Abstract

A solution procedure is developed for the determination of the electromagnetic field that results from the interaction of a focused light sheet with a plane surface. The effects of angle of incidence, relative index of refraction, polarization, and incident light sheet profile on the resulting electromagnetic field distribution are demonstrated.

© 2005 Optical Society of America

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References

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  1. J. P. Barton, “Internal and near-surface electromagnetic fields for an infinite cylinder illuminated by an arbitrary focused beam,” J. Opt. Soc. Am. A 16, 160–166 (1999).
    [CrossRef]
  2. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, New York, 1966).
  3. J. P. Barton, “Electromagnetic field calculations for irregularly shaped, layered cylindrical particles with focused illumination,” Appl. Opt. 36, 1312–1319 (1997).
    [CrossRef] [PubMed]
  4. P. Lorrain, D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, Calif., 1970).
  5. J. P. Barton, “Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
    [CrossRef] [PubMed]
  6. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]

1999

1997

1989

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Barton, J. P.

Clemmow, P. C.

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

Corson, D. R.

P. Lorrain, D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, Calif., 1970).

Lorrain, P.

P. Lorrain, D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, Calif., 1970).

Appl. Opt.

J. Appl. Phys.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Other

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

P. Lorrain, D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, Calif., 1970).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the geometrical arrangement.

Fig. 2
Fig. 2

Plot of electric-field magnitude E y in the x z plane for a focused light sheet (perpendicular polarization) incident on a plane surface. The plot extends ± 10 external wavelengths in both the x- and the z-axis directions. Relative index of refraction n ¯ = ( 1.5 , 0.0 ) , external dielectric constant ϵ ext = 1.0 , light sheet waist half-width w 0 = 2.0 λ ext , focal point location ( x 0 , z 0 ) = ( 0.0 , 0.0 ) , and angle of incidence θ b d = 30 ° .

Fig. 3
Fig. 3

Same as Fig. 2, but for θ b d = 45 ° .

Fig. 4
Fig. 4

Same as for Fig. 2, but for θ b d = 60 ° .

Fig. 5
Fig. 5

Same as Fig. 2, but for n ¯ = ( 1.5 , 0.05 ) .

Fig. 6
Fig. 6

Same as Fig. 2, but for n ¯ = ( 0.666667 , 0.0 ) , ϵ ext = 2.25 .

Fig. 7
Fig. 7

Same as Fig. 6, but for θ b d = 60 ° .

Fig. 8
Fig. 8

Plot of magnetic-field magnitude H y in the x z plane for a focused light sheet (parallel polarization) incident on a plane surface. All else as in Fig. 2.

Fig. 9
Fig. 9

Plot of electric field magnitude E y in the x z plane for a “doughnut-mode” focused light sheet (perpendicular polarization) incident on a plane surface. All else as in Fig. 2.

Equations (51)

