Интегральные представления решений системы уравнений Максвелла для анизотропных сред

Досколович Л.Л., Казанский Н.Л., Харитонов С.И.

Аннотация:
В работе получены интегральные представления решений системы уравнений Максвелла для анизотропных сред. Наряду с представлением решений в трехмерном пространстве, получены интегральные представления для решений системы уравнений Максвелла в виде поверхностных волн на границе диэлектрика с отрицательной диэлектрической проницаемостью и анизотропным материалом. Интегральные представления получены с помощью разложения по собственным волнам однородной анизотропной среды, распространяющимся в положительном направлении.

Abstract:
Solutions of Maxwell’s equations for anisotropic media are deduced in the integral form. Alongside solutions in three-dimensional space, integral relations are derived to represent solutions of Maxwell’s equations in the form of surface plasmons propagating along the interface between a dielectric with negative refraction and an anisotropic material. The integral relationships are derived using the expansion in terms of eigