Abstract

Experiments have been carried out to investigate the excitation of molecules by evanescent light, and the emission of evanescent light in the fluorescence of excited molecules. It is confirmed that the absorption proceeds at a rate proportional to the second-order (normally ordered) product of the complex field amplitude, whether the light field is homogeneous or evanescent, and that the emission process follows a reciprocity principle.

© 1972 Optical Society of America

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  1. G. Quincke, Ann. Phys. Chem. 127, 1 (1866).
  2. E. E. Hall, Phys. Rev. 15, 73 (1902).
  3. P. Selenyi, Compt. Rend. 157, 1408 (1913).
  4. P. Fröhlich, Ann. Physik (4) 65, 577 (1921).
    [CrossRef]
  5. D. D. Coon, Am. J. Phys. 34, 240 (1966).
    [CrossRef]
  6. For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
    [CrossRef]
  7. H. Nassenstein, Phys. Letters 28A, 249 (1968); also Optik 29, 597 (1969) and Optik 30, 44 (1969).
  8. O. Bryngdahl, J. Opt. Soc. Am. 59, 1645 (1969).
    [CrossRef]
  9. R. N. Smartt, Appl. Opt. 9, 970 (1970).
    [CrossRef] [PubMed]
  10. C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
    [CrossRef]
  11. E. Wolf, Proc. Phys. Soc. (London) 74, 269 (1959).
    [CrossRef]
  12. G. Toraldo di Francia, Nuovo Cimento 16, 61 (1960).
  13. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields, 1st ed. (Pergamon, New York, 1966).
  14. G. C. Sherman, J. Opt. Soc. Am. 57, 1160 (1967); J. Opt. Soc. Am. 57, 1490 (1967).
    [CrossRef]
  15. J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968).
    [CrossRef]
  16. E. Lalor, J. Opt. Soc. Am. 58, 1235 (1968).
    [CrossRef]
  17. A. Walther, J. Opt. Soc. Am. 58, 1256 (1968); J. Opt. Soc. Am. 59, 1325 (1969).
    [CrossRef]
  18. R. Asby and E. Wolf, J. Opt. Soc. Am. 61, 52 (1971).
    [CrossRef]
  19. P. J. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983(A) (1947).
  20. See, for example, N. J. Harrick, Internal Reflection Spectroscopy (Wiley-Interscience, New York, 1967).
  21. C. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1971).
    [CrossRef]
  22. See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 38.
  23. The experiments were actually conducted with two different dielectrics on opposite sides of the interface, rather than with one dielectric and air. However as the ratio n of the two refractive indices is the only significant parameter, we have simplified the treatment.
  24. L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
    [CrossRef]
  25. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
    [CrossRef]
  26. The set of fatty-acid layers constitutes a uniaxial, birefringent medium, whose optic axis is perpendicular to the plane of the layers. By using only T.E.-polarized light in the experiment, we avoided complications arising from the birefringence. The ordinary refractive index of the layers matched the refractive index of the glass slide, so that the fatty-acid–glass interface had no effect on the light beam passing through.
  27. See also L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).
  28. K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615 (1962).
    [CrossRef]
  29. E. Lalor and G. C. Sherman, unpublished.
  30. The refractive index of the Clerici solution varied over a period of days, but the index ratio was determined after each experimental run. That is why different n values were chosen for the theoretical curves in Figs. 5 and 7.

1971 (2)

C. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1971).
[CrossRef]

R. Asby and E. Wolf, J. Opt. Soc. Am. 61, 52 (1971).
[CrossRef]

1970 (1)

1969 (1)

1968 (4)

1967 (2)

G. C. Sherman, J. Opt. Soc. Am. 57, 1160 (1967); J. Opt. Soc. Am. 57, 1490 (1967).
[CrossRef]

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

1966 (1)

D. D. Coon, Am. J. Phys. 34, 240 (1966).
[CrossRef]

1964 (1)

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

1963 (1)

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

1962 (1)

1960 (1)

G. Toraldo di Francia, Nuovo Cimento 16, 61 (1960).

1959 (1)

E. Wolf, Proc. Phys. Soc. (London) 74, 269 (1959).
[CrossRef]

1954 (1)

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[CrossRef]

1947 (1)

P. J. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983(A) (1947).

1921 (1)

P. Fröhlich, Ann. Physik (4) 65, 577 (1921).
[CrossRef]

1913 (1)

P. Selenyi, Compt. Rend. 157, 1408 (1913).

1902 (1)

E. E. Hall, Phys. Rev. 15, 73 (1902).

1866 (1)

G. Quincke, Ann. Phys. Chem. 127, 1 (1866).

Asby, R.

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 38.

Bouwkamp, C. J.

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[CrossRef]

Brekhovskikh, L. M.

See also L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

Bryngdahl, O.

Bücher, H.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Carniglia, C.

C. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1971).
[CrossRef]

Clemmow, P. C.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields, 1st ed. (Pergamon, New York, 1966).

Coon, D. D.

D. D. Coon, Am. J. Phys. 34, 240 (1966).
[CrossRef]

Drexhage, K.H.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Fleck, M.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Fröhlich, P.

