Abstract

We describe and demonstrate a novel method to measure directly excitation-energy migration distances in fluorescing materials. In any desired direction, migration distances corresponding to 1/10 to 3 times the fluorescence wavelength can be determined with an accuracy of ~10%. Fluorescing materials in the form of typically 10-μm-thick samples are coated with a mirror on one surface. A coherent excitation beam is used to create a standing-wave pattern in the sample. The fluorescence radiation is shown to possess an interference peak in one particular direction. In the case of energy diffusion, this peak becomes indistinct. From the amplitude of the peak, the energy-diffusion distance is directly obtained. The existence of the peak, its position and amplitude are experimentally verified by use of a fluorescing film of rhodamine 6G doped polyurethane.

© 1974 Optical Society of America

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  1. Th. Förster, Ann. Physik 2, 55 (1948); D. L. Dexter, J. Chem. Phys. 21, 836 (1953). For a recent review, see W. J. G. Grant, Phys. Rev. B 4, 648 (1971) and the references cited therein.
    [CrossRef]
  2. See, for example, L. G. Van Uitert and S. Ida, J. Chem. Phys. 37, 986 (1962); G. E. Peterson and P. M. Bridenbaugh, J. Opt. Soc. Am. 54, 644 (1964); J. P. Van der Ziel, L. Kopf, and L. G. Van Uitert, Phys. Rev. B 6, 615 (1972).
    [CrossRef]
  3. See, for example, L. G. Van Uitert, in Luminescence of Inorganic Solids, edited by P. Goldberg (Academic, New York, 1966), p. 465; M. J. Weber, J. Appl. Phys. 44, 4058 (1973).
    [CrossRef]
  4. C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
    [CrossRef]
  5. H. G. Danielmeyer, J. Appl. Phys. 42, 3125 (1971).
    [CrossRef]
  6. M. Yokota and O. Tamimoto, J. Phys. Soc. Jpn. 22, 779 (1967); M. Inokuti and F. Hirayama, J. Chem. Phys. 43, 1978 (1965); M. J. Weber, Phys. Rev. B 4, 2932 (1971).
    [CrossRef]
  7. M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
    [CrossRef]
  8. For purpose for this paper, we shall refer to the mirror as a reflecting metal; however, a dielectric mirror or total-internal reflection may serve the same purpose.
  9. See, for example, W. Macke, Thermodyamik und Statistik, (Akademische Verlagsgesellschaft, Leipzig, 1962), p. 22.
  10. The presence of a reflecting surface also affects the lifetime of fluorescing centers that are closer to the surface than ~λf. See, e.g., K. H. Drexhage, J. Lumin. 1,2, 693 (1970). For samples of thickness b≫ λf this effect influences our results insignificantly.
    [CrossRef]
  11. R. Ulrich and H. P. Weber, Appl. Opt. 11, 428 (1972).
    [CrossRef] [PubMed]
  12. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 628–630.
  13. W. J. Tomlinson and H. P. Weber, J. Opt. Soc. Am. 63, 685 (1973).
    [CrossRef]

1973 (2)

M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
[CrossRef]

W. J. Tomlinson and H. P. Weber, J. Opt. Soc. Am. 63, 685 (1973).
[CrossRef]

1972 (1)

1971 (1)

H. G. Danielmeyer, J. Appl. Phys. 42, 3125 (1971).
[CrossRef]

1970 (1)

The presence of a reflecting surface also affects the lifetime of fluorescing centers that are closer to the surface than ~λf. See, e.g., K. H. Drexhage, J. Lumin. 1,2, 693 (1970). For samples of thickness b≫ λf this effect influences our results insignificantly.
[CrossRef]

1967 (1)

M. Yokota and O. Tamimoto, J. Phys. Soc. Jpn. 22, 779 (1967); M. Inokuti and F. Hirayama, J. Chem. Phys. 43, 1978 (1965); M. J. Weber, Phys. Rev. B 4, 2932 (1971).
[CrossRef]

1963 (1)

C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
[CrossRef]

1962 (1)

See, for example, L. G. Van Uitert and S. Ida, J. Chem. Phys. 37, 986 (1962); G. E. Peterson and P. M. Bridenbaugh, J. Opt. Soc. Am. 54, 644 (1964); J. P. Van der Ziel, L. Kopf, and L. G. Van Uitert, Phys. Rev. B 6, 615 (1972).
[CrossRef]

1948 (1)

Th. Förster, Ann. Physik 2, 55 (1948); D. L. Dexter, J. Chem. Phys. 21, 836 (1953). For a recent review, see W. J. G. Grant, Phys. Rev. B 4, 648 (1971) and the references cited therein.
[CrossRef]

Blätte, M.

