Abstract

We predict the existence of an unexpected interference pattern in the profile of light reflected from a multilayered surface under the conditions for excitation of a waveguide mode or surface plasmon. Observation of the interference effect is shown to require passage of the incident light through a lens or pinhole to produce a spread of incident angles on either side of the resonance angle. The effect has possible application to enhancement of the sensitivity of measurements of changes in the index of refraction of substrate materials.

© 2005 Optical Society of America

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References

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  1. P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325-1336 (1970).
    [CrossRef]
  2. J. E. Midwinter and F. Zernike, "Experimental studies of evanescent wave coupling into a thin-film waveguide," Appl. Phys. Lett. 16, 198-200 (1970).
    [CrossRef]
  3. T. Tamir and H. L. Bertoni, "Lateral displacement of optical beams at multilayered and periodic structures," J. Opt. Soc. Am. 61, 1397-1401 (1971).
    [CrossRef]
  4. W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
    [CrossRef]
  5. R. T. Deck, D. Sarid, G. A. Olson and J. M. Elson, "Coupling between finite electromagnetic beam and long-range surface-plasmon mode," Appl. Opt. 22, 3397-3405 (1983).
    [CrossRef] [PubMed]
  6. M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
    [CrossRef]
  7. R. V. Andaloro, H. J. Simon, and R. T. Deck, "Temporal pulse reshaping with surface waves," Appl. Opt. 33, 6340-6347 (1994).
    [CrossRef] [PubMed]
  8. See, for example, R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), pp. 91-94.
  9. R. V. Andaloro, "Refractometry using beam profile reshaping with surface waves and its application to bioassay," Ph.D. dissertation (University of Toledo, Toledo, Ohio, 2003).
  10. A. A. Maradudin, "Effects of surface roughness on the surface-polariton dispersion relation," Phys. Rev. B 14, 484-499 (1976).
    [CrossRef]

1994 (1)

1986 (1)

M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
[CrossRef]

1983 (1)

1976 (2)

A. A. Maradudin, "Effects of surface roughness on the surface-polariton dispersion relation," Phys. Rev. B 14, 484-499 (1976).
[CrossRef]

W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
[CrossRef]

1971 (1)

1970 (2)

P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325-1336 (1970).
[CrossRef]

J. E. Midwinter and F. Zernike, "Experimental studies of evanescent wave coupling into a thin-film waveguide," Appl. Phys. Lett. 16, 198-200 (1970).
[CrossRef]

Andaloro, R. V.

R. V. Andaloro, H. J. Simon, and R. T. Deck, "Temporal pulse reshaping with surface waves," Appl. Opt. 33, 6340-6347 (1994).
[CrossRef] [PubMed]

R. V. Andaloro, "Refractometry using beam profile reshaping with surface waves and its application to bioassay," Ph.D. dissertation (University of Toledo, Toledo, Ohio, 2003).

Bertoni, H. L.

Boyd, R. W.

See, for example, R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), pp. 91-94.

Burstein, E.

W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
[CrossRef]

Chen, W. P.

W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
[CrossRef]

Deck, R. T.

Elson, J. M.

Fukui, M.

M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, "Effects of surface roughness on the surface-polariton dispersion relation," Phys. Rev. B 14, 484-499 (1976).
[CrossRef]

Midwinter, J. E.

J. E. Midwinter and F. Zernike, "Experimental studies of evanescent wave coupling into a thin-film waveguide," Appl. Phys. Lett. 16, 198-200 (1970).
[CrossRef]

Oda, K.

M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
[CrossRef]

Olson, G. A.

Ritchie, G.

W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
[CrossRef]

Sarid, D.

Simon, H. J.

Tago, S.

M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
[CrossRef]

Tamir, T.

Tien, P. K.

Ulrich, R.

Zernike, F.

J. E. Midwinter and F. Zernike, "Experimental studies of evanescent wave coupling into a thin-film waveguide," Appl. Phys. Lett. 16, 198-200 (1970).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. E. Midwinter and F. Zernike, "Experimental studies of evanescent wave coupling into a thin-film waveguide," Appl. Phys. Lett. 16, 198-200 (1970).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Soc. Jpn. (1)

M. Fukui, S. Tago, and K. Oda, "Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam," J. Phys. Soc. Jpn. 55, 973-980 (1986).
[CrossRef]

Phys. Rev. B (1)

A. A. Maradudin, "Effects of surface roughness on the surface-polariton dispersion relation," Phys. Rev. B 14, 484-499 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

W. P. Chen, G. Ritchie, and E. Burstein, "Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations," Phys. Rev. Lett. 37, 993-997 (1976).
[CrossRef]

Other (2)

See, for example, R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), pp. 91-94.

