Abstract

A previously developed theoretical method for determining the electromagnetic fields for arbitrary monochromatic light incident on an irregularly shaped particle, the boundary-matching method, is used to investigate the effects of small surface perturbations on the quality Q and the focused-beam excitation of resonances in microspheres. Axisymmetric particles with periodic surface roughness and irregular surface roughness are considered. For a given resonance the resonance Q is found to be relatively unaffected by the presence of the surface perturbations until the surface perturbation amplitude reaches a threshold value, beyond which the Q decreases rapidly with increasing . For the perfect sphere, focused-beam excitation of the resonance is most efficient with the beam focused outside the surface of the sphere at a location consistent with the prediction of van de Hulst’s localization principle. However, calculations indicate that, for conditions under which the surface perturbation amplitude is large enough to appreciably decrease the resonance Q, focused-beam excitation of the resonance is most efficient with the beam focused just inside the particle surface.

© 1999 Optical Society of America

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  1. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
    [Crossref]
  2. V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [Crossref]
  3. P. Chylek, H.-B. Lin, J. D. Eversole, A. J. Campillo, “Absorption effects on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
    [Crossref] [PubMed]
  4. A. L. Huston, H.-B. Lin, J. D. Eversole, A. J. Campillo, “Effect of bubble formation on microdroplet cavity quality factors,” J. Opt. Soc. Am. B 13, 521–532 (1996).
    [Crossref]
  5. M. Essien, J. B. Gillespie, R. L. Armstrong, “Observation of suppression of morphology-dependent resonances in singly levitated micrometer-sized droplets,” Appl. Opt. 31, 2148–2153 (1992).
    [Crossref] [PubMed]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  7. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [Crossref]
  8. E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
    [Crossref] [PubMed]
  9. H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
    [Crossref]
  10. J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
    [Crossref]
  11. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [Crossref] [PubMed]
  12. H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
    [Crossref]
  13. A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
    [Crossref] [PubMed]
  14. E. S.-C. Ching, P.-T. Leung, K. Young, “The role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 1.
  15. M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.
  16. 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]
  17. 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]

1998 (2)

1997 (1)

1996 (1)

1995 (1)

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

1993 (1)

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

1992 (2)

1991 (3)

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

1989 (2)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

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, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[Crossref]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

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]

Armstrong, R. L.

Barber, P. W.

E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[Crossref] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Barton, J. P.

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
[Crossref]

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]

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[Crossref]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

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]

Brune, M.

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Campillo, A. J.

Chang, R. K.

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.

Chen, G.

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

Ching, E. S.-C.

E. S.-C. Ching, P.-T. Leung, K. Young, “The role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 1.

Chowdhury, D. Q.

E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[Crossref] [PubMed]

M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.

Chylek, P.

Essien, M.

Eversole, J. D.

Gillespie, J. B.

Haroche, S.

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Hill, S. C.

E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[Crossref] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.

Huston, A. L.

Ilchenko, V. S.

Khaled, E. E. M.

Kimble, H. J.

Lai, H. M.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lam, C. C.

Lefevre-Seguin, V.

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Leung, P.-T.

E. S.-C. Ching, P.-T. Leung, K. Young, “The role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 1.

Lin, H.-B.

Mabuchi, H.

Mazumder, M. M.

M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.

Mekis, A.

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

Nockel, J. U.

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

Raimond, J. M.

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

Stone, A. D.

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

Streed, E. W.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vernooy, D. W.

Young, K.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

E. S.-C. Ching, P.-T. Leung, K. Young, “The role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 1.

Appl. Opt. (3)

Europhys. Lett. (1)

V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering gallery mode resonances observed on fused silicon microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

J. Appl. Phys. (3)

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. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[Crossref]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Lett. (3)

Phys. Rev. A (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. Mekis, J. U. Nockel, G. Chen, A. D. Stone, R. K. Chang, “Chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2684 (1995).
[Crossref] [PubMed]

Other (3)

E. S.-C. Ching, P.-T. Leung, K. Young, “The role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 1.

M. M. Mazumder, D. Q. Chowdhury, S. C. Hill, R. K. Chang, “Perturbation effects on the resonances of a spherical dielectric microsphere,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 6.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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Figures (6)

Fig. 1
Fig. 1

Geometrical arrangement for the boundary-matching-method solution.