M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 628–630.

Danielmeyer, H. G.

M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
[CrossRef]

H. G. Danielmeyer, J. Appl. Phys. 42, 3125 (1971).
[CrossRef]

de Mars, G. A.

C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
[CrossRef]

Drexhage, K. H.

The presence of a reflecting surface also affects the lifetime of fluorescing centers that are closer to the surface than ~λf. See, e.g., K. H. Drexhage, J. Lumin. 1,2, 693 (1970). For samples of thickness b≫ λf this effect influences our results insignificantly.
[CrossRef]

Förster, Th.

Th. Förster, Ann. Physik 2, 55 (1948); D. L. Dexter, J. Chem. Phys. 21, 836 (1953). For a recent review, see W. J. G. Grant, Phys. Rev. B 4, 648 (1971) and the references cited therein.
[CrossRef]

Ida, S.

See, for example, L. G. Van Uitert and S. Ida, J. Chem. Phys. 37, 986 (1962); G. E. Peterson and P. M. Bridenbaugh, J. Opt. Soc. Am. 54, 644 (1964); J. P. Van der Ziel, L. Kopf, and L. G. Van Uitert, Phys. Rev. B 6, 615 (1972).
[CrossRef]

Macke, W.

See, for example, W. Macke, Thermodyamik und Statistik, (Akademische Verlagsgesellschaft, Leipzig, 1962), p. 22.

Statz, H.

C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
[CrossRef]

Tamimoto, O.

M. Yokota and O. Tamimoto, J. Phys. Soc. Jpn. 22, 779 (1967); M. Inokuti and F. Hirayama, J. Chem. Phys. 43, 1978 (1965); M. J. Weber, Phys. Rev. B 4, 2932 (1971).
[CrossRef]

Tang, C. L.

C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
[CrossRef]

Tomlinson, W. J.

Ulrich, R.

M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
[CrossRef]

R. Ulrich and H. P. Weber, Appl. Opt. 11, 428 (1972).
[CrossRef] [PubMed]

Van Uitert, L. G.

See, for example, L. G. Van Uitert and S. Ida, J. Chem. Phys. 37, 986 (1962); G. E. Peterson and P. M. Bridenbaugh, J. Opt. Soc. Am. 54, 644 (1964); J. P. Van der Ziel, L. Kopf, and L. G. Van Uitert, Phys. Rev. B 6, 615 (1972).
[CrossRef]

See, for example, L. G. Van Uitert, in Luminescence of Inorganic Solids, edited by P. Goldberg (Academic, New York, 1966), p. 465; M. J. Weber, J. Appl. Phys. 44, 4058 (1973).
[CrossRef]

Weber, H. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 628–630.

Yokota, M.

M. Yokota and O. Tamimoto, J. Phys. Soc. Jpn. 22, 779 (1967); M. Inokuti and F. Hirayama, J. Chem. Phys. 43, 1978 (1965); M. J. Weber, Phys. Rev. B 4, 2932 (1971).
[CrossRef]

Ann. Physik (1)

Th. Förster, Ann. Physik 2, 55 (1948); D. L. Dexter, J. Chem. Phys. 21, 836 (1953). For a recent review, see W. J. G. Grant, Phys. Rev. B 4, 648 (1971) and the references cited therein.
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

M. Blätte, H. G. Danielmeyer, and R. Ulrich, Appl. Phys. 1, 275 (1973); H. P. Weber, B. C. Tofield, and T. C. Damen, in Optical Society Topical Meeting on Integrated Optics, Paper MB8, New Orleans, 21–24 January 1974.
[CrossRef]

