Abstract

Transient intensities inside a large dielectric sphere (circumference/incident wavelength > 50) are computed for excitation with plane-wave pulses having a Gaussian time dependence. The center frequency of the pulse is either on or near a morphology-dependent resonance (MDR). For each internal point considered, the time dependence of the electric field is determined from the frequency spectrum of the field at that point. The frequency spectrum is the product of the incident field spectrum and the transfer function at that point. In a sphere both the internal spectrum and the associated time dependence vary with spatial location, particularly when the incident frequency is near a MDR. The time dependence of the intensity at an internal location near the surface shows an exponential tail with a time constant of 1/Δωr, where Δωr is the resonant linewidth of the MDR, so long as the incident spectrum overlaps the MDR significantly, i.e., when Δω ≤ Δω0 and Δω0 ≥ Δωr, where Δω0 is the width of the incident pulse spectrum and Δω is the detuning, the difference between the MDR frequency and the center frequency of the incident Gaussian pulse.

© 1992 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  16. W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  30. R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
    [CrossRef]
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    [CrossRef]

1992

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]

D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres via Mie theory and geometrical optics,” Appl. Opt. 31, 3558–3563 (1992).
[CrossRef]

1991

1990

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

S. Kinoshita, T. Kushida, “Quantum interference between resonant and nonresonant contributions in nearly resonant Raman scattering,” Phys. Rev. A 42, 2751–2755 (1990).
[CrossRef] [PubMed]

1989

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

W. P. Acker, D. H. Leach, R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized liquid droplets,” Opt. Lett. 14, 402–404 (1989).
[CrossRef] [PubMed]

1988

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. Jpn. Part 1 71, 74–86 (1988).
[CrossRef]

H. Chew, “Radiation lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

1987

1986

1985

1984

1979

K. Ikeda, “Multiple-valued stationary state and instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

1972

R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
[CrossRef]

1968

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. 16, 89–97 (1968).
[CrossRef]

Acker, W. P.

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Armstrong, R. L.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Benincasa, D. S.

Biswas, A.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Campillo, A. J.

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamics enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Chang, R. K.

Chew, H.

H. Chew, “Radiation lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

Ching, S. C.

Chowdhury, D. Q.

Chylek, P.

Eversole, J. D.

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamics enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hammel, S. M.

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]

D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres via Mie theory and geometrical optics,” Appl. Opt. 31, 3558–3563 (1992).
[CrossRef]

D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hosono, T.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. Jpn. Part 1 71, 74–86 (1988).
[CrossRef]

Howell, W. E.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

Hsieh, W-F.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Ikeda, K.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. Jpn. Part 1 71, 74–86 (1988).
[CrossRef]

K. Ikeda, “Multiple-valued stationary state and instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Itoh, A.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. Jpn. Part 1 71, 74–86 (1988).
[CrossRef]

Jarzembski, M. A.

Jones, C. K. R. T.

Khaled, E. E. M.

Kinoshita, S.

S. Kinoshita, T. Kushida, “Quantum interference between resonant and nonresonant contributions in nearly resonant Raman scattering,” Phys. Rev. A 42, 2751–2755 (1990).
[CrossRef] [PubMed]

Kushida, T.

S. Kinoshita, T. Kushida, “Quantum interference between resonant and nonresonant contributions in nearly resonant Raman scattering,” Phys. Rev. A 42, 2751–2755 (1990).
[CrossRef] [PubMed]

Lai, H. M.

Lamb, W. E.

R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
[CrossRef]

Lang, R.

R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
[CrossRef]

Latifi, H.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Leach, D. H.

Lin, H.-B.

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamics enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Long, M. B.

Mittra, R.

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, L. B. Felson, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

Moloney, J. V.

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1966).

Pendleton, J. D.

Pinnick, R. G.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

P. Chylek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Qian, S.-X.

Rheinstein, J.

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. 16, 89–97 (1968).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Scully, M. O.

R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
[CrossRef]

Shirai, H.

H. Shirai, “Time transient analysis of waves scattering by simple shapes,” presented at the Analytic and Numerical Methods in Wave Theory Seminar, Adana, Turkey (1991); H. Shirai, A. Hamakoshi, “Transient response by a dielectric cylinder due to a line source at the center,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. E74, 157–166 (1991).

Snow, J. B.

Snow, J. R.

Srivastava, V.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Tzeng, H. M.

Überall, H.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Wall, K. F.

Young, K.

Zhang, J.-Z.

Appl. Opt.

Electron. Commun. Jpn. Part 1

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. Jpn. Part 1 71, 74–86 (1988).
[CrossRef]

IEEE Trans. Antennas Propag.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. 16, 89–97 (1968).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

K. Ikeda, “Multiple-valued stationary state and instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

H. Chew, “Radiation lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

S. Kinoshita, T. Kushida, “Quantum interference between resonant and nonresonant contributions in nearly resonant Raman scattering,” Phys. Rev. A 42, 2751–2755 (1990).
[CrossRef] [PubMed]

R. Lang, M. O. Scully, W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1972).
[CrossRef]

Phys. Rev. Lett.

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamics enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, L. B. Felson, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

H. Shirai, “Time transient analysis of waves scattering by simple shapes,” presented at the Analytic and Numerical Methods in Wave Theory Seminar, Adana, Turkey (1991); H. Shirai, A. Hamakoshi, “Transient response by a dielectric cylinder due to a line source at the center,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. E74, 157–166 (1991).

R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1966).