R. V. Andaloro, "Refractometry using beam profile reshaping with surface waves and its application to bioassay," Ph.D. dissertation (University of Toledo, Toledo, Ohio, 2003).

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Figures (3)

Fig. 1
Fig. 1

Prism-coupling geometry used to excite surface or waveguide modes on or within the boundaries of medium 2.

Fig. 2
Fig. 2

Comparison between the incident beam profile (dotted curve) and the calculated profile of the reflected beam as a function of the lateral surface coordinate x , under the conditions for excitation of a long-range surface plasmon (solid curve). Parameter values are λ = 0.76 μ m , w o = 2.0 mm , f = 10 cm , R = 6 cm , d = 4.0 cm , n o = 1.472 , n 1 = n 3 = 1.35 , ϵ 2 = ϵ gold = 23.0 + 1.6 i , d 1 = 2.0 μ m , d 2 = 0.014 μ m , θ o = θ plasmon = 66.9 o . Inset, same profile calculated on the basis of the pole approximation for the reflection coefficient.

Fig. 3
Fig. 3

Calculated profile of the reflected beam, in comparison with the incident beam (dotted curve), as a function of the lateral surface coordinate x under conditions for excitation of a waveguide mode in medium 2. Note the change in scale here compared with that in Fig. 2. Parameter values are λ = 1.064 μ m , w o = 5.33 mm , f = 50 cm , R = 46 cm , d = 4.0 cm , n o = 1.755 , n 1 = 1.536 , n 2 = 2.482 , n 3 = 1.536 , d 1 = 0.95 μ m , d 2 = 0.08 μ m , θ o = θ plasmon = 80.32 o . Inset, comparison graphs showing the effect of an increase in the substrate index equal to 0.001 on segment of the reflected profile curve in Fig. 3. Dark and light curves correspond to initial and detuned index values respectively.

Equations (19)

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r 0123 ( k x ) = A ( k ̃ x ) + C ( k ̃ x ) k x k ̃ x .
B o ( r ) = A ( r ) exp ( i k z ) ,
A ( r ) = w o w ( z ) A o exp [ x 2 + y 2 w 2 ( z ) ] exp [ i k ( x 2 + y 2 ) 2 R ( z ) ] exp [ i tan 1 ( z z o ) ] .
R ( z ) = z [ 1 + ( z o z ) 2 ( 1 z f ) 2 ] [ 1 ( z o z ) 2 z f ( 1 z f ) ] ,
w ( z ) w o [ ( 1 z f ) 2 + ( z z o ) 2 ] 1 2 .
B o ( x , 0 ) = w o w ( d ) A o exp { [ 1 w 2 ( d ) i k 2 R ( d ) ] ( x cos θ o ) 2 } × exp [ i k ( d + x sin θ o ) i tan 1 ( d z o ) ] .
Λ λ R ( d ) x n cos 2 θ o .
B ref ( x , 0 ) = d k x r 0123 ( k x ) B ̃ o ( k x ) exp ( i k x x ) ,
B ̃ o ( k x ) = 1 2 π d x B o ( x , 0 ) exp ( i k x x ) .
C ( k ̃ x ) d x B o ( x , 0 ) 1 2 π d k x exp [ i k x ( x x ) ] k x k ̃ x .
B ref ( x , 0 ) = A ( k ̃ x ) B o ( x , 0 ) + i C ( k ̃ x ) × x d x B o ( x , 0 ) × exp [ i k ̃ x ( x x ) ] .
B ref ( x , 0 ) = N o A ( k ̃ x ) exp ( i k x ) exp [ cos 2 θ o w 2 ( d ) x 2 ] × exp [ i k cos 2 θ o 2 R ( d ) x 2 ] + i N o C ( k ̃ x ) π 2 K × exp [ ( k ̃ x k ) 2 4 K 2 ] exp ( i k ̃ x x ) × { 1 + erf [ K x + i ( k ̃ x k ) 2 K ] } ,
N o = w o w ( d ) A o exp [ i k d i tan 1 ( d z o ) ] ,
K = [ 1 w 2 ( d ) i k 2 R ( d ) ] 1 2 cos θ o .
2 λ x n cos θ o d [ 1 + ( z o d ) 2 ( 1 d f ) 2 ] 1 ( z o d ) 2 d f ( 1 d f ) < w o [ ( 1 d f ) 2 + ( d z o ) 2 ] 1 2 .
Λ = λ ( 1 d f ) f x n cos 2 θ o ,
Λ = λ d x n cos 2 θ o [ 1 + ( z o d ) 2 ] = π 2 n w o 4 λ x d cos 2 θ o .
w o > 2 λ x n cos θ o f ,
w o < ( λ x d cos θ o 2 n π 2 ) 1 3 ,

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