1R2A2,Tsi=1-R11-R2A1-R1R2A2
R3+R2B2-2R2R3B2R2+R3B2-2R2R3B2θB11+O1-B2δR1.
B2=R0-RRRR0+1-2R.
δ1-B2B=2+2R+R2δRR-21+RδR0R0.
1-r11-r21-r3=γ1+r11+r21+r3,
γ=s2-sin2 θ1/2s2 cos θ
rk=-rm+rn1+rmrn,
rkθn=-rmθn.
n2=dRpdθdRsdθθπ/2.
n12=dRpdθdRsdθθπ/2,n22=dRpdθdRsdθθπ/2,
Δ=R00-R01-R00,
Δ=n12n22+1n12+1n22+n12-11/2,

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