Abstract

It is shown analytically and numerically that a matched ε=μ reciprocal object with rotational symmetry will not produce any backscattering when illuminated along the axis of symmetry unless the body is invariant under a rotation by 180°. The purpose of this work is to generalize the monostatic theorem of Weston to arbitrary rotational symmetry, thereby providing a basic rule for scattering by complex bodies. The theory is illustrated by application to a few selected scatterers.

© 2005 Optical Society of America

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  1. V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963).
    [CrossRef]
  2. C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
    [CrossRef]
  3. 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]
  4. P. L. E. Uslenghi, “Scattering by an impedance sphere coated with a chiral layer,” Electromagnetics 10, 201–211 (1990).
    [CrossRef]
  5. P. L. E. Uslenghi, “Three theorems on zero backscattering,” IEEE Trans. Antennas Propag. 44, 269–270 (1996).
    [CrossRef]
  6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).
  11. D. C. Jenn, Radar and Laser Cross Section Engineering (American Institute of Aeronautics and Astronautics, Washington, D.C., 1995).
  12. C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. 38, 227–235 (1990).
    [CrossRef]
  13. 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]
  14. 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,” Phys. Rev. E 70, 036605 (2004).
    [CrossRef]
  15. L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for three-dimensional penetrable scatters,” 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. 35, 69–71 (1993).
    [CrossRef]
  17. C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” J. Opt. Soc. Am. A 21, 2311–2319 (2004).
    [CrossRef]

2004 (2)

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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” J. Opt. Soc. Am. A 21, 2311–2319 (2004).
[CrossRef]

2003 (1)

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 (1)

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

2000 (2)

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 (1)

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 (1)

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

1994 (1)

1993 (1)

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag. 35, 69–71 (1993).
[CrossRef]

1991 (1)

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 (2)

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

C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. 38, 227–235 (1990).
[CrossRef]

1968 (1)

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

1963 (1)

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

Barrick, D.

G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

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. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” J. Opt. Soc. Am. A 21, 2311–2319 (2004).
[CrossRef]

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]

Gedera, M. B.

L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for three-dimensional penetrable scatters,” 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. 35, 69–71 (1993).
[CrossRef]

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]

Jenn, D. C.

D. C. Jenn, Radar and Laser Cross Section Engineering (American Institute of Aeronautics and Astronautics, Washington, D.C., 1995).

Kesler, O.

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

Kirchbaum, C.

G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

Loschialpo, P. F.

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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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]

Medgyesi-Mitschang, L. N.

Monzon, C.

C. Monzon, D. W. Forester, L. N. Medgyesi-Mitschang, “Scattering properties of an ideal homogeneous, causal ‘left handed’ sphere,” J. Opt. Soc. Am. A 21, 2311–2319 (2004).
[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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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

C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. 38, 227–235 (1990).
[CrossRef]

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 three-dimensional penetrable scatters,” 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. 35, 69–71 (1993).
[CrossRef]

Rachford, F. J.

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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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]

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]

Ruck, G.

G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

Schelleng, J.

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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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]

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. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left handed’ material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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]

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]

Stuart, W.

G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

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]

Electromagnetics (1)

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

IEEE Antennas Propag. Mag. (1)

J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag. 35, 69–71 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. 38, 227–235 (1990).
[CrossRef]

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

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

C. Monzon, O. Kesler, “On the depolarization of bodies invariant under a rotation,” IEEE Trans. Antennas Propag. 49, 1868–1874 (2001).
[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. (1)

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. Opt. Soc. Am. A (2)

Phys. Rev. E (2)

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,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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]

Sov. Phys. Usp. (1)

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

Other (2)

G. Ruck, D. Barrick, W. Stuart, C. Kirchbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

D. C. Jenn, Radar and Laser Cross Section Engineering (American Institute of Aeronautics and Astronautics, Washington, D.C., 1995).

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