Abstract

A theoretical treatment of the morphology-dependent resonances of a dielectric sphere on or near a plane surface of infinite conductivity is presented. The scattering theory for this problem is reviewed, and computational procedures are described. Resonance peaks are identified and correlated with the corresponding resonances in the isolated sphere. The study examines how the locations and widths of the resonances change as the particle approaches the surface. The locations of the TE resonances (expressed as size parameter) shift to higher values, the locations of the TM resonances shift to a lower values, and the widths are broadened. As the particle approaches the surface, 90% of the change in location occurs within a distance of ∼ 0.1 of a particle radius from the surface. The reason for this behavior is discussed. An example case is presented that shows how a narrow resonance that is completely suppressed by internal losses in an isolated sphere can become an active and strong resonance when the sphere is brought near a conducting surface.

© 1994 Optical Society of America

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References

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    [CrossRef]
  9. D. R. Smith, “Evidence for off-axis leakage radiance in high-altitude IR rocket borne measurements,” in Stray Light and Contamination in Optical Systems, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 30–36 (1988).
    [CrossRef]
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    [CrossRef]
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  12. J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).
  13. L. M. Folan, S. Arnold, “Microparticle fluorescence and energy transfer,” in Biochemical Applications, J. R. Lakowitcz, ed., Vol. 3 of Topics in Fluorescence Spectroscopy (Plenum, New York, 1992), pp. 345–386.
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    [CrossRef]

1993

1992

1991

1989

1987

1985

1984

1981

1974

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Armstrong, R. L.

Arnold, S.

Barber, P. W.

Benner, R. E.

Burstein, E.

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Chang, R. K.

Chen, W. P.

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Chen, Y. J.

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Chylek, P.

J. Li, P. Chylek, “Resonances of a dielectric sphere illuminated by two counterpropagating plane waves,” J. Opt. Soc. Am. A 10, 687–692 (1993).
[CrossRef]

G. Videen, P. Chylek, “Light scattering resonance enhancement and suppression in cylinders and spheres using two coherent plane waves,” Opt. Commun. 98, 313–322 (1993).
[CrossRef]

Communale, J.

Conwell, P. R.

Essien, M.

Folan, L. M.

L. M. Folan, S. Arnold, “Microparticle fluorescence and energy transfer,” in Biochemical Applications, J. R. Lakowitcz, ed., Vol. 3 of Topics in Fluorescence Spectroscopy (Plenum, New York, 1992), pp. 345–386.

Fuller, K. A.

Gillespie, J. B.

Hartstein, A.

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Hill, S. C.

Johnson, B. R.

Li, J.

Liu, C. T.

Owens, J. F.

Ramsey, J. M.

Rushforth, C. K.

Schlicht, B.

Smith, D. R.

D. R. Smith, “Evidence for off-axis leakage radiance in high-altitude IR rocket borne measurements,” in Stray Light and Contamination in Optical Systems, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 30–36 (1988).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).

Videen, G.

G. Videen, P. Chylek, “Light scattering resonance enhancement and suppression in cylinders and spheres using two coherent plane waves,” Opt. Commun. 98, 313–322 (1993).
[CrossRef]

G. Videen, “Light scattering from a sphere on or near a surfaco,” J. Opt. Soc. Am. A 8, 483–489 (1991);J. Opt. Soc. Am. A errata 9, 844–845 (1992).
[CrossRef]

Wall, K. F.

Whitten, W. B.

Appl. Opt.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Vac. Sci. Technol.

E. Burstein, W. P. Chen, Y. J. Chen, A. Hartstein, “Surface polaritons—propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[CrossRef]

Opt. Commun.

G. Videen, P. Chylek, “Light scattering resonance enhancement and suppression in cylinders and spheres using two coherent plane waves,” Opt. Commun. 98, 313–322 (1993).
[CrossRef]

Opt. Lett.

Other

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

B. R. Johnson, “Exact calculation of light scattering from a particle on a mirror,” in Optical System Contamination: Effects, Measurement, Control III, A. P. Glassford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1754, 72–83 (1992).
[CrossRef]

D. R. Smith, “Evidence for off-axis leakage radiance in high-altitude IR rocket borne measurements,” in Stray Light and Contamination in Optical Systems, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 30–36 (1988).
[CrossRef]

M. Abramowitz, I. A. Stegun, eds. Handbook of Mathematical Functions (Dover, New York, 1965).

J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).

L. M. Folan, S. Arnold, “Microparticle fluorescence and energy transfer,” in Biochemical Applications, J. R. Lakowitcz, ed., Vol. 3 of Topics in Fluorescence Spectroscopy (Plenum, New York, 1992), pp. 345–386.

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem of a particle on a mirror.

Fig. 2
Fig. 2

Geometry of the two-particle problem that is equivalent, by the method of images, to the problem shown in Fig. 1.

Fig. 3
Fig. 3

TE20,1 resonance as a function of distance parameter δ = d/a, where d is the distance of the center of the sphere from the conducting plane and a is the radius of the sphere. The vertical dashed line is at the location of this resonance in an isolated sphere. The quantity plotted is the normalized intensity variable IV defined by Eq. (14).

Fig. 4
Fig. 4

TM20,1 resonance as a function of distance parameter δ = d/a. The vertical dashed line is the location of this resonance in an isolated sphere.