P. Fröhlich, Ann. Physik (4) 65, 577 (1921).
[CrossRef]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Hall, E. E.

E. E. Hall, Phys. Rev. 15, 73 (1902).

Harrick, N. J.

See, for example, N. J. Harrick, Internal Reflection Spectroscopy (Wiley-Interscience, New York, 1967).

Kuhn, H.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Lalor, E.

E. Lalor, J. Opt. Soc. Am. 58, 1235 (1968).
[CrossRef]

E. Lalor and G. C. Sherman, unpublished.

Leurgans, P. J.

P. J. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983(A) (1947).

Mandel, L.

C. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1971).
[CrossRef]

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

Miyamoto, K.

Möbius, D.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Nassenstein, H.

H. Nassenstein, Phys. Letters 28A, 249 (1968); also Optik 29, 597 (1969) and Optik 30, 44 (1969).

Quincke, G.

G. Quincke, Ann. Phys. Chem. 127, 1 (1866).

Schäfer, F. P.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Selenyi, P.

P. Selenyi, Compt. Rend. 157, 1408 (1913).

Sherman, G. C.

Shewell, J. R.

Smartt, R. N.

Sondermann, J.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Sperling, W.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

Tillmann, P.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Toraldo di Francia, G.

G. Toraldo di Francia, Nuovo Cimento 16, 61 (1960).

Turner, A. F.

P. J. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983(A) (1947).

Walther, A.

Wiegand, J.

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Wolf, E.

R. Asby and E. Wolf, J. Opt. Soc. Am. 61, 52 (1971).
[CrossRef]

J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968).
[CrossRef]

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615 (1962).
[CrossRef]

E. Wolf, Proc. Phys. Soc. (London) 74, 269 (1959).
[CrossRef]

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 38.

Am. J. Phys. (1)

D. D. Coon, Am. J. Phys. 34, 240 (1966).
[CrossRef]

Ann. Phys. Chem. (1)

G. Quincke, Ann. Phys. Chem. 127, 1 (1866).

Ann. Physik (4) (1)

P. Fröhlich, Ann. Physik (4) 65, 577 (1921).
[CrossRef]

Appl. Opt. (1)

Compt. Rend. (1)

P. Selenyi, Compt. Rend. 157, 1408 (1913).

J. Opt. Soc. Am. (8)

Mol. Cryst. (1)

For example, see H. Bücher, K.H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, Mol. Cryst. 2, 199 (1967) and K H. Drexhage, Sci. Am. 222, 108 (1970).
[CrossRef]

Nuovo Cimento (1)

G. Toraldo di Francia, Nuovo Cimento 16, 61 (1960).

Phys. Letters (1)

H. Nassenstein, Phys. Letters 28A, 249 (1968); also Optik 29, 597 (1969) and Optik 30, 44 (1969).

Phys. Rev. (2)

E. E. Hall, Phys. Rev. 15, 73 (1902).

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Phys. Rev. D (1)

C. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1971).
[CrossRef]

Proc. Phys. Soc. (London) (2)

E. Wolf, Proc. Phys. Soc. (London) 74, 269 (1959).
[CrossRef]

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

Rept. Progr. Phys. (1)

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[CrossRef]

Other (8)

See, for example, M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 38.

The experiments were actually conducted with two different dielectrics on opposite sides of the interface, rather than with one dielectric and air. However as the ratio n of the two refractive indices is the only significant parameter, we have simplified the treatment.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields, 1st ed. (Pergamon, New York, 1966).

See, for example, N. J. Harrick, Internal Reflection Spectroscopy (Wiley-Interscience, New York, 1967).

The set of fatty-acid layers constitutes a uniaxial, birefringent medium, whose optic axis is perpendicular to the plane of the layers. By using only T.E.-polarized light in the experiment, we avoided complications arising from the birefringence. The ordinary refractive index of the layers matched the refractive index of the glass slide, so that the fatty-acid–glass interface had no effect on the light beam passing through.

See also L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

E. Lalor and G. C. Sherman, unpublished.

The refractive index of the Clerici solution varied over a period of days, but the index ratio was determined after each experimental run. That is why different n values were chosen for the theoretical curves in Figs. 5 and 7.

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Figures (7)

Fig. 1
Fig. 1

Illustrating the principle whereby an atom or molecule is immersed in an evanescent optical field. A dipole excited by a. T.E. wave would be perpendicular to the plane of the paper.

Fig. 2
Fig. 2

Illustrating the predicted variations of I(θ,a), which is proportional to the molecular absorption probability, with angle of incidence θ, for several different ratios of distance a of molecule from interface to wavelength λ. The curves refer to T.E. polarization and to a refractive index n = 1.09.

Fig. 3
Fig. 3

Top and side views of the vessel holding the Clerici solution, in which the slide with monomolecular layers is immersed.

Fig. 4
Fig. 4

The experimental setup for the absorption experiment. The slide and the detector assembly are coupled so as to rotate together about the axis of the cylindrical window.