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2 E y + k 2 E y = 0 ,
E y ( x , z ) exp ( i k z z ) exp ( ± i k x x ) ,
k x ( r ) = ( k ext 2 k z 2 ) 1 2 ,
E y ( r ) ( x , z ) = a ( k z ) exp ( i k z z ) exp ( i k x ( r ) x ) d k z ,
H x ( r ) ( x , z ) = ϵ ext k ext k z a ( k z ) exp ( i k z z ) exp ( i k x ( r ) x ) d k z ,
H y ( r ) ( x , z ) = 0 ,
H z ( r ) ( x , z ) = + ϵ ext k ext k x ( r ) a ( k z ) exp ( i k z z ) exp ( i k x ( r ) x ) d k z .
k x ( t ) = ( n ¯ 2 k ext 2 k z 2 ) 1 2 ,
E y ( t ) ( x , z ) = c ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
H x ( t ) ( x , z ) = ϵ ext k ext k z c ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
H y ( t ) ( x , z ) = 0 ,
H z ( t ) ( x , z ) = ϵ ext k ext k x ( t ) c ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
E y ( t ) ( 0 , z ) E y ( r ) ( 0 , z ) = E y ( i ) ( 0 , z ) ,
H z ( t ) ( 0 , z ) H z ( r ) ( 0 , z ) = H z ( i ) ( 0 , z ) .
E y ( i ) ( 0 , z ) = A ( k z ) exp ( i k z z ) d z ,
H z ( i ) ( 0 , z ) = C ( k z ) exp ( i k z z ) d z ,
A ( k z ) = 1 2 π E y ( i ) ( 0 , z ) exp ( i k z z ) d z ,
C ( k z ) = 1 2 π H z ( i ) ( 0 , z ) exp ( i k z z ) d z .
c ( k z ) a ( k z ) = A ( k z ) ,
ϵ ext k ext k x ( t ) c ( k z ) ϵ ext k ext k x ( r ) a ( k z ) = C ( k z ) .
a ( k z ) = k x ( t ) A ( k z ) k ext C ( k z ) ϵ ext k x ( r ) + k x ( t ) ,
c ( k z ) = k x ( r ) A ( k z ) k ext C ( k z ) ϵ ext k x ( r ) + k x ( t ) .
2 H y + k 2 H y = 0
H y ( x , z ) exp ( i k z z ) exp ( ± k x x ) .
H y ( r ) ( x , z ) = b ( k z ) exp ( i k z z ) exp ( i k x ( r ) x ) d k z ,
E x ( r ) ( x , z ) = + 1 ϵ ext k ext k z b ( k z ) exp ( i k z z ) exp ( i k x ( r ) x ) d k z ,
E y ( t ) ( x , z ) = 0 ,
E z ( r ) ( x , z ) = 1 ϵ ext k ext k x ( r ) b ( k z ) exp ( i k z z ) × exp ( i k x ( r ) x ) d k z ,
H y ( t ) ( x , z ) = d ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
E x ( t ) ( x , z ) = + 1 n ¯ 2 ϵ ext k ext k z d ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
E y ( t ) ( x , z ) = 0 ,
E z ( t ) ( x , z ) = + 1 n ¯ 2 ϵ ext k ext k x ( t ) d ( k z ) exp ( i k z z ) exp ( i k x ( t ) x ) d k z ,
E z ( t ) ( 0 , z ) E z ( r ) ( 0 , z ) = E z ( i ) ( 0 , z ) ,
H y ( t ) ( 0 , z ) H y ( r ) ( 0 , z ) = H y ( i ) ( 0 , z ) ,
b ( k z ) = n ¯ 2 ϵ ext k ext B ( k z ) k x ( t ) D ( k z ) n ¯ 2 k x ( r ) + k x ( t ) ,
d ( k z ) = n ¯ 2 ϵ ext k ext B ( k z ) n ¯ 2 k x ( r ) D ( k z ) n ¯ 2 k x ( r ) + k x ( t ) ,
B ( k z ) = 1 2 π E z ( i ) ( 0 , z ) exp ( i k z z ) d z ,
D ( k z ) = 1 2 π H y ( i ) ( 0 , z ) exp ( i k z z ) d z .
E x = 0 ,
E y = E 0 [ 1 + s 2 ( i Q 4 2 η 2 Q 2 + i η 4 Q 3 ) + s 4 ( 3 Q 2 32 + 9 i η 2 Q 3 4 + 7 η 4 Q 4 4 i η 6 Q 5 η 8 Q 6 2 ) ] ψ 0 exp ( i ζ s 2 ) ,
E z = 0 ,
H x = ϵ E 0 [ 1 + s 2 ( 5 i Q 4 4 η 2 Q 2 + i η 4 Q 3 ) + s 4 ( 27 Q 2 32 + 51 i η 2 Q 3 4 + 18 η 4 Q 4 6 i η 6 Q 5 η 8 Q 6 2 ) ] ψ 0 exp ( i ζ s 2 ) ,
H y = 0 ,
H z = ϵ E 0 [ s ( 2 η Q ) + s 3 ( 9 i η Q 2 2 + 8 η 3 Q 3 2 i η 5 Q 4 ) + s 5 ( 75 η Q 3 16 65 i η 3 Q 4 2 38 η 5 Q 5 + 12 i η 7 Q 6 + η 9 Q 7 ) ] ψ 0 exp ( i ζ s 2 ) .
s = 1 ( k w 0 ) ,
ζ = z ( k w 0 2 ) ,
η = x w 0 ,
Q = 1 ( i + 2 ζ ) ,
ψ 0 = i Q exp ( i η 2 Q ) ,
E ( mag ) = H ( elec ) ϵ ,
H ( mag ) = ϵ E ( elec ) .

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