Abstract

This paper explores the possibility of using the focusing property of left-handed materials to estimate the location of a visually obscured target. The field scattered by the target and measured on a surface can be considered as incident upon a left-handed half-space and should converge to a point resembling the mirror image of the scatterer’s location. The results are obtained using the method of auxiliary sources as adapted to double-negative media. Two-dimensional scattering is considered, either from a single object or from several targets, using pointlike and Gaussian sources of illumination. The method gives reasonable results when the sizes of the scatterers are comparable to the wavelength.

© 2009 Optical Society of America

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  1. D. J. Daniels, "Ground Penetrating Radar for Buried Landmine and IED Detection," in Unexploded Ordnance Detection and Mitigation, J. Byrnes, ed., pp. 89-111 (Springer Netherlands, Dordrecht, 2009).
    [CrossRef]
  2. A. Karellas and S. Vedantham, "Breast cancer imaging: A perspective for the next decade," Med. Phys. 35, 4878-4897 (2008).
    [CrossRef] [PubMed]
  3. F. S. Grant and G. F. West, Interpretation Theory in Applied Geophysics (McGraw-Hill, New York, 1965).
  4. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. S. A. Ramakrishna and T. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press/SPIE Press, Boca Raton, FL, 2008).
    [CrossRef]
  6. N. Engheta and R. W. Ziolkowski, eds., Metamaterials: Physics and Engineering Explorations (IEEE Press/ Wiley-Interscience, Piscataway, NJ, 2006).
  7. R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
    [CrossRef]
  8. Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
    [CrossRef]
  9. T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
    [CrossRef]
  10. S. A. Ramakrishna and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
    [CrossRef]
  11. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  12. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  13. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
    [CrossRef]
  14. N. Engheta and R. W. Ziolkowski, "A Positive Future for Double-Negative Metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
    [CrossRef]
  15. R. W. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
    [CrossRef] [PubMed]
  16. R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  17. Q2. V. D. Kupradze, "On the approximate solution of problems of mathematical physics," Usp. Mat. Nauk 22(2), 59-107 (1967).
  18. F. G. Bogdanov, D. D. Karkashadze, and R. S. Zaridze, "The Method of Auxiliary Sources in Electromagnetic Scattering Problems," in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed., pp. 143-172 (Elsevier Science, Amsterdam, 1999).
  19. R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
    [CrossRef]
  20. F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
    [CrossRef]
  21. H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
    [CrossRef]
  22. F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
    [CrossRef]
  23. V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," in Polaritons: Proc. of 1st Taormina Research Conf. on the Structure of Matter, E. Burstein and F. D. Martini, eds., pp. 5-13 (1972).
  24. Q3. V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Phys. Usp. 46, 764-768 (2003).
    [CrossRef]
  25. J. G. Van Bladel, Electromagnetic Fields, 1st ed. (McGraw-Hill, New York, 1964).
  26. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

2008 (2)

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

A. Karellas and S. Vedantham, "Breast cancer imaging: A perspective for the next decade," Med. Phys. 35, 4878-4897 (2008).
[CrossRef] [PubMed]

2007 (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

2005 (2)

N. Engheta and R. W. Ziolkowski, "A Positive Future for Double-Negative Metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

2004 (2)

S. A. Ramakrishna and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
[CrossRef]

2003 (2)

Q3. V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Phys. Usp. 46, 764-768 (2003).
[CrossRef]

R. W. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
[CrossRef] [PubMed]

2002 (3)

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

2001 (2)

R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1994 (1)

R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
[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]

1967 (1)

Q2. V. D. Kupradze, "On the approximate solution of problems of mathematical physics," Usp. Mat. Nauk 22(2), 59-107 (1967).

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Anastassiu, H. T.

F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
[CrossRef]

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

Bit-Babik, G.

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

Breinbjerg, O.

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

Chen, X.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Economou, D. P.

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

Engheta, N.

N. Engheta and R. W. Ziolkowski, "A Positive Future for Double-Negative Metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

Fink, M.

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Haider, S. A.

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

Heyman, E.

R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Kaklamani, D. I.

F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
[CrossRef]

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

Karellas, A.

A. Karellas and S. Vedantham, "Breast cancer imaging: A perspective for the next decade," Med. Phys. 35, 4878-4897 (2008).
[CrossRef] [PubMed]

Kleinman, R. E.

R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Kupradze, V. D.

