Abstract

We present a theoretical approach to the problem of mode scattering by a spherical object that is placed inside a circular dielectric waveguide. This approach is based on the separation-of-variables method for each subsystem, namely, the spherical inclusion and the circular dielectric cylinder, and on the concept of the generalized recursive T-matrix algorithm for multilayered structures. We apply the technique to the backward and the forward scattering of a quasi-optical beam in the form of the fundamental HE11 mode by a sphere inside a circular hollow dielectric waveguide. The results calculated for the perfectly conducting spherical objects inside the circular hollow dielectric waveguide are compared with corresponding measured data of the backward- and the forward-scattering characteristics at the 4-mm wave band.

© 2001 Optical Society of America

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References

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  1. C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
  2. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  3. V. K. Kiselyev, T. M. Kushta, “Method for radar cross section measurements in millimeter and submillimeter wave regions,” Int. J. Infrared Millim. Waves 16(6), 1159–1165 (1995).
    [CrossRef]
  4. V. K. Kiseliov, T. M. Kushta, P. K. Nesterov, “Quasi-optical waveguide modeling method and microcompact scattering range for the millimeter and submillimeter wave bands,” IEEE Trans. Antennas Propag. (to be published).
  5. N. K. Uzanoglu, “Scattering from inhomogeneities inside a fiber waveguide,” J. Opt. Soc. Am. 71, 259–273 (1981).
    [CrossRef]
  6. N. Morita, N. Kumagai, “Scattering and mode conversion of guided modes by a spherical object in an optical fiber,” IEEE Trans. Microwave Theory Tech. 28, 137–141 (1980).
    [CrossRef]
  7. W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 471–475.
  8. W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 463–465.
  9. R. J. Pogorzelski, E. Lum, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
    [CrossRef]
  10. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 411.
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 397–399.
  12. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 417.
  13. W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 163–167.
  14. E. A. J. Marcatili, E. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
    [CrossRef]
  15. A. I. Goroshko, Y. M. Kuleshov, “Investigation of a hollow dielectric beamguide in the millimeter and submillimeter wave bands,” (in Russian) Radiotekhnika (Moscow) 21, 215–219 (1972).
  16. C. Dragone, “High-frequency behavior of waveguides with finite surface impedances,” Bell Syst. Tech. J. 60, 89–115 (1981).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics, 7th ed., expanded (Cambridge U. Press, Cambridge, 1999), pp. 716–734.
  18. J. T. Hodges, G. Gréhan, G. Gousbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
    [CrossRef] [PubMed]

1995

V. K. Kiselyev, T. M. Kushta, “Method for radar cross section measurements in millimeter and submillimeter wave regions,” Int. J. Infrared Millim. Waves 16(6), 1159–1165 (1995).
[CrossRef]

J. T. Hodges, G. Gréhan, G. Gousbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

1981

N. K. Uzanoglu, “Scattering from inhomogeneities inside a fiber waveguide,” J. Opt. Soc. Am. 71, 259–273 (1981).
[CrossRef]

C. Dragone, “High-frequency behavior of waveguides with finite surface impedances,” Bell Syst. Tech. J. 60, 89–115 (1981).
[CrossRef]

1980

N. Morita, N. Kumagai, “Scattering and mode conversion of guided modes by a spherical object in an optical fiber,” IEEE Trans. Microwave Theory Tech. 28, 137–141 (1980).
[CrossRef]

1976

R. J. Pogorzelski, E. Lum, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

1972

A. I. Goroshko, Y. M. Kuleshov, “Investigation of a hollow dielectric beamguide in the millimeter and submillimeter wave bands,” (in Russian) Radiotekhnika (Moscow) 21, 215–219 (1972).

1964

E. A. J. Marcatili, E. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Bohern, C. F.

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed., expanded (Cambridge U. Press, Cambridge, 1999), pp. 716–734.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 471–475.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 163–167.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 463–465.

Dragone, C.

C. Dragone, “High-frequency behavior of waveguides with finite surface impedances,” Bell Syst. Tech. J. 60, 89–115 (1981).
[CrossRef]

Goroshko, A. I.

A. I. Goroshko, Y. M. Kuleshov, “Investigation of a hollow dielectric beamguide in the millimeter and submillimeter wave bands,” (in Russian) Radiotekhnika (Moscow) 21, 215–219 (1972).

Gousbet, G.

Gréhan, G.

Hodges, J. T.

Huffman, D. R.

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Kiseliov, V. K.

V. K. Kiseliov, T. M. Kushta, P. K. Nesterov, “Quasi-optical waveguide modeling method and microcompact scattering range for the millimeter and submillimeter wave bands,” IEEE Trans. Antennas Propag. (to be published).

Kiselyev, V. K.