Fig. 5
Fig. 5

Experimental results for the absorption of evanescent light by dye molecules located at a distance a = 450 Å = 0.14λ from the interface. The full curve is the theoretical value of I(θ,a)/|u(k)|2 and is based on Eqs. (9) with n = 1.10. The experimental values have been scaled so as to agree with the theory at the peak.

Fig. 6
Fig. 6

The experimental setup for the emission experiment. The position of the slide remains fixed while the detector assembly rotates about the axis of the cylindrical window.

Fig. 7
Fig. 7

Experimental results for the emission of evanescent light by excited dye molecules located at a distance a = 450Å = 0.14λ from the interface. The lightly drawn theoretical curve is based on Eqs. (22) with n = 1.08. The broken theoretical curve is based on Eq. (23), and takes the effect of finite aperture size into account. The units are arbitrary, and the experimental values have been scaled so as to agree with the theoretical values near the peak.

Equations (26)

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E ( I ) ( r , t ) = u ( k ) ɛ exp i ( k · r - K t ) + c . c . ,
E ( R ) ( r , t ) = u ( k ) ɛ [ ( k 3 - K 3 ) / ( k 3 + K 3 ) ] × exp i ( k ( R ) · r - K t ) + c . c . ,
E ( T ) ( r , t ) = u ( k ) ɛ [ 2 k 3 / ( k 3 + K 3 ) ] × exp i ( K · r - K t ) + c . c .
K 1 = k 1 ,             K 2 = k 2 ,
K 1 2 + K 2 2 + K 3 3 = K 2 ,
k 1 2 + k 2 2 + k 3 2 = n 2 K 2 ,
k 3 = n K cos θ ,
K 3 = K ( 1 - n 2 sin 2 θ ) .
I ( θ , a ) = u ( k ) 2 [ 4 k 3 2 / ( k 3 + K 3 ) 2 ] = u ( k ) 2 4 [ 1 + ( 1 - n 2 sin 2 θ ) / n cos θ ] - 2
I ( θ , a ) = u ( k ) 2 [ 4 k 3 2 / ( k 3 2 + K 3 2 ) ] × exp ( - 2 K 3 a ) = u ( k ) 2 4 [ n 2 cos 2 θ / ( n 2 - 1 ) ] × exp [ - 2 a K ( n 2 sin 2 θ - 1 ) ]
E ( x , y , 0 , t ) = - i 2 π - d K 1 d K 2 exp ( i K 3 a ) K 3 × [ ( P · K ) K - K 2 P ] exp i ( K 1 x + K 2 y - K t ) + c . c .
ɛ = ( K × e 3 ) / ( K 1 2 + K 2 2 ) 1 2 = ( K 2 e 1 - K 1 e 2 ) / ( K 1 2 + K 2 2 ) 1 2 ,
c × ɛ = ( K 3 K - K 2 e 3 ) / K ( K 1 2 + K 2 2 ) 1 2 ,
( P · K ) K - K 2 P = P 0 [ α ɛ + β ( c × ɛ ) ] ,
α = K 2 ( K 1 sin ψ - K 2 cos ψ ) / ( K 1 2 + K 2 2 ) 1 2 ,
β = - K K 3 ( K 1 cos ψ + K 2 sin ψ ) / ( K 1 2 + K 2 2 ) 1 2 ,
P = P 0 ( e 1 cos ψ + e 2 sin ψ ) ,
E ( r , t ) = - i P 0 2 π - d k 1 d k 2 × exp ( i K 3 a ) [ ( 2 α k 3 + K 3 ) ɛ + ( 2 n β k 3 + n 2 K 3 ) ( κ × ɛ ) ] × exp i ( k · r - K t ) + c . c . ,
E ( R , t ) = - P 0 R exp ( i K 3 a ) [ ( 2 α k 3 k 3 + K 3 ) ɛ + 2 n β k 3 k 3 + n 2 K 3 ( κ × ɛ ) ] exp i ( n K R - K t ) + c . c . ,
k 1 = n K sin θ cos χ , k 2 = n K sin χ , k 3 = n K cos θ cos χ .
E ( R , t ) = - P 0 R exp ( i K 3 a ) [ sin ψ ( 2 K 2 k 3 k 3 + K 3 ) ɛ - cos ψ ( 2 n K K 3 k 3 k 3 + n 2 K 3 ) ( κ × ɛ ) ] exp i K ( n R - t ) + c . c .
( T . E . ) I ( θ , a ) = P 0 2 K 4 R 2 | 2 k 3 k 3 + K 3 exp ( i K 3 a ) | 2 sin 2 ψ .
( T . E . ) I ( θ , a ) = P 0 2 K 4 2 R 2 4 k 3 2 ( k 3 + K 3 ) 2             for             θ < θ c
= P 0 2 K 4 2 R 2 4 k 3 2 k 3 2 + K 3 2 exp ( - 2 K 3 a )             for             θ > θ c .
Detector output = const × - 1 2 δ χ 1 2 δ χ d χ θ 0 - 1 2 δ θ θ 0 + 1 2 δ θ d θ cos χ I ( θ , χ a ) ,
I ( θ χ a ) = P 0 2 R 2 | 2 k 3 α k 3 + K 3 exp ( i K 3 a ) | 2 .