J. Appl. Phys. (2)

C. L. Tang, H. Statz, and G. A. de Mars, J. Appl. Phys. 35, 2289 (1963).
[CrossRef]

H. G. Danielmeyer, J. Appl. Phys. 42, 3125 (1971).
[CrossRef]

J. Chem. Phys. (1)

See, for example, L. G. Van Uitert and S. Ida, J. Chem. Phys. 37, 986 (1962); G. E. Peterson and P. M. Bridenbaugh, J. Opt. Soc. Am. 54, 644 (1964); J. P. Van der Ziel, L. Kopf, and L. G. Van Uitert, Phys. Rev. B 6, 615 (1972).
[CrossRef]

J. Lumin. (1)

The presence of a reflecting surface also affects the lifetime of fluorescing centers that are closer to the surface than ~λf. See, e.g., K. H. Drexhage, J. Lumin. 1,2, 693 (1970). For samples of thickness b≫ λf this effect influences our results insignificantly.
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Soc. Jpn. (1)

M. Yokota and O. Tamimoto, J. Phys. Soc. Jpn. 22, 779 (1967); M. Inokuti and F. Hirayama, J. Chem. Phys. 43, 1978 (1965); M. J. Weber, Phys. Rev. B 4, 2932 (1971).
[CrossRef]

Other (4)

See, for example, L. G. Van Uitert, in Luminescence of Inorganic Solids, edited by P. Goldberg (Academic, New York, 1966), p. 465; M. J. Weber, J. Appl. Phys. 44, 4058 (1973).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 628–630.

For purpose for this paper, we shall refer to the mirror as a reflecting metal; however, a dielectric mirror or total-internal reflection may serve the same purpose.

See, for example, W. Macke, Thermodyamik und Statistik, (Akademische Verlagsgesellschaft, Leipzig, 1962), p. 22.

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Figures (7)

Fig. 1
Fig. 1

Generation of excited pattern. Experimental situation. The pump beam (λp) enters the fluorescing material (np) at the angle βp and at the angle αp at the metal boundary.

Fig. 2
Fig. 2

Resulting pumped pattern using excitation as shown in Fig. 1, where kxp is the x component of the wave vector in the material and ψ is the phase shift at the boundary of the metal for the angle αp.

Fig. 3
Fig. 3

Radiation from point source P at distance x from boundary of the metal. αf is the internal, βf the external, angle of observation. P′ is the mirror image and 2x cosαf is the phase delay between P′ and P, for the angle αf.

Fig. 4
Fig. 4

Calculated contrast ratios Q as functions of diffusion distance for pulsed (⋯) and cw (———) excitation. For pulsed excitation, t is the time of observation after the excitation, for cw excitation, t = τf, the fluorescence-decay time.

Fig. 5
Fig. 5

Experimental arrangement of diffusiometer. A silver mirror is coated with a 8-μm-thick layer of polyurethane doped with rhodamine 6G. A microscope cover glass is sealed to it with an index-matching fluid. Placed in the center of a rotatable table, the coated mirror is optically excited with a polarized, chopped beam (λ = 473 nm) of an argon-ion laser, incident at angle βp. The detection system consists of an angle-limiting iris, a narrow-band filter (λ = 550 nm, Δλ = 1.0 nm), polarizer, a photomultiplier, and a lock-in amplifier for synchronous detection. The detection system is on a second rotatable platform; observation is at angle βf.

Fig. 6
Fig. 6

Measured angular dependence of fluorescence irradiance at 550 nm for βp = 63°, with arrangement of Fig. 5. The arrows show the calculated positions of the peaks.

Fig. 7
Fig. 7

Measured dependence of fluorescence irradiance for angle of observation βf = 0°, as a function of pumped periodicity, by variation of the angle of incidence βp. The dots give the calculated fluorescence irradiances.