V. K. Kiselyev, T. M. Kushta, “Method for radar cross section measurements in millimeter and submillimeter wave regions,” Int. J. Infrared Millim. Waves 16(6), 1159–1165 (1995).
[CrossRef]

Kuleshov, Y. M.

A. I. Goroshko, Y. M. Kuleshov, “Investigation of a hollow dielectric beamguide in the millimeter and submillimeter wave bands,” (in Russian) Radiotekhnika (Moscow) 21, 215–219 (1972).

Kumagai, N.

N. Morita, N. Kumagai, “Scattering and mode conversion of guided modes by a spherical object in an optical fiber,” IEEE Trans. Microwave Theory Tech. 28, 137–141 (1980).
[CrossRef]

Kushta, T. M.

V. K. Kiselyev, T. M. Kushta, “Method for radar cross section measurements in millimeter and submillimeter wave regions,” Int. J. Infrared Millim. Waves 16(6), 1159–1165 (1995).
[CrossRef]

V. K. Kiseliov, T. M. Kushta, P. K. Nesterov, “Quasi-optical waveguide modeling method and microcompact scattering range for the millimeter and submillimeter wave bands,” IEEE Trans. Antennas Propag. (to be published).

Lum, E.

R. J. Pogorzelski, E. Lum, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, E. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Morita, N.

N. Morita, N. Kumagai, “Scattering and mode conversion of guided modes by a spherical object in an optical fiber,” IEEE Trans. Microwave Theory Tech. 28, 137–141 (1980).
[CrossRef]

Nesterov, P. K.

V. K. Kiseliov, T. M. Kushta, P. K. Nesterov, “Quasi-optical waveguide modeling method and microcompact scattering range for the millimeter and submillimeter wave bands,” IEEE Trans. Antennas Propag. (to be published).

Pogorzelski, R. J.

R. J. Pogorzelski, E. Lum, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Presser, C.

Schmeltzer, E. A.

E. A. J. Marcatili, E. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 397–399.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 411.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 417.

Uzanoglu, N. K.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed., expanded (Cambridge U. Press, Cambridge, 1999), pp. 716–734.

Appl. Opt.

Bell Syst. Tech. J.

C. Dragone, “High-frequency behavior of waveguides with finite surface impedances,” Bell Syst. Tech. J. 60, 89–115 (1981).
[CrossRef]

E. A. J. Marcatili, E. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

N. Morita, N. Kumagai, “Scattering and mode conversion of guided modes by a spherical object in an optical fiber,” IEEE Trans. Microwave Theory Tech. 28, 137–141 (1980).
[CrossRef]

Int. J. Infrared Millim. Waves

V. K. Kiselyev, T. M. Kushta, “Method for radar cross section measurements in millimeter and submillimeter wave regions,” Int. J. Infrared Millim. Waves 16(6), 1159–1165 (1995).
[CrossRef]

J. Opt. Soc. Am.

Radio Sci.

R. J. Pogorzelski, E. Lum, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Radiotekhnika (Moscow)

A. I. Goroshko, Y. M. Kuleshov, “Investigation of a hollow dielectric beamguide in the millimeter and submillimeter wave bands,” (in Russian) Radiotekhnika (Moscow) 21, 215–219 (1972).

Other

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 471–475.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 463–465.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 411.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 397–399.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 417.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 163–167.

V. K. Kiseliov, T. M. Kushta, P. K. Nesterov, “Quasi-optical waveguide modeling method and microcompact scattering range for the millimeter and submillimeter wave bands,” IEEE Trans. Antennas Propag. (to be published).

M. Born, E. Wolf, Principles of Optics, 7th ed., expanded (Cambridge U. Press, Cambridge, 1999), pp. 716–734.

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (5)

Fig. 1
Fig. 1

Scattering geometry of an object placed inside a circular dielectric waveguide.

Fig. 2
Fig. 2

Coefficient of variation of the backscattering efficiency ΔσRCS for perfectly conducting spheres plotted versus the diffraction parameter kb.

Fig. 3
Fig. 3

Coefficient of variation of the extinction efficiency Δσext for perfectly conducting spheres and dielectric spheres with 1=2.3+i0.2 plotted versus the diffraction parameter kb.

Fig. 4
Fig. 4

Relative radar cross section σrel of metallic spheres inside a circular HDW plotted versus the diffraction parameter kb.

Fig. 5
Fig. 5

Modulus of the transmission coefficient c11 of the fundamental HE11 mode by metallic spheres inside a circular HDW plotted versus the diffraction parameter kb.

