Abstract

The critical angle technique is modified for the accurate measurement of the refractive index of bio-optical materials. Based on the analysis of reflection from the boundary of the material as a function of incident angle and polarization direction, the critical illumination angle is obtained by numerical differentiation of the reflection curve. As an example, the dispersion curve of bacteriorhodopsin is given. The measurement error and the effect of the host bovine skin gelatin on the results are analyzed.

© 1995 Optical Society of America

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References

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  1. D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
    [CrossRef]
  2. R. R. Birge, "Nature of the primary photochemical events in rhodopsin and bacteriorhodopsin," Biochem. Biophys. Acta 1016, 293–327 (1990).
    [CrossRef] [PubMed]
  3. R. R. Birge and C. F. Zhang, "Two-photo double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag∗−-like and 1Bu∗+-like π, π states," J. Chem. Phys. 92, 7178–7195 (1990).
    [CrossRef]
  4. Q. Wang Song, Chunping Zhang, R. Gross, and R. Birge, "Optical limiting by chemically enhanced bacteriorhodopsin films," Opt. Lett. 18, 775–777 (1993).
    [CrossRef]
  5. O. Werner, B. Fiscfer, and A. Lewis, "Strong self-defocusing and four-wave mixing in bacteriorhodopsin," Opt. Lett. 17, 241–243 (1992).
    [CrossRef] [PubMed]
  6. O. Werner, B. Fiscfer, A. Lewis, and I. Nebenzahl, "Saturable absorption, wave mixing, and phase conjugation with bacteriorhodopsin," Opt. Lett. 15, 1117–1119 (1990).
    [CrossRef] [PubMed]
  7. R. E. Anderson and A. J. Lightman, "Measurements of the refractive-index variations with temperature of a photomonomer," Appl. Opt. 30, 3792–3793 (1991).
    [CrossRef] [PubMed]
  8. P. P. Herrmann, "Determination of thickness, refractive index, and dispersion of waveguiding thin films with an Abbe refractometer," Appl. Opt. 19, 3261–3262 (1980).
    [CrossRef] [PubMed]
  9. O. Hunderi, "New method for accurate determination of optical constants," Appl. Opt. 11, 1572–1578 (1972).
    [CrossRef] [PubMed]
  10. R. Tousey, "On calculating the optical constants from reflection coefficients," J. Opt. Soc. Am. 29, 235–239 (1939).
    [CrossRef]
  11. A. C. Traub and H. Osterberg, "Brewster angle apparatus for thin film index measurement," J. Opt. Soc. Am. 47, 62–64 (1957).
    [CrossRef]
  12. R. M. A. Azzam, "Maximum minimum reflectance of parallelpolarized light at interfaces between transparent and absorbing media," J. Opt. Soc. Am. B 73, 959–962 (1983).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1986).
  14. R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).
  15. D. Zeisel and N. Hampp, "Spectral relationship of lightinduced refractive index and absorption changes in bacteriorhodopsin films containing wildtype BRwt and the variant BRd96n," J. Phys. Chem. 96, 7788–7792 (1992).
    [CrossRef]
  16. R. B. Gross, K. Can Izgi, and R. R. Birge, "Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin," in Image Storage and Retrieval Systems, A. A. Jamberdino and W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1662, 187–196 (1992).
    [CrossRef]
  17. L. E. Nielsen, Predicting the Properties of Mixture (Dekker, New York, 1978).
  18. J. C. Maxwel-Garnett, "Colours in metal glasses and in metal films," Philos. Trans. R. Soc. London 203, 385–420 (1904).
    [CrossRef]
  19. C. T. O'Konski, "Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes," J. Phys. Chem. 64, 605–619 (1960).
    [CrossRef]

1993 (1)

1992 (2)

O. Werner, B. Fiscfer, and A. Lewis, "Strong self-defocusing and four-wave mixing in bacteriorhodopsin," Opt. Lett. 17, 241–243 (1992).
[CrossRef] [PubMed]

D. Zeisel and N. Hampp, "Spectral relationship of lightinduced refractive index and absorption changes in bacteriorhodopsin films containing wildtype BRwt and the variant BRd96n," J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

1991 (2)

D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef]

R. E. Anderson and A. J. Lightman, "Measurements of the refractive-index variations with temperature of a photomonomer," Appl. Opt. 30, 3792–3793 (1991).
[CrossRef] [PubMed]

1990 (3)

O. Werner, B. Fiscfer, A. Lewis, and I. Nebenzahl, "Saturable absorption, wave mixing, and phase conjugation with bacteriorhodopsin," Opt. Lett. 15, 1117–1119 (1990).
[CrossRef] [PubMed]

R. R. Birge, "Nature of the primary photochemical events in rhodopsin and bacteriorhodopsin," Biochem. Biophys. Acta 1016, 293–327 (1990).
[CrossRef] [PubMed]

R. R. Birge and C. F. Zhang, "Two-photo double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag∗−-like and 1Bu∗+-like π, π states," J. Chem. Phys. 92, 7178–7195 (1990).
[CrossRef]

1988 (1)

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

1983 (1)

R. M. A. Azzam, "Maximum minimum reflectance of parallelpolarized light at interfaces between transparent and absorbing media," J. Opt. Soc. Am. B 73, 959–962 (1983).
[CrossRef]

1980 (1)

1972 (1)

1960 (1)

C. T. O'Konski, "Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes," J. Phys. Chem. 64, 605–619 (1960).
[CrossRef]

1957 (1)

1939 (1)

1904 (1)

J. C. Maxwel-Garnett, "Colours in metal glasses and in metal films," Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Anderson, R. E.