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Figures (11)

Fig. 1
Fig. 1

Stylized drawing of an input pulse spectrum and transfer function at some point inside the sphere. In (a) the Fourier transform of the incident pulse Ei(ω) is shown at the left, and the Fourier transform of the envelope Êi(ω) is shown at the right. In (b) the Fourier transform of the transfer function Eδ(ω) is shown at the left, and the translated function Eδ(ωω0) is shown at the right. The maximum amplitudes of the incident and the resonant spectra are shown by p and q, respectively.

Fig. 2
Fig. 2

Points in the xz plane where the internal intensities are computed. The coordinates of the points are (a) r = 0.87a, = 60°, ϕ = 0°; (b) r = 0.7a, θ = 0°, ϕ = 0°; (c) r = 0.707a, θ = 45°, ϕ = 0°. Points (a), (b), and (c) are superimposed upon contour plots of the internal intensities generated by resonant and off-resonant y-polarized incident plane waves. Surface plots of the internal intensities for resonant and off-resonant incidence are also shown.

Fig. 3
Fig. 3

Transient internal intensities at the three points shown in Fig. 2. The incident y-polarized plane wave has a Gaussian time dependence and propagates along the z axis. The scaled (×10) incident pulse is also shown. Curve (a) is at point (a), (b) is at point (b), and (c) is at point (c). The incident Gaussian pulse is on resonance with a pulse duration of 0.125 ns.

Fig 4
Fig 4

Transient internal intensities at the same locations as in Fig. 3, except that the incident pulse duration is 1.25 ns. The scaled (×200) incident pulse is also shown.

Fig. 5
Fig. 5

Frequency spectrum of the internal fields at points (a), (b), and (c) of Fig. 2 for the case shown in Fig. 3. The frequency is plotted as a shift from the incident frequency (ω0) expressed as the number of resonant linewidths (Δωr).

Fig. 6
Fig. 6

Transient internal intensities at point (a) of Fig. 2 for an incident pulse duration of 0.125 ns with different center frequencies given by ω0= ωr + NΔωr, where Δωr is the resonant linewidth. The intensity is shown for N = 0–9.

Fig. 7
Fig. 7

Transient internal intensities at point (a) of Fig. 2, except for an incident pulse duration of 1.25 ns. (a) Shows the intensities, and (b) shows the logarithm of the intensities.

Fig. 8
Fig. 8

Frequency spectrum of the internal fields for each of the cases shown in Fig. 6. The frequency is plotted as a shift from the incident frequency (ω0) expressed as the number of resonant linewidths (Δωr). The inset shows expanded curves for N = 7, 8, and 9.

Fig. 9
Fig. 9

Sample frequency spectra and inverse Fourier transforms to explain the kink noted in Fig. 7. A Gaussian and a Lorentzian are added to make up the frequency spectrum in (a). The frequency axis is shown as ω′ = ωω0. The inverse Fourier transform of the Gaussian is shown in (b), and the inverse transform of the Lorentzian is shown in (c). The magnitude of the sum of (b) and (c) is shown in a log scale in (d).

Fig. 10
Fig. 10

Transient internal intensity at the same location as in Fig. 6, except that N = 15. The internal intensity is computed by using Eq. (5) with only the n = 94 term and with all the n’s.

Fig. 11
Fig. 11

Transient internal intensity at point (a) of Fig. 2 for a train of mode-locked pulses. In each part the upper panel shows the incident intensity, the lower panel shows the internal intensity, and the inset shows the frequency spectrum of the internal field. The abscissa of the inset is the same as in Fig. 7. In (a) each incident pulse has a half-width (intensity) of 0.5 ns and is separated from the next incident pulse by 10 ns, and the incident pulse train is on resonance. In (b) the incident pulse is the same as in (a), except that the pulses are separated by 5 ns. In (c) the incident pulse is the same as in (a), except that the incident frequency is detuned by five linewidths from the resonance.

Equations (15)

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E i ( z , t ) = i y E ^ i ( t - z / c ) exp [ - j ω 0 ( t - z / c ) ] ,
E int ( τ , r ) = F - 1 [ E i ( ω ) E δ ( ω , r ) ] ,
E i ( ω ) = F [ E i ( τ ) ] = F [ E ^ i ( τ ) exp ( - j ω 0 τ ) ] .
E i ( ω ) = E ^ i ( ω + ω 0 ) ,
E δ ( ω , r ) = n = 1 ( c e 1 n M e 1 n 1 + d o 1 n N o 1 n 1 ) ,
c e 1 n = - j n 2 n + 1 n ( n + 1 ) × { j / x j n ( m x ) [ x h n ( 1 ) ( x ) ] - h n ( 1 ) ( x ) [ m x j n ( m x ) ] } ,
d o 1 n = - j n + 1 2 n + 1 n ( n + 1 ) × { m j / x m 2 j n ( m x ) [ x h n ( 1 ) ( x ) ] - h n ( 1 ) ( x ) [ m x j n ( m x ) ] } ,
E int ( τ , r ) = F - 1 [ E ^ i ( ω + ω 0 ) E δ ( ω , r ) ] .
E ^ int ( τ , r ) = F - 1 [ E ^ i ( ω ) E δ ( ω - ω 0 , r ) ] .
ω 0 = ω r + N Δ ω r ,
E δ ( ω , r ) = Δ ω r 2 ( ω r - ω ) 2 + Δ ω r 2 .
E i ( ω ) = exp { - [ ( ω 0 - ω ) / Δ ω 0 ] 2 } .
N = ω r - ω 0 Δ ω r = Δ ω Δ ω r ,
η = Δ ω 0 Δ ω r .
S ω r = exp [ - ( N / η ) 2 ] , S ω 0 = 1 N 2 + 1 1 N 2             for N 1.

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