Abstract

The scattered intensity patterns of large dielectric cylinders (ka ≅ 1000) are studied using the exact solution for the case of normal incidence. The two different polarizations of the incident electric field, parallel and normal to the axis of the cylinder, are considered. A comparison between the scattered patterns of the two polarizations is presented. The fine structure of the scattering pattern is also presented. It is shown that the scattered intensity has resonances as the wavelength is scanned. An experimental investigation is carried out to illustrate the theory, and good agreement between theory and experiment is achieved.

© 1985 Optical Society of America

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References

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  1. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  4. J. J. Bowman, T. B. A. Senior, P. L. E. Vslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).
  5. Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1881).
  6. Rayleigh, “The Dispersal of Light by a Dielectric Cylinder,” Philos. Mag. 36, 365 (1918).
  7. J. Van Bladel, “Resonant Scattering by Dielectric Cylinders,” IEEE J. Microwave Opt. Acoust. (GB) 1, 41 (1977).
    [CrossRef]
  8. A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
    [CrossRef] [PubMed]
  9. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
    [CrossRef] [PubMed]
  10. J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electrical Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
    [CrossRef] [PubMed]
  11. M. A. G. Abushagur, “Scattering of Light From Large Cylinders,” Ph.D. Thesis, California Institute of Technology, Pasadena (1984).
  12. M. A. G. Abushagur, N. George, “Measurement of Optical Fiber Diameter Using the Fast Fourier Transform,” Appl. Opt. 19, 2031 (1980).
    [CrossRef] [PubMed]
  13. M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
    [CrossRef]
  14. G. J. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  15. A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  16. N. George, “Scattering by Glass Microballoons and Multitone Interferometry,” J. Opt. Soc. Am. 66, 1135 (1976).
  17. J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
    [CrossRef]
  18. M. W. Pospiezalski, “Cylindrical Dielectric Resonantors and Their Application in TEM Line Microwave Circuits,” IEEE Trans. Microwave Theory Tech. MMT-27, 233 (1979).
    [CrossRef]
  19. M. W. Pospieszalski, “On the Theory and Application of the Dielectric Post Resonator,” IEEE Trans. Microwave Theory Tech. MMT-25, 228 (1977).
    [CrossRef]
  20. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).
  21. J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1981).

1981

1980

M. A. G. Abushagur, N. George, “Measurement of Optical Fiber Diameter Using the Fast Fourier Transform,” Appl. Opt. 19, 2031 (1980).
[CrossRef] [PubMed]

G. J. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

1979

M. W. Pospiezalski, “Cylindrical Dielectric Resonantors and Their Application in TEM Line Microwave Circuits,” IEEE Trans. Microwave Theory Tech. MMT-27, 233 (1979).
[CrossRef]

1977

M. W. Pospieszalski, “On the Theory and Application of the Dielectric Post Resonator,” IEEE Trans. Microwave Theory Tech. MMT-25, 228 (1977).
[CrossRef]

J. Van Bladel, “Resonant Scattering by Dielectric Cylinders,” IEEE J. Microwave Opt. Acoust. (GB) 1, 41 (1977).
[CrossRef]

1976

N. George, “Scattering by Glass Microballoons and Multitone Interferometry,” J. Opt. Soc. Am. 66, 1135 (1976).

1967

M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[CrossRef]

1918

Rayleigh, “The Dispersal of Light by a Dielectric Cylinder,” Philos. Mag. 36, 365 (1918).

1881

Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1881).

Abushagur, M. A. G.

M. A. G. Abushagur, N. George, “Measurement of Optical Fiber Diameter Using the Fast Fourier Transform,” Appl. Opt. 19, 2031 (1980).
[CrossRef] [PubMed]

M. A. G. Abushagur, “Scattering of Light From Large Cylinders,” Ph.D. Thesis, California Institute of Technology, Pasadena (1984).

Ashkin, A.

Barber, P. W.

Benner, G. J.

G. J. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Bowman, J. J.

J. J. Bowman, T. B. A. Senior, P. L. E. Vslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).

Chang, R. K.

Courtois, L.

M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[CrossRef]

Dorman, J. L.

M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[CrossRef]

Dziedzic, J. M.

Gastine, M.

M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[CrossRef]

George, N.

M. A. G. Abushagur, N. George, “Measurement of Optical Fiber Diameter Using the Fast Fourier Transform,” Appl. Opt. 19, 2031 (1980).
[CrossRef] [PubMed]

N. George, “Scattering by Glass Microballoons and Multitone Interferometry,” J. Opt. Soc. Am. 66, 1135 (1976).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Messinger, B. J.

Moser, P. J.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

Murphy, J. D.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

Nagl, A.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

Owen, J. F.

Pospieszalski, M. W.

M. W. Pospieszalski, “On the Theory and Application of the Dielectric Post Resonator,” IEEE Trans. Microwave Theory Tech. MMT-25, 228 (1977).
[CrossRef]

Pospiezalski, M. W.

M. W. Pospiezalski, “Cylindrical Dielectric Resonantors and Their Application in TEM Line Microwave Circuits,” IEEE Trans. Microwave Theory Tech. MMT-27, 233 (1979).
[CrossRef]

Rayleigh,

Rayleigh, “The Dispersal of Light by a Dielectric Cylinder,” Philos. Mag. 36, 365 (1918).

Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1881).

Senior, T. B. A.

J. J. Bowman, T. B. A. Senior, P. L. E. Vslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

Stolen, R. H.

Stratton, J. A.

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

Überall, H.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

Van Bladel, J.

J. Van Bladel, “Resonant Scattering by Dielectric Cylinders,” IEEE J. Microwave Opt. Acoust. (GB) 1, 41 (1977).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1981).

Vslenghi, P. L. E.

J. J. Bowman, T. B. A. Senior, P. L. E. Vslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).

Appl. Opt.

IEEE J. Microwave Opt. Acoust. (GB)

J. Van Bladel, “Resonant Scattering by Dielectric Cylinders,” IEEE J. Microwave Opt. Acoust. (GB) 1, 41 (1977).
[CrossRef]

IEEE Trans. Antennas Propag.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, “A Surface Wave Interpretation for the Resonances of a Dielectric Sphere,” IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

M. W. Pospiezalski, “Cylindrical Dielectric Resonantors and Their Application in TEM Line Microwave Circuits,” IEEE Trans. Microwave Theory Tech. MMT-27, 233 (1979).
[CrossRef]

M. W. Pospieszalski, “On the Theory and Application of the Dielectric Post Resonator,” IEEE Trans. Microwave Theory Tech. MMT-25, 228 (1977).
[CrossRef]

M. Gastine, L. Courtois, J. L. Dorman, “Electromagnetic Resonances of Free Dielectric Spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[CrossRef]

J. Opt. Soc. Am.

N. George, “Scattering by Glass Microballoons and Multitone Interferometry,” J. Opt. Soc. Am. 66, 1135 (1976).

Opt. Lett.

Philos. Mag.

Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1881).

Rayleigh, “The Dispersal of Light by a Dielectric Cylinder,” Philos. Mag. 36, 365 (1918).

Phys. Rev. Lett.

G. J. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Other

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1981).

M. A. G. Abushagur, “Scattering of Light From Large Cylinders,” Ph.D. Thesis, California Institute of Technology, Pasadena (1984).

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

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

J. J. Bowman, T. B. A. Senior, P. L. E. Vslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).

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Figures (11)

Fig. 1
Fig. 1

Incident field as it illuminates the cylinder.

Fig. 2
Fig. 2

Normalized scattered field plotted as a function of ϕ for (a) the parallel polarization case and (b) the normal polarization case.

Fig. 3
Fig. 3

Optical-hybrid system setup used in the experimental investigations.

Fig. 4
Fig. 4

Normalized scattered intensity patterns by a dielectric cylinder for the parallel polarization case using (a) rigorous solution of Eq. (2) and (b) experimental data.

Fig. 5
Fig. 5

Scattered intensity pattern plotted for a dielectric cylinder with ka = 945, n = 1.45 for (a) parallel polarization case, and (b) normal polarization case using the experimental setup in Fig. 3. (a) 30° ≤ ϕ ≤ 60°.

Fig. 6
Fig. 6

Scattered intensity pattern of a dielectric cylinder for 60° ≤ ϕ ≤ 90°.

Fig. 7
Fig. 7

Scattered intensity pattern of a dielectric cylinder for 90° ≤ ϕ ≤ 120°.

Fig. 8
Fig. 8

Scattered intensity pattern of a dielectric cylinder for 120° ≤ ϕ ≤ 150°.

Fig. 9
Fig. 9

Scattered intensity pattern of a dielectric cylinder for 150° ≤ ϕ ≤ 180°.

Fig. 10
Fig. 10

Scattered intensity from a dielectric cylinder with a = 95 μm and n = 1.46 at ϕ = 5° is plotted as a function of wavelength.

Fig. 11
Fig. 11

Scattered intensity from the cylinder in Fig. 10 is plotted as a function of the wavelength at ϕ = 90°.

Tables (1)

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Table I Frings contrast for Dlelectric Cylinder ka = 50, n = 1.45

Equations (7)

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E inc ( ρ , ϕ , t ) = e z exp ( i ω t ) exp ( i k ρ cos ϕ ) ,
E z s ( ρ , ϕ ) = m = a m H m ( 1 ) ( k ρ ) exp ( i m ϕ ) , ρ > a ,
a m = ( i ) m n J m ( k a ) J m ( n k a ) J m ( k a ) J m ( n k a ) n J m ( n k a ) H m ( 1 ) ( k a ) J m ( k a ) H m ( 1 ) ( k a ) ,
H inc ( ρ , ϕ ) = e z exp ( i k ρ cos ϕ ) .
H z s ( ρ , ϕ ) = m = b m H m ( 1 ) ( k ρ ) exp ( i m ϕ ) , ρ > a ,
b m = ( i ) m J m ( k a ) J m ( n k a ) n J m ( k a ) J m ( n k a ) H m ( 1 ) ( k a ) J m ( n k a ) n H m ( 1 ) ( k a ) J m ( n k a ) .
I ( ρ , ϕ ) 2 π k ρ [ | a 0 | 2 + 2 p = 1 ( i ) p a 0 a p * cos p ϕ + 2 m = 1 ( i ) m a 0 * a m cosm ϕ + 4 m p = 1 ( i ) p m a m a p * cos m ϕ cos p ϕ + 4 m = 1 | a m | 2 cos 2 m ϕ ] .

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