Azzam, R. M. A.

R. M. A. Azzam, "Maximum minimum reflectance of parallelpolarized light at interfaces between transparent and absorbing media," J. Opt. Soc. Am. B 73, 959–962 (1983).
[CrossRef]

Birge, R.

Birge, R. R.

R. R. Birge and C. F. Zhang, "Two-photo double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag∗−-like and 1Bu∗+-like π, π states," J. Chem. Phys. 92, 7178–7195 (1990).
[CrossRef]

R. R. Birge, "Nature of the primary photochemical events in rhodopsin and bacteriorhodopsin," Biochem. Biophys. Acta 1016, 293–327 (1990).
[CrossRef] [PubMed]

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

R. B. Gross, K. Can Izgi, and R. R. Birge, "Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin," in Image Storage and Retrieval Systems, A. A. Jamberdino and W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1662, 187–196 (1992).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1986).

Brauchle, C.

D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef]

Einterz, C. M.

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

Fiscfer, B.

Gross, R.

Gross, R. B.

R. B. Gross, K. Can Izgi, and R. R. Birge, "Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin," in Image Storage and Retrieval Systems, A. A. Jamberdino and W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1662, 187–196 (1992).
[CrossRef]

Hampp, N.

D. Zeisel and N. Hampp, "Spectral relationship of lightinduced refractive index and absorption changes in bacteriorhodopsin films containing wildtype BRwt and the variant BRd96n," J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef]

Herrmann, P. P.

Hunderi, O.

Izgi, K. Can

R. B. Gross, K. Can Izgi, and R. R. Birge, "Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin," in Image Storage and Retrieval Systems, A. A. Jamberdino and W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1662, 187–196 (1992).
[CrossRef]

Knapp, H. M.

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

Lewis, A.

Lightman, A. J.

Maxwel-Garnett, J. C.

J. C. Maxwel-Garnett, "Colours in metal glasses and in metal films," Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Murray, L. P.

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

Nebenzahl, I.

Nielsen, L. E.

L. E. Nielsen, Predicting the Properties of Mixture (Dekker, New York, 1978).

O'Konski, C. T.

C. T. O'Konski, "Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes," J. Phys. Chem. 64, 605–619 (1960).
[CrossRef]

Oseterhelt, D.

D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef]

Osterberg, H.

Song, Q. Wang

Tousey, R.

Traub, A. C.

Werner, O.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1986).

Zeisel, D.

D. Zeisel and N. Hampp, "Spectral relationship of lightinduced refractive index and absorption changes in bacteriorhodopsin films containing wildtype BRwt and the variant BRd96n," J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

Zhang, C. F.

R. R. Birge and C. F. Zhang, "Two-photo double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag∗−-like and 1Bu∗+-like π, π states," J. Chem. Phys. 92, 7178–7195 (1990).
[CrossRef]

Zhang, Chunping

Appl. Opt. (3)

Biochem. Biophys. Acta (1)

R. R. Birge, "Nature of the primary photochemical events in rhodopsin and bacteriorhodopsin," Biochem. Biophys. Acta 1016, 293–327 (1990).
[CrossRef] [PubMed]

Biophys. J. (1)

R. R. Birge, C. M. Einterz, H. M. Knapp, and L. P. Murray, "The nature of the primary photochemical events in rhodopsin and isorhodopsin," Biophys. J. 53, 367–385 (1988).

J. Chem. Phys. (1)

R. R. Birge and C. F. Zhang, "Two-photo double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag∗−-like and 1Bu∗+-like π, π states," J. Chem. Phys. 92, 7178–7195 (1990).
[CrossRef]

J. Opt. Soc. Am. (2)

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

R. M. A. Azzam, "Maximum minimum reflectance of parallelpolarized light at interfaces between transparent and absorbing media," J. Opt. Soc. Am. B 73, 959–962 (1983).
[CrossRef]

J. Phys. Chem. (2)

D. Zeisel and N. Hampp, "Spectral relationship of lightinduced refractive index and absorption changes in bacteriorhodopsin films containing wildtype BRwt and the variant BRd96n," J. Phys. Chem. 96, 7788–7792 (1992).
[CrossRef]

C. T. O'Konski, "Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes," J. Phys. Chem. 64, 605–619 (1960).
[CrossRef]

Opt. Lett. (3)

Philos. Trans. R. Soc. London (1)

J. C. Maxwel-Garnett, "Colours in metal glasses and in metal films," Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Q. Rev. Biophys. (1)

D. Oseterhelt, C. Brauchle, and N. Hampp, "Bacteriorhodopsin: a biological material for information processing," Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef]

Other (3)

R. B. Gross, K. Can Izgi, and R. R. Birge, "Holographic thin films, spatial light modulators and optical associative memories based on bacteriorhodopsin," in Image Storage and Retrieval Systems, A. A. Jamberdino and W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1662, 187–196 (1992).
[CrossRef]

L. E. Nielsen, Predicting the Properties of Mixture (Dekker, New York, 1978).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1986).

