Abstract

The field properties of surface plasmons produced by realistically bounded beams incident in various attenuated total reflection (ATR) geometries are examined. Analytical results are first derived for the general case dealing with a beam field incident in a multilayered configuration. We show that, at the phase matching condition, the reflected field can be severely distorted in comparison with the incident beam shape. We also find that the power intensity inside the metal medium can be much smaller than that expected under the assumption of plane wave incidence. However, when the beamwidth is larger than the proportion range of the excited plasmon, the power intensity profiles and find that they exhibit distinguishing characteristics. In particular, for an incident Gaussian beam, the location of maximum power density on the metal surface shifts with respect to the center of the incident beam by a distance of the order of the plasmon propagation length. For a rectangular beam incident at the phase matching condition, on the other hand, the propagation range of the coupled surface plasmon can be found directly from the profile of the reflected field. We also show the overall process of beam wave coupling in the ATR geometry can be simulated by a spatial operating system having the response of either a differentiator (for the reflected field) or an integrator (for the transmitted field).

© 1989 Optical Society of America

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References

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  1. T. Tamir, “Nonspecular Phenomena in Beam Fields Reflected by Multilayered Media,” J. Opt. Soc. Am. A 3, 558 (1986).
    [CrossRef]
  2. J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).
  3. T. Tamir, H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61, 1397 (1971).
    [CrossRef]
  4. C. W. Hsue, T. Tamir, “Lateral Displacement and Distortion of Beams Incident upon a Transmitting-Layer Configuration,”J. Opt. Soc. Am. A 2, 978 (1985).
    [CrossRef]
  5. R. T. Deck, D. Sarid, G. A. Olson, J. M. Elson, “Coupling Between Finite Electromagnetic Beam and Long-Range Surface-Plasmon Modes,” Appl. Opt. 22, 3397 (1983).
    [CrossRef] [PubMed]
  6. R. A. Booman, G. A. Olson, D. Sarid, “Determination of Loss Coefficients of Long-Range Surface Plasmons,” Appl. Opt. 25, 2729 (1986).
    [CrossRef] [PubMed]
  7. A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
    [CrossRef]
  8. E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
    [CrossRef]
  9. D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
    [CrossRef]
  10. G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
    [CrossRef]
  11. F. Y. Kou, T. Tamir, “Range Extension of Surface Plasmons by Dielectric Layers,” Opt. Lett. 12, 367 (1987).
    [CrossRef] [PubMed]
  12. R. Ulrich, “Theory of Prism–Film Coupler by Plane-Wave Analysis,” J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  13. E. F.-Y. Kou, “Excitation of Leaky Waves and Surface Plasmons Along Dielectric and Metallic Layers,” Ph. D. Dissertation, Polytechnic University, Brooklyn, NY 11201 (1988), Sec. 2.2.
  14. E. F. Y. Kou, T. Tamir, “Incidence Angles for Optimized ATR Excitation of Surface Plasmons,” Appl. Opt. 27, 4098 (1988).
    [CrossRef] [PubMed]

1988

1987

1986

1985

1983

1982

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[CrossRef]

1981

D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

1973

J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).

1971

T. Tamir, H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61, 1397 (1971).
[CrossRef]

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

1970

1968

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[CrossRef]

Bertoni, H. L.

J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).

T. Tamir, H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61, 1397 (1971).
[CrossRef]

Booman, R. A.

Burke, J. J.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[CrossRef]

Deck, R. T.

Elson, J. M.

Felsen, L. B.

J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).

Hall, D. G.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[CrossRef]

Hsue, C. W.

Kou, E. F. Y.

Kou, E. F.-Y.

E. F.-Y. Kou, “Excitation of Leaky Waves and Surface Plasmons Along Dielectric and Metallic Layers,” Ph. D. Dissertation, Polytechnic University, Brooklyn, NY 11201 (1988), Sec. 2.2.

Kou, F. Y.

Kretschmann, E.

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

Olson, G. A.

Otto, A.