Equations (23)

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E ( α p , x ) = E 0 [ exp { i ( ω t + k x p x ) } + R p 1 2 exp { i ( ω t - k x p x + ψ ) } ] ,
A ( α p , x ) = I p ( α p , x ) / I 0 = 1 2 E ( α p , x ) 2 / E 0 2 = 1 2 ( 1 + R p ) + R p 1 2 cos ( 2 k x p x - ψ ) .
g ( d = 0 , x ) = A ( α p , x ) = 1 2 ( 1 + R p ) + R p 1 2 · cos ( 2 k x p x - ψ ) .
g ( d , x ) 1 2 ( 1 + R p ) .
g ( t , d , x ) = ( 4 π · t · d ) - 1 2 · - g ( d = 0 , x ) exp { - ( x - x ) 2 4 · t · d } d x ,
g ( t , d , x ) = 1 2 ( 1 + R p ) + R p 1 2 · exp [ - ( 2 k x p ) 2 · t · d ] · cos ( 2 k x p x - ψ ) .
g ( cw , d , x ) = τ f - 1 0 g ( t , d , x ) exp ( - t / τ f ) d t = 1 2 ( 1 + R p ) + R p 1 2 · [ 1 + τ f · ( 2 k x p ) 2 · d ] - 1 · cos ( 2 k x p x - ψ ) .
E ( α f , x ) = e i ω t + R f 1 2 exp { i ( ω t + 2 k x f x + ϕ ) } ,
I f ( α f , x ) = 1 2 E ( α f , x ) 2 = 1 2 ( 1 + R f ) + R f 1 2 cos ( 2 k x f x + ϕ ) .
I f ( α f ) = ( b · cos α p ) - 1 0 b I f ( α f , x ) · g ( d , x ) d x .
I f ( d = 0 , α p , α r ) = ( b · cos α p ) - 1 0 b [ 1 2 ( 1 + R f ) + R f 1 2 cos ( 2 k x f x + ϕ ) ] · [ 1 2 ( 1 + R p ) + R p 1 2 cos ( 2 k x p x - ψ ) ] d x .
I f ( d = 0 , α p , α f ) = ( cos α p ) - 1 · { 1 4 ( 1 + R f ) · ( 1 + R p ) + 1 2 · b ( R f · R p ) 1 2 · 0 b cos [ 2 ( k x f - k x p ) x + ( ϕ - ψ ) ] d x } = ( cos α p ) - 1 { 1 4 ( 1 + R f ) ( 1 + R p ) + 1 2 ( R f · R p ) 1 2 · cos [ Δ k · b + ( ϕ - ψ ) ] · 1 Δ k · b sin Δ k · b } ,
I f ( t , α p , α f ) = ( cos α p ) - 1 { 1 4 ( 1 + R f ) ( 1 + R p ) + 1 2 ( R f · R p ) 1 2 exp [ - ( 2 k x p ) 2 · t · d ] · 1 Δ k · b cos [ Δ k · b + ( ϕ - ψ ) ] · sin Δ k · b } .
I f ( α p , α f ) = ( cos α p ) - 1 { 1 4 ( 1 + R f ) ( 1 + R p ) + 1 2 ( R f R p ) 1 2 [ 1 + ( 2 k x p ) 2 · τ f · d ] - 1 · cos [ Δ k · b + ( ϕ - ψ ) ] 1 Δ k · b sin Δ k · b } .
Q ( t ) = ( cos α p 0 / cos α p ) { 1 + 1 2 · exp [ - ( 2 k x p ) 2 · t · d ] } .
Q ( cw ) = ( cos α p 0 / cos α p ) { 1 + 1 2 [ 1 + ( 2 k x p ) 2 · τ f · d ] - 1 } .
Δ k = k x f - k x p = 0
cos α f = [ ( n p λ f ) / ( n f λ p ) ] · cos α p .
0 < k x p < 2 π n f / λ f = k u .
( 2 k x p ) 2 · t · d 1.
D m k u - 1 ( τ f / t ) 1 2 = λ f 2 π n f ( τ f / t ) 1 2 .
Δ λ f λ f < ( b · k x f ) - 1 ,
I f ( α p , α f ) = cos α p 0 cos α p [ 1 + 1 2 ( 2 Δ k · b ) - 1 sin ( 2 Δ k · b ) ] .