Abstract

For an axially incident plane wave, two theorems are stated in which sufficient conditions are imposed on the constitutive parameters ε and μ of a three-dimensional scatterer to ensure the identity of scattering patterns in orthogonal planes, both near and far zone, such as E and H planes. The theorems represent an extension of existing scattering theorems that apply to bodies of revolution. The theorems are proven analytically, and the results are validated through detailed finite-difference–time-domain and method-of-moments computer simulations on a few noncanonical complex shapes characterized by quite general causal permittivity ε and permeability μ functions. The selected materials have Lorentzian functional forms and encompass ordinary materials as well as left-handed materials as special cases.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
    [CrossRef]
  2. V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963).
    [CrossRef]
  3. C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” manuscript available from the authors (see above).
  4. K. S. Yee, A. H. Chang, “Scattering theorems with anisotropic surface boundary conditions for bodies of revolution,” IEEE Trans. Antennas Propag. 39, 1041–1043 (1991).
    [CrossRef]
  5. P. L. E. Uslenghi, “Scattering by an impedance sphere coated with a chiral layer,” Electromagnetics 10, 201–211 (1990).
    [CrossRef]
  6. P. L. E. Uslenghi, “Three theorems on zero backscattering,” IEEE Trans. Antennas Propag. 44, 269–270 (1996).
    [CrossRef]
  7. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  9. J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
    [CrossRef]
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  11. D. S. Jones, The Theory of Electromagnetism (MacMillan, New York, 1964).
  12. P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
    [CrossRef]
  13. P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).
  14. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  15. L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for 3D penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
    [CrossRef]
  16. J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag.April1993, pp. 69–71.
  17. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–443 (1908).
    [CrossRef]
  18. G. T. Ruck, ed., Radar Cross Section Handbook (Plenum, New York, 1970).

2003

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

2001

C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

1996

P. L. E. Uslenghi, “Three theorems on zero backscattering,” IEEE Trans. Antennas Propag. 44, 269–270 (1996).
[CrossRef]

1994

L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for 3D penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1993

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag.April1993, pp. 69–71.

1991

K. S. Yee, A. H. Chang, “Scattering theorems with anisotropic surface boundary conditions for bodies of revolution,” IEEE Trans. Antennas Propag. 39, 1041–1043 (1991).
[CrossRef]

1990

P. L. E. Uslenghi, “Scattering by an impedance sphere coated with a chiral layer,” Electromagnetics 10, 201–211 (1990).
[CrossRef]

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

1963

V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963).
[CrossRef]

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–443 (1908).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Chang, A. H.

K. S. Yee, A. H. Chang, “Scattering theorems with anisotropic surface boundary conditions for bodies of revolution,” IEEE Trans. Antennas Propag. 39, 1041–1043 (1991).
[CrossRef]

Forester, D. W.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” manuscript available from the authors (see above).

Gedera, M. B.

L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for 3D penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag.April1993, pp. 69–71.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (MacMillan, New York, 1964).

Kesler, O.

C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
[CrossRef]

Loschialpo, P. F.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

Medgyesi-Mitschang, L. N.

L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for 3D penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” manuscript available from the authors (see above).

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–443 (1908).
[CrossRef]

Monzon, C.

C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
[CrossRef]

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” manuscript available from the authors (see above).

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Putnam, J. M.

L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for 3D penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag.April1993, pp. 69–71.

Rachford, F. J.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Schelleng, J.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Smith, D. L.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Uslenghi, P. L. E.

P. L. E. Uslenghi, “Three theorems on zero backscattering,” IEEE Trans. Antennas Propag. 44, 269–270 (1996).
[CrossRef]

P. L. E. Uslenghi, “Scattering by an impedance sphere coated with a chiral layer,” Electromagnetics 10, 201–211 (1990).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Weston, V. H.

V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963).
[CrossRef]

Yee, K. S.

K. S. Yee, A. H. Chang, “Scattering theorems with anisotropic surface boundary conditions for bodies of revolution,” IEEE Trans. Antennas Propag. 39, 1041–1043 (1991).
[CrossRef]

Ann. Phys. (Leipzig)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–443 (1908).
[CrossRef]

Electromagnetics

P. L. E. Uslenghi, “Scattering by an impedance sphere coated with a chiral layer,” Electromagnetics 10, 201–211 (1990).
[CrossRef]

IEEE Antennas Propag. Mag.