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[CrossRef]

Ra, J. W.

J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).

Sarid, D.

Stegeman, G. I.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[CrossRef]

Tamir, T.

Ulrich, R.

Appl. Opt.

Appl. Phys. Lett.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[CrossRef]

J. Appl. Math.

J. W. Ra, H. L. Bertoni, L. B. Felsen, “Reflection and Transmission of Beams at a Dielectric Interface,” J. Appl. Math. 24, 396 (1973).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. Lett.

D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Z. Phys

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[CrossRef]

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

Other

E. F.-Y. Kou, “Excitation of Leaky Waves and Surface Plasmons Along Dielectric and Metallic Layers,” Ph. D. Dissertation, Polytechnic University, Brooklyn, NY 11201 (1988), Sec. 2.2.

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Figures (10)

Fig. 1
Fig. 1

Geometry of a bounded beam incident on a general multilayered structure. Here xj is the longitudinal distance that the principal ray travels inside the jth layer.

Fig. 2
Fig. 2

(a) Typical LRSP geometry and (b) its pertinent response functions Hu and Hs+. The curves show the exact results whereas the points indicated by crosses are obtained from Eq. (15).

Fig. 3
Fig. 3

Gaussian beam Pi (dashed line) and its reflected beam Pr (solid line) calculated at z = 0 in the geometry of Fig. 2.

Fig. 4
Fig. 4

Power densities Ps (and Pm) produced at zs = 0 (and z2 = 0) in Fig. 2 by Gaussian beams of various beamwidths.

Fig. 5
Fig. 5

Distributions of Ps showing the shift of the Gaussian beam center for the cases when 0.5 w k κ p 1.5. Here Δx = xBc.

Fig. 6
Fig. 6

Rectangular beam Pi (thinner line) and its reflected beam Pr (thicker line) calculated at z = 0 in the geometry of Fig. 2.

Fig. 7
Fig. 7

Power densities Ps (Pm) produced at zs = 0 (z2 = 0) in Fig. 2 by rectangular beams of various beamwidths.

Fig. 8
Fig. 8

(a) Variation of ∣r(κi)∣ in a Kretschmann geometry with a thin aluminum film. (b) Power densities produced at the substrate of (a) by rectangular beams incident at θi = θp and θi and θn.

Fig. 9
Fig. 9

Profiles of the reflected beams Pr of a rectangular beam incident in an ERSP geometry with (a) θi = θpo and (b) θi = θpe.

Fig. 10
Fig. 10

Variations of the power intensities P0, Pe1, and Pe2. The smaller slopes in Pe1 and Pe2 indicate larger propagation ranges of the plasmon modes in the ERSP geometry. Here Δx = xBr.

Equations (41)