Equations (60)

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U0(k0, r0)=Rg Ψ¯(k0, R0)A¯inc+Rg Ψ¯(k0, R0)A¯0+Ψ¯(k0, R1)B¯0.
U1(k1, r1)=Rg Ψ¯(k1, R1)A¯.
U2(k2, r0)=Φ¯(k2, R0)B¯2.
Ψ¯=[m(o)mm(e),n(o)mn(e)],
m(o)mn(e)=[ρψ(o)mn(e)],
(n)(o)mn(e)=1k m(o)mn(e),
ψ(o)mn(e)=cos mφsin mφPnm(cos θ)hn(1)(kρ),
Φ¯=[M(o)mγ(e), N(o)mγ(e)],
M(o)mγ(e)=z|z| ϕ(o)mγ(e),
(N)(o)mγ(e)=1k M(o)mγ(e),
ϕ(o)mγ(e)=cos mφsin mφHm(1)(γr)exp(ihz),
A¯g=β¯10 A¯inc+β¯10 R¯02β¯01B¯0,
B¯0=R¯01 A¯g,
A¯g=(I¯-β¯10 R¯02β¯01R¯01)-1β¯10 A¯inc.
B¯0=R¯01(I¯-β¯10 R¯02β¯01 R¯01)-1β¯10 A¯inc.
A¯1=T¯01(I¯-β¯10 R¯02β¯01R¯01)-1β¯10 A¯inc.
B¯2=T¯02 β01R¯01(I¯-β10 R¯02β¯01R¯01)-1β¯10 A¯inc.
m(o)mn(e)=0π[AmαM(o)mα(e)+BmαN(c)mα(o)]sin αdα,
n(o)mn(e)=0π[BmαM(e)mα(o)+AmαN(o)mα(e)]sin αdα,
jn(kρ)Pnm(cos θ)=i-n20πexp(ikz cos α)×Jm(kr sin α)Pnm(cos α)sin αdα.
M(o)mα(e)=n=m(2n+1)(n-m)!n(n+1)(n+m)! in-mk×i sin α [Pnm(cos α)]αm(o)mn(e)±mPnm(cos α)n(e)mn(o),
N(o)mα(e)=n=m(2n+1)(n-m)!n(n+1)(n+m)! in-mk×i sin α [Pnm(cos α)]αn(o)mn(e)±mPnm(cos α)m(e)mn(o)
0πPnmαPnmα+m2PnmPnmsin2 αsin αdα
=2n(n+1)(n+m)!(2n+1)(n-m)!,
Amα=im-n-12k sin α[Pnm(cos α)]α,
Bmα=im-nmPnm(cos α)2k sin2 α.
R¯02=0πρ ¯sin αdα,
ρ¯=K¯L¯L¯K¯ r¯mmr¯nmr¯nmr¯nm A¯B¯B¯A¯,
A¯=[Amαδmn],
B¯=[Bmαδmn],
K¯=[Kmn],
L¯=[Lmn],
Kmn=(2n+1)(n-m)!n(n+1)(n+m)! in-m+1k sin α [Pnm(cos α)]α,
Lmn=±m(2n+1)(n-m)!n(n+1)(n+m)! in-mkPnm(cos α),
r¯nmr¯mnr¯nmr¯nm=δmnD¯-1[Hn(1)(γ0a)D¯-1(γ2a)-Hn(1)(γ2a)H¯n(1)(γ0a)],
D¯=[J¯n(γ0a)Hn(1)(γ2a)-H¯n(1)(γ2a)Jn(γ0a)],
F¯n(γla)
=J¯n(γla)H¯n(1)(γla)=1γl2aiωlγlaFn(γla)-nhlFn(γla)-nhlFn(γla)-iωμlγlaFn(γla),
S0+S1+S2+S3(En×Hsc*+Esc*×Hn) nds=0,
Esc=nc±nE±n,
Hsc=nc±nH±n,
c±n=1NnS1(E±n*×Hsc+Esc×H±n*)  nds,
Em=J0(u0mr/a)exp(ih0mz)iy,
Hm=-(0/μ0)1/2J0(u0mr/a)exp(ih0mz)ix,
Aninc=-in(2n+1)n(n+1) Pn(cos α01),
Bninc=in-1n(n+1) [(n+1)Pn-1(cos α01)+nPn-1(cos α01)],
cos α01=h01/k.
Cextf=S3Re(Einc×Hsc*+Esc×Hinc*)  nds2Iinc,
Cscf=S3Re(Esc×Hsc*)  nds2Iinc,
Cabsf=Cextf-Cscf,
CRCSf=4π|X(180°)|2k02,
Cextf=4πk2Re{[X(0°)ix]},
Cextw=0.5NiRe c+i,
0.5(ε0/μ0)1/2(Einc0)2=1.
CRCSw=k2Ni2|c-i|2π.
σextw=CextwPinc,σscw=CscwPinc,
σabsw=CabswPinc,σRCSw=CRCSwPinc,
Pinc=2π0b[bi]J02(u01r/a)rdr=πb2[J02(u01b/a)+J12(u01b/a)].
ΔσRCS=10 log10(σRCSf / σRCSw).
Δσext=10 log10(σextf / σextw).

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