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag.April1993, pp. 69–71.

IEEE Trans. Antennas Propag.

P. L. E. Uslenghi, “Three theorems on zero backscattering,” IEEE Trans. Antennas Propag. 44, 269–270 (1996).
[CrossRef]

C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
[CrossRef]

V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963).
[CrossRef]

K. S. Yee, A. H. Chang, “Scattering theorems with anisotropic surface boundary conditions for bodies of revolution,” IEEE Trans. Antennas Propag. 39, 1041–1043 (1991).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

J. Comput. Phys.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. E

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Other

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” manuscript available from the authors (see above).

D. S. Jones, The Theory of Electromagnetism (MacMillan, New York, 1964).

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Manuscript available from the authors (see above).

G. T. Ruck, ed., Radar Cross Section Handbook (Plenum, New York, 1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Identity of the E- and H-plane scattering patterns. (a) Original geometry showing incident fields and scattering planes, (b) effect of duality operation on the original problem. On comparison of the two figures, and a π/2 rotation, the identity of the E- and H-plane patterns is established.

Fig. 2
Fig. 2

Lorentzian frequency-dependent model F(f ) for K=3.88, f0=3.362 GHz and G=3.362×10-3 GHz.

Fig. 3
Fig. 3

Bistatic scattering patterns dBsm for a 10-cm-radius Lorentzian sphere. The material characteristics are (f )=μ(f )=F(f ), where F(f ) is presented in Fig. 2. The figure shows bistatic CARLOS-BOR calculations for illumination at 0° with data points every degree. The deep backscatter null agrees with Weston’s theorem.

Fig. 4
Fig. 4

Geometry of the star-shaped homogeneous scatterer. We are dealing with axial incidence; i.e., the direction of incidence is parallel to the body axes.

Fig. 5
Fig. 5

Bistatic scattering patterns dBsm for the star-shaped body of ordinary material composition. The material is defined by =μ=2-j0.0001 at each frequency of interest. The figure shows bistatic CARLOS calculations in both E and H planes at 1, 3, and 5 GHz, under illumination at 0°. The forward-scattering direction corresponds to 180°. The backscatter values are low, as expected in view of Weston’s theorem. The graph shows that the scattering patterns in the E and H planes are identical.

Fig. 6
Fig. 6

Geometry of the Jerusalem-cross-type scatterer. The body is invariant under a rotation by 90°. Provided that L2L3, the body has no plane of symmetry that contains the X axis. The dimensions are L1=5 cm, L2=2 cm, L3=5 cm, W1=2 cm, W2=2 cm, and W3=2 cm.

Fig. 7
Fig. 7

Lorentzian functional form F(f ) for K=4, f0=6.3 GHz, and G=4.0×10-3 GHz.

Fig. 8
Fig. 8

FDTD snapshots for the unbalanced Jerusalem cross taken as the exciting narrow pulse is about to exit the scatterer. The views represent the fields in planes that pass through the center of the scatterer. Top view (left), front view (center), and side view (right).

Fig. 9
Fig. 9

FDTD snapshots for the unbalanced Jerusalem cross taken long after the exciting narrow pulse had passed. The views represent the fields in planes that pass through the center of the scatterer. Top view (left), front view (center), and side view (right). The late time behavior shows the resonance behavior of the structure composed of high-Q material.

Fig. 10
Fig. 10

Comparison of E- and H-plane scattering patterns for the unbalanced Jerusalem cross made up of the low-index material presented in Fig. 7. FDTD simulations at (a) 12 GHz, (b) 14 GHz, (c) 16 GHz, and (d) 18 GHz. Here 0° denotes the forward-scattering direction, and 180° corresponds to monostatic. In view of the low-index (even negative-index) nature of the material, these are very demanding numerical calculations, for which the agreement between E- and H-plane patterns is deemed to be very good.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

F(f )=1+K-11+j(fG/fo2)-(f/fo)2,

Metrics