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( x i z i ) = [ cos θ i −sin θ i sin θ i cos θ i ]   ( x z + h ) .
H i ( x i , z i ) = 1 2 π A ( s )  exp [ i k n u   ( s x i + c z i ) ] d s ,
A ( s ) = H i ( x i , 0 )  exp ( i k n u , s x i ) d x i
s = s + i s = sin ( θ θ i ) ,
c = c + i c = cos ( θ θ i ) = ( 1 s 2 ) 1 / 2 .
H i ( x , z ) = 1 2 π A ( s )  exp [ i k n u   ( c  cos θ i s  sin θ i ) h ] ×  exp [ i k ( κ x + τ u z ) ]   d s ,
1 n u ( κ τ u ) = [  cos θ i  sin θ i −sin θ i  cos θ i ]   [ s c ]   .
H ( x , z ) = 1 2 π A ( s )  exp [ i k n u   ( c  cos θ i s  sin θ i ) h + i k κ x ] × ( H j +  exp [ i k τ j z j ] H j  exp [ i k τ j z j ] ) d s ,
τ j = ( ϵ j κ 2 ) 1 / 2
c 1 s 2 2
τ u , j τ u , j ( 0 ) + d τ u , j ( 0 ) d s s + d 2 τ u , j ( 0 ) d s 2 s 2 2 ,
A ( s ) =  exp [ In A ( s ) ] A ( 0 )  exp ( P s + B s 2 ) ,
P = d A ( 0 ) / d s A ( 0 ) ,
B = A ( 0 ) d 2 A ( 0 ) d s 2 [ d A ( 0 ) d s ] 2 2 A 2 ( 0 ) .
H j ± R j ± κ κ j ± κ κ p ,
H j ± R j ± [ 1 + ( κ p κ j ± ) / ( cos θ i s p  sin θ i ) n u   ( s s p ) ]  ,
H i ( x i , 0 ) =  exp [ ( x i / w ) 2 ]  ,
A ( s ) = k n u w π  exp [ ( k n u w s / 2 ) 2 ]  .
H ( x , z ) = A ( 0 ) 2 π { R j ( 1 + r j + s s p )  exp [ q +   ( s ) ] R j −  ( 1 + r j s s p )  exp [ q ( s ) ] } d s ,
r j ± = κ p κ j ± n u   ( cos θ i s p  sin θ i ) ,
q ± ( s ) = ( k n u w s 2 ) 2 + i k n ( s ξ + c η ) ± i k τ j z j ,
( ξ η ) = [  cos θ i −sin θ i  sin θ i  cos θ i ]   ( x h )   .
q ( s ) q ( 0 ) + d q ( 0 ) d s s + d 2 q ( 0 ) d s 2 s 2 2 ,
H ( x , z ) = R j [ G j + i r j A ( 0 ) 2 L j + ] R j −  [ G j + i r j −  A ( 0 ) 2 L j ]  ,
G j ± = exp { i k ( n u η ± τ j 0 z j ) ( ξ ± z j n u  sin ( 2 θ i ) / τ j 0 w ) 2 } ,
L j ± =  exp [ ( k w κ p 2  cos θ i ) 2 + i k ( τ u p h + κ p x ± τ j p z j ) ] × erfc ( k w κ p 2  cos θ i + ξ w ) ,
τ j ( 0   ,   p ) = ( ϵ j κ j   ,   p 2 ) 1 / 2
n j  sin θ j = n u  sin θ u   , j = u , s , 1 , 2 , , l ,
G j ± = G p ±  G a ±  ,
G p ± =  exp [ i k ( τ u 0 h + κ i ν = 1 j 1 t ν  tan θ ν ) + i k n j   ( x j  sin θ j ± z j  cos θ j ) ]  ,
G a ± =  exp { [ ( x j + ν = 1 j 1 t ν  tan θ ν )  cos θ j z j  sin θ j w  cos θ j /  cos θ i ] 2 }  .
D t 1 k κ p .
H i ( x i , 0 ) = { 1 | x i | w , 0 | x i | > w ,
A ( s ) = 2  sin ( k n u w s ) s ,
H ( x , z ) = 1 2   { R j +   [   ( 1 r j + s p )   G ˜ j + + r j + s p L ˜ j + ] R j −  [   ( 1 r j s p )   G ˜ j + r j s p L ˜ j ]   } ,
G ˜ j ± =  exp [ i k   ( n u η ± τ j 0 z j ) ]   [ erfc  ( a l ) erfc  ( a r ) ] ,
L ˜ j ± =  exp [ i k ( τ u p h + κ p x ± τ j p z j ) w k κ p cos θ i ] + [ erfc  ( a l + ϕ )  exp  ( 2 w k κ p cos θ i )  erfc  ( a r + ϕ ) ] ,
a r l = ( k n u η 2 ) 1 / 2 ξ z j  tan θ i  cos θ i ± w η  exp ( i 3 π 4 ) ,
ϕ = ( k n u η 2 ) 1 / 2 κ p cos θ i  exp  ( i π 4 )   .
H r ( x , 0 ) = R u 2 [ ( 1 r u s p ) G ˜ u + r u s p L ˜ u ]   ,
κ p ln   ( p r 1 / p r 2 ) 2 k ( x 2 x 1 ) ,

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