Fig. 2
Fig. 2

Resonance quality Q as a function of perturbation amplitude for each of the three magnetic-wave resonances. Corrugated particle, rˆ(θ)=1+ cos(Nθ), with N=20. Relative index of refraction n=1.332 (nonabsorbing), and particle size parameters αd97,1=78.557854283, αd94,2=81.2557685, and αd91,3=83.06530.

Fig. 3
Fig. 3

Q as a function of N for each of the three magnetic-wave resonances. Corrugated particle with =0.001.

Fig. 4
Fig. 4

Resonance quality Q as a function of perturbation amplitude for each of the three magnetic-wave resonances. Combined surface roughness particle, rˆ=1+(/3)[-cos(18θ)+cos(30θ)+cos(42θ)].

Fig. 5
Fig. 5

|d97|2 as a function of incident-beam focal-point positioning (y0/a) for =0.00, 0.000001, 0.00001, and 0.0001. Corrugated (N=20) particle at the d971 resonance.

Fig. 6
Fig. 6

|d94|2 as a function of incident beam focal-point positioning (y0/a) for =0.00, 0.00001, 0.0001, and 0.0005. Combined surface roughness particle at the d942 resonance.

Tables (1)

Tables Icon

Table 1 Size Parameters (α), Quality Factors (Q), and C2 Modeling Constants for Each of the Six Resonances for the Perfect Sphere, =0.001 Corrugated (N=20), and =0.001 Combined Surface Roughness Particles

Equations (19)

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r0/a=(l+1/2)/α0,
Er(w)=1r˜2 l=1Lm=-ll[l(l+1)clmψl(n¯αr˜)Ylm(θ, ϕ)],
Eθ(w)=αr˜ l=1Lm=-lln¯clmψl(n¯αr˜) Ylm(θ, ϕ)θ-mext dlmψl(n¯αr˜) Ylm(θ, ϕ)sin θ,
Eϕ(w)=αr˜ l=1Lm=-lli m n¯clmψl(n¯αr˜) Ylm(θ, ϕ)sin θ-iext dlmψl(n¯αr˜) Ylm(θ, ϕ)θ,
Hr(w)=1r˜2 l=1Lm=-ll[l(l+1)dlmψl(n¯αr˜)Ylm(θ, ϕ)],
Hθ(w)=αr˜ l=1Lm=-lln¯dlmψl(n¯αr˜) Ylm(θ, ϕ)θ+mextn¯2clmψl(n¯αr˜) Ylm(θ, ϕ)sin θ,
Hϕ(w)=αr˜ l=1Lm=-lli m n¯dlmψl(n¯αr˜) Ylm(θ, ϕ)sin θ+iextn¯2clmψl(n¯αr˜) Ylm(θ, ϕ)θ,
nˆ×(E(i)+E(s))=nˆ×E(w),
nˆ×(H(i)+H(s))=nˆ×H(w),
U=116π V [Re(extn¯2)|E|2+|H|2]dV.
U=l=1Lm=-ll(Cl|clm|2+Dl|dlm|2),
U=l=1L(Cl|cl|2+Dl|dl|2),
|cl|2=m=-ll|clm|2,
|dl|2=m=-ll|dlm|2.
Q=α0Δα,
rˆ(θ)=1+ cos(Nθ),
rˆ=1+3 [-cos(18θ)+cos(30θ)+cos(42θ)].
1/Q=1/Qsp+C1+C22+C33+,
1/Q1/Qsp+C22.

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