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Figures (10)

Fig. 1
Fig. 1

Diagram illustrating the principle for the index measurement setup.

Fig. 2
Fig. 2

Reflection of the TE wave as a function of the incident angle for n1 = 1.73 and n2 = 1.52. Curves a, b, c, d, e, and f are for k2 = 0.00, 0.0005, 0.001, 0.002, 0.004, and 0.006, respectively.

Fig. 3
Fig. 3

Reflection of the TM wave as a function of the angle for n1 = 1.73 and n2 = 1.52. Curves a, b, c, d, e, and f are for k2 = 0.00, 0.0005, 0.001, 0.002, 0.004, and 0.006, respectively.

Fig. 4
Fig. 4

(a) Reflection waves and (b) their derivatives for n1 = 1.73 and n2 = 1.52. The dashed curves are for the TE wave, and the solid curves are for the TM wave. The curves with an abrupt reflection are for k2 = 0.0, and the smooth curves are for k2 = 0.001.

Fig. 5
Fig. 5

Shift of the maximum derivatives from the critical illumination angle as a function of the attenuation k2: (a) TE wave, (b) TM wave. The curves from top to bottom are for n2 = 1.525, 1.530, 1.535, and 1.540, respectively.

Fig. 6
Fig. 6

Reflection of the TM wave as a function of the incident angle for k2 = 0.004 and n = 1.73. Curves a, b, c, d, e, and f are for n2 = 1.520, 1.525, 1.530, 1.535, 1.540, and 1.545, respectively.

Fig. 7
Fig. 7

Reflection of the TM wave as a function of the incident angle. Curves a, b, and c are for divergences of the Gaussian probe beam of 0′, 2′, and 4′, respectively.

Fig. 8
Fig. 8

Various schemes to eliminate the reflection on the top surface of the test sample in order to obtain the critical illumination angle.

Fig. 9
Fig. 9

Measured reflection of BR film as a function of the incident angle and the maximum derivative of the reflection curve.

Fig. 10
Fig. 10

Dispersion of BR film versus wavelength.

Equations (21)

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θ = β ± arcsin ( sin α n 1 ) ,
2 u 2 2 = n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ + { [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ ] 2 + 4 n 2 4 k 2 2 } 1 / 2 , 2 υ 2 2 = [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ ] + { [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ ] 2 + 4 n 2 4 k 2 2 } 1 / 2 .
R s , = | n 1 cos θ ( u 2 + i υ 2 ) n 1 cos θ + ( u 2 + i υ 2 ) | 2 .
R s , = | [ n 2 2 ( 1 k 2 2 ) cos θ n 1 u 2 ] 2 + ( 2 n 2 2 k 2 cos θ n 1 υ 2 ) 2 [ n 2 2 ( 1 k 2 2 ) cos θ + n 1 u 2 ] 2 + ( 2 n 2 2 k 2 cos θ + n 1 υ 2 ) 2 | 2 .
R p , = | cos α n 1 cos [ arcsin ( sin α n 1 ) ] cos α + n 1 cos [ arcsin ( sin α n 1 ) ] | 2
R p , = | n 1 / cos [ arcsin ( sin α n 1 ) ] 1 / cos α n 1 / cos [ arcsin ( sin α n 1 ) ] + 1 / cos α | 2
R = R s , ( 1 R p , ) 2
R = R s , ( 1 R p , ) 2
n 2 = n 1 sin [ β ± arcsin ( a n 1 sin α c , M ) ] ,
δ n 2 = δ n 2 ( β ) + δ n 2 ( δ ) + δ n 2 ( n 1 ) = | n 2 β | δ β + | n 2 α c | δ α c + | n 2 n 1 | δ n 1 ,
δ n 2 ( β ) = | n 1 cos [ β ± arcsin ( 1 n 1 sin α c ) ] | δ β ,
δ n 2 ( α ) = n 1 ( ( sin β ) sin α n 1 2 cos { α [ 1 sin ( α / n 1 ) 2 ] 1 / 2 } + cos β cos ( α n 1 ) ) δ α ,
δ n 2 ( n 1 ) = sin [ β ± arcsin ( 1 / n 1 ) sin α ] + n 1 cos [ β ± arcsin ( 1 / n 1 ) ] δ n 1 .
δ n 2 ( β ) δ β ,
δ n 2 ( α ) 0.5 δ α ,
δ n 2 ( n 1 ) δ n 1 ,
δ n 2 = δ β + 0.5 δ α + δ n 1 .
n 2 = q n + q 3 n 3 ,
n 2 = q ( n 3 + Δ n ) + q 3 n 3 = n 3 + q Δ n
Δ n = ( n 2 n 3 ) / q .
n = n 2 + q 3 Δ n .

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