Q2. V. D. Kupradze, "On the approximate solution of problems of mathematical physics," Usp. Mat. Nauk 22(2), 59-107 (1967).

Lu, J.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Minonzio, J.-G.

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

Moss, C. D.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

O’Neill, K.

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

Pacheco, J.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

Paulsen, K. D.

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Philippe, F. D.

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Prada, C.

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shubitidze, F.

F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
[CrossRef]

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sun, K.

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

Tavzarashvili, K.

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

Uzunoglu, N. K.

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

van den Berg, P. M.

R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
[CrossRef]

Vedantham, S.

A. Karellas and S. Vedantham, "Breast cancer imaging: A perspective for the next decade," Med. Phys. 35, 4878-4897 (2008).
[CrossRef] [PubMed]

Veselago, V. G.

Q3. V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Phys. Usp. 46, 764-768 (2003).
[CrossRef]

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

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Zaridze, R.

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, "A Positive Future for Double-Negative Metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

R. W. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
[CrossRef] [PubMed]

Ziolkowski, R.W.

R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

R. Zaridze, G. Bit-Babik, K. Tavzarashvili, D. P. Economou, and N. K. Uzunoglu, "Wave Field Singularity Aspects in Large-Size Scatterers and Inverse Problems," IEEE Trans. Antennas Propag. 50, 50-58 (2002).
[CrossRef]

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary conditions (SIBC)," IEEE Trans. Antennas Propag. 50, 59-66 (2002).
[CrossRef]

F. Shubitidze, H. T. Anastassiu, and D. I. Kaklamani, "An improved accuracy version of the method of auxiliary sources for computational electromagnetics," IEEE Trans. Antennas Propag. 52, 302-309 (2004).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun, and K. D. Paulsen, "Application of the Method of Auxiliary Sources to theWide-Band Electromagnetic Induction Problem," IEEE Trans. Geosci. Remote Sens. 40, 928-942 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, Jr., and J. A. Kong, "Properties of Left-Handed Metamaterials: Transmission, Backward Phase, Negative Refraction, and Focusing," IEEE Trans. Microwave Theory Tech. 53, 2956-2967 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A Positive Future for Double-Negative Metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

Inv. Prob. (1)

Q1. J.-G. Minonzio, F. D. Philippe, C. Prada, and M. Fink, "Characterization of an elastic cylinder and an elastic sphere with the time-reversal operator: application to the sub-resolution limit," Inv. Prob. 24, 025014 (2008).
[CrossRef]

Med. Phys. (1)

A. Karellas and S. Vedantham, "Breast cancer imaging: A perspective for the next decade," Med. Phys. 35, 4878-4897 (2008).
[CrossRef] [PubMed]

Nature Mater. (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, "Negative refraction in semiconductor materials," Nature Mater. 6, 946-950 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

S. A. Ramakrishna and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

Phys. Rev. E (1)

R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Phys. Usp. (1)

Q3. V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Phys. Usp. 46, 764-768 (2003).
[CrossRef]

Radio Sci. (1)

R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[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]

Usp. Mat. Nauk (1)

Q2. V. D. Kupradze, "On the approximate solution of problems of mathematical physics," Usp. Mat. Nauk 22(2), 59-107 (1967).

Other (8)

F. G. Bogdanov, D. D. Karkashadze, and R. S. Zaridze, "The Method of Auxiliary Sources in Electromagnetic Scattering Problems," in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed., pp. 143-172 (Elsevier Science, Amsterdam, 1999).

D. J. Daniels, "Ground Penetrating Radar for Buried Landmine and IED Detection," in Unexploded Ordnance Detection and Mitigation, J. Byrnes, ed., pp. 89-111 (Springer Netherlands, Dordrecht, 2009).
[CrossRef]

S. A. Ramakrishna and T. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press/SPIE Press, Boca Raton, FL, 2008).
[CrossRef]

N. Engheta and R. W. Ziolkowski, eds., Metamaterials: Physics and Engineering Explorations (IEEE Press/ Wiley-Interscience, Piscataway, NJ, 2006).

F. S. Grant and G. F. West, Interpretation Theory in Applied Geophysics (McGraw-Hill, New York, 1965).

J. G. Van Bladel, Electromagnetic Fields, 1st ed. (McGraw-Hill, New York, 1964).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," in Polaritons: Proc. of 1st Taormina Research Conf. on the Structure of Matter, E. Burstein and F. D. Martini, eds., pp. 5-13 (1972).

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Figures (9)

Fig. 1.
Fig. 1.

A visually obscured object responds to the field of a sensor by emitting a measurable scattered field (left). Using a virtual half-space of left-handed material one can effect a numerical refraction of this field to estimate the location of the object (right).

Fig. 2.
Fig. 2.

Interface between free space and a left-handed medium showing a negative angle of refraction. The electric field E, the magnetic field H, and the wave vector k form a left-handed triad within the metamaterial. The Poynting vector and the propagation of energy are in the usual direction and satisfy causality.

Fig. 3.
Fig. 3.

MAS geometry for modelling a uniform half-space.

Fig. 4.
Fig. 4.

Electric field distribution (top) and corresponding phase (bottom) around three point sources to the left of the interface (left) and MAS-predicted equivalents in the virtual LHM half-space (right).

Fig. 5.
Fig. 5.

Electric field distribution around a Gaussian source in vacuum (left) and MAS-reconstructed distribution in the virtual LHM half-space (right).

Fig. 6.
Fig. 6.

Reconstruction of the electromagnetic field for the case of a Gaussian beam illuminating two different cylinders, a good dielectric (top) and a perfect conductor (bottom). Electric field distribution around the object (left) and MAS-reconstructed distribution in the virtual LHM half-space (right).

Fig. 7.
Fig. 7.

Electric-field distribution (left) and corresponding phase (right), in vacuum and in the virtual LHM half-space, when a directed source shines on five nonmagnetic conducting cylinders.

Fig. 8.
Fig. 8.

Electric field distribution for three objects separated by more than one wavelength: actual (in free space, at left) and reconstructed (in the LHM, at right).

Fig. 9.
Fig. 9.

Electric-field distribution around a compound object in free space (left) and MAS reconstruction within a virtual LHM (right).

Equations (25)

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

K×E=ωμLHMHandK×H=ωεLHME,
n̂×(Ei+Er)=n̂×ELHM,
n̂×(Hi+Hr)=n̂×HLHM,
n̂·ε0(Ei+Er)=n̂·εLHMELHM,
n̂ · μ0 (Hi+Hr)=n̂·μLHMHLHM,
2 A+k2A=μJ,
J = I ŷ δ(2) (ρρ),
A(ρ)=4IŷH0(2)(kρρ)=4IŷH0(2)(k(xx)2+(zz')2)
E(ρ)=A=μω4IŷH0(2)(k(xx)2+(zz)2)
E(ρ)=1μ×A=jk4I(xx)Ẑ(zz)x̂(xx)2+(zz)2H1(2)(k(xx)2+(zz)2).
Er (ρ)=μ0ω4ŷiξ1,iH0(2)(k0(xxi)2+(zd1)2),
Hr (ρ)=jk04i(xxi)ẑ(zd1)x̂(xxi)2+(zd1)2ξ1,iH1(2)(k0(xxi)2+(zd1)2),
ELHM(ρ)=μLHMω4ŷiξ2,iH0(2)(kLHM(xxi)2+(z+d2)2),
HLHM(ρ)=jkLHM4i(xxi)ẑ(z+d2)x̂(xxi)2+(z+d2)2ξ2,iH1(2)(kLHM(xxi)2+(z+d2)2),
kLHM=k0cεLHMμLHM=k0.
μ0 iξ1,iH0(2)(k0(xmxi)2+d12)μLHMiξ2,iH0(2)(kLHM(xmxi)2+d22)+Eymeas(xm)
k0iξ1,id1(xmxi)2+d12H1(2)(k0(xmxi)2+d12)
+kLHMiξ2,id2(xmxi)2+d22H1(2)(kLHM(xmxi)2+d22)=Hxmeas(xm)
E=I0H0(2)()ejωtŷI02πkρej(+ωt+π4)ŷ,
H=jkωμrμ0I0H1(2)()ejωt(ŷ×ρ̂)kωμrμ0I02πkρej(+ωt+π4)(ŷ×ρ̂),
S=12Re{E×H*}=I02k*e2Imωμr*μ0πkρρ̂.
vphasevac=ωk0andSvac=I02ωμ0πρρ̂,
vphaseLHM=ωk0andSLHM=I02ωμ0πρρ̂.
ELHM=I0 H0(1) (k0ρ)ŷ,
HLHM=jk0ωμ0I0H1(1)(k0ρ)(ŷ×ρ̂),

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