Fig. 5
Fig. 5

Radial dependence of the angle-averaged electric-field intensity, normalized to a unit-amplitude incident wave 〈|E|2Ω/〈|Einc|2〉, for a particle with m = 1.59 + 0i at the resonance size parameter of the TE20,1 resonance in the isolated sphere, ka = 15.38087. The two vertical dashed lines are the radius of the sphere and the outer turning point.

Fig. 6
Fig. 6

Shift in the center of the TE20,1 resonance from its position in an isolated sphere versus distance parameter δ. The vertical dashed line marks the outer boundary of the near region defined in the text. The horizontal dashed line marks a value of shift that is 25% of the width of unperturbed TE20,1 resonance in an isolated sphere.

Fig. 7
Fig. 7

Plot of the normalized volume average internal electric-field intensity, IV, as a function of the size parameter for a sphere with m = 1.59 + 0i that is resting on a conducting plane. A total of 33 resonances are identified and labeled; the parameters of these resonances are given in Table 1. The graph has been divided into two parts for convenience; note the change in intensity scale.

Fig. 8
Fig. 8

Enlarged view of the resonances labeled 20, 21, and 22. Plotted are the intensity variable IV and the mode coefficients |c23|2, |d23|2, and |d27|2 that make the largest contributions to these resonances.

Fig. 9
Fig. 9

Scattering efficiency versus size parameter over the spectrum of 33 resonances: (a) isolated sphere, (b) sphere resting on a conducting plane. The resonance parameters for both cases are given in Table 1.

Fig. 10
Fig. 10

Plot of the intensity IV versus size parameter showing the resonance TE35,1 for a sphere resting on a conducting plane. The real part of the index of refraction is mr = 1.59; the imaginary part is assigned three different values: mi = 0.0, 0.00001, and 0.00003.

Tables (1)

Tables Icon

Table 1 Resonance Parameters for the Isolated Particle and the Particle on a Conducting Surface

Equations (22)

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E inc = ( ê x + i ê y ) exp ( i k z ) ,
E ext = E i + E s ( 1 ) + E s ( 2 ) ,
E i = ( ê x + i ê y ) [ exp ( i k z ) exp ( i k z ) ]
M n ( j ) = 1 k r f n ( j ) ( m k r ) exp ( i ϕ ) X n ( θ ) , N n ( j ) = 1 m k r exp ( i ϕ ) { [ f n ( j ) ( m k r ) ] Y n ( θ ) + 1 m k r f n ( j ) ( m k r ) Z n ( θ ) } ,
X n ( θ ) = i π n ( θ ) ê θ τ n ( θ ) ê ϕ , Y n ( θ ) = τ n ( θ ) ê θ + i π n ( θ ) ê ϕ , Z n ( θ ) = n ( n + 1 ) P n 1 ( cos θ ) ê r ,
π n ( θ ) = 1 sin ( θ ) P n 1 ( cos θ ) , τ n ( θ ) = θ P n 1 ( cos θ ) .
E s ( j ) ( r j ) = n = 1 [ a n ( j ) M n ( 3 ) ( r j ) + b n ( j ) N n ( 3 ) ( r j ) ] , j = 1 , 2 .
E int ( j ) ( r j ) = n = 1 [ c n ( j ) M n ( 1 ) ( r j ) + d n ( j ) N n ( 1 ) ( r j ) ] , j = 1 , 2 .
E inc ( 2 ) ( r 2 ) = n = 1 [ α n ( 2 ) M n ( 1 ) ( r 2 ) + β n ( 2 ) N n ( 1 ) ( r 2 ) ] .
α n ( 2 ) = a n ( 2 ) / u n , β n ( 2 ) = b n ( 2 ) / υ n ,
E ext = n = 0 [ α n ( 2 ) M n ( 1 ) ( r 2 ) + β n ( 2 ) N n ( 1 ) ( r 2 ) + a n ( 2 ) M n ( 3 ) ( r 2 ) + b n ( 2 ) N n ( 3 ) ( r 2 ) ] .
c n ( 2 ) = [ α n ( 2 ) ψ n ( x ) + a n ( 2 ) ξ n ( x ) ] / ψ n ( m x ) , d n ( 2 ) = [ β n ( 2 ) ψ n ( x ) + b n ( 2 ) ξ n ( x ) ] / ψ n ( m x ) ,
| E int ( 2 ) | 2 V = n = 1 [ | c n ( 2 ) | 2 | M n | 2 V + | d n ( 2 ) | 2 | N n | 2 V ] ,
I V = | E int | 2 V | E inc | 2 .
I V = 3 8 m r m i x Q abs ,
w = w 0 + 2 x 0 m i m r ,
| M n ( 1 ) ( r ) | 2 d 3 r = 4 π k 3 n n 2 ( n + 1 ) 2 2 n + 1 J n ( 1 ) ,
| N n ( 1 ) ( r ) | 2 d 3 r = 4 π k 3 n n 2 ( n + 1 ) 2 2 n + 1 [ J n ( 2 ) + J n ( 3 ) ] ,
J n ( 1 ) = 0 x | ψ n ( m ρ ) | 2 d ρ ,
J n ( 2 ) = 0 x | ψ n ( m ρ ) | 2 d ρ ,
J n ( 3 ) = n ( n + 1 ) | m | 2 0 x 1 ρ 2 | ψ n ( m ρ ) | 2 d ρ .
I V = 3 2 x 3 n n 2 ( n + 1 ) 2 2 n + 1 { | c n | 2 J n ( 1 ) + | d n | 2 [ J n ( 2 ) + J n ( 3 ) | m | 2 ] } ,

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