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Maximizing Absorption and Scattering by Dipole Particles

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This is a review and tutorial paper which discusses the fundamental limitations on the maximal power which can be received, absorbed, and scattered by an electrically small electrically polarizable particle and infinite periodical arrays of such particles.

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  1. Balanis (1997) Antenna theory: analysis and design, 2nd edn. Wiley, New York

    Google Scholar 

  2. Bohren CF, Huffman DR (1983) Radiation and scattering of light by small particles. Wiley, New York

    Google Scholar 

  3. Bohren CF (1983) How can a particle absorb more than the light incident on it? Am J Phys 51(4):323–327

    Article  CAS  Google Scholar 

  4. Paul H, Fischer R (1983) Light absorption by a dipole. Sov Phys Uspekhi 26(10):923–926

    Article  Google Scholar 

  5. TribelskyM(1984) Resonant scattering of light by small particles. Zh Exp Teor Fiz 86:915–926

  6. Zumofen G, Mojarad NM, Sandoghdar V, Agio M (2008) Perfect absorption of light by an oscillating dipole. Phys Rev Lett 101:180404

    Article  CAS  Google Scholar 

  7. Tretyakov S (2003) Analytical modeling in applied electromagnetics. Artech House, Norwood

    Google Scholar 

  8. Munk B (2000) Frequency selective surfaces: theory and design. Wiley, New York

    Book  Google Scholar 

  9. Slovick B, Zhi Gang Yu, Berding M, Krishnamurthy S (2013) Perfect dielectric-metamaterial reflector. Phys Rev B 88:165116

    Article  Google Scholar 

  10. Kwon D-H, Pozar DM (2009) Analysis of maximum received power by arbitrary lossless arrays.In: Antennas and propagation society international symposium, pp 1–4

  11. Kwon D-H, Pozar DM (2009) Optimal characteristics of an arbitrary receive antenna. IEEE Trans Antennas Propag 57(12):3720–3727

    Article  Google Scholar 

  12. Bach Andersen J, Frandsen A (2005) Absorption efficiency of receiving antennas. IEEE Trans Antennas Propag 53(9):2843–2849

    Article  Google Scholar 

  13. Liberal I, Ziolkowski RW (2013) Analytical and equivalent circuit models to elucidate power balance in scattering problems. IEEE Trans Antennas Propag 61(5):2714–2726

    Article  Google Scholar 

  14. Liberal I, Ederra I, Gonzalo R, Ziolkowski RW (2013) A multipolar analysis of near-field absorption and scattering processes. IEEE Trans Antennas Propag 61(10):5184–5199

    Article  Google Scholar 

  15. Fleury R, Soric J, Alù A (2013) Physical bounds on absorption and scattering for cloaked sensors. arXiv:1309.3619

  16. Ra’di Y, Tretyakov SA (2013) Balanced and optimal bianisotropic particles: maximizing power extracted from electromagnetic fields. New J Phys 15:053008

    Article  Google Scholar 

  17. Belov PA, Maslovski SI, Simovski KR, Tretyakov SA (2003) A condition imposed on the electromagnetic polarizability of a bianisotropic scatterer. Tech Phys Lett 29(9):718–720

    Article  CAS  Google Scholar 

  18. Tretyakov SA, Maslovski SI, Belov PA (2003) An analytical model of metamaterials based on loaded wire dipoles. IEEE Trans Antennas Propag 51(10):2652–2658

    Article  Google Scholar 

  19. Hansen RC (2006) Electrically small, superdirective and superconducting antennas. Wiley, Hoboken

    Book  Google Scholar 

  20. Tribelsky M, Lukyanchuk B (2006) Anomalous light scattering by small particles. Phys Rev Lett 97:263902

    Article  Google Scholar 

  21. Yang T, Chen H, Luo X, Ma H (2008) Superscatterer: enhancement of scattering with complementary media. Opt Express 16(22):18545

    Article  Google Scholar 

  22. Ng J, Chen H, Chan CT (2009) Metamaterial frequency-selective superabsorber. Opt Lett 34(5):644

    Article  Google Scholar 

  23. Ruan Z, Fan S (2010) Superscattering of light from subwavelength nanostructures. Phys Rev Lett 105:013901

    Article  Google Scholar 

  24. Ruan Z, Fan S (2011) Design of subwavelength superscattering nanospheres. Appl Phys Lett 98:043101

    Article  Google Scholar 

  25. Steshenko S, Capolino F (2009) Single dipole approximation for modeling collections of nanoscatterers. In: Capolino F (ed) Metamaterials handbook: theory and phenomena of metamaterials. CRC, Boca Raton

    Google Scholar 

  26. Alù A, Engheta N (2009) Cloaking a sensor. Phys Rev Lett 102:233901

    Article  Google Scholar 

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Most of this text was written when the author was visiting the Technical University of Denmark (DTU Fotonik), in January–April 2013. Financial support from the Otto Mønsted Foundation and Aalto School of Electrical Engineering is appreciated. Special thanks to the host, prof. A. Lavrinenko, to Dr. A. Andryieuski for sharing his knowledge of the optical literature, and to prof. O. Breinbjerg for explaining that the reciprocity relation between the antenna gain and effective area can be used to find the maximum received power (Section 1). The last stages of this work got inspirations from discussions with prof. A. Alù (University of Texas at Austin), who kindly shared a preprint [15] with the author. Useful discussions with prof. C. Simovski (Aalto University) of extinction by particles in regular arrays are also acknowledged.

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Correspondence to Sergei Tretyakov.

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Tretyakov, S. Maximizing Absorption and Scattering by Dipole Particles. Plasmonics 9, 935–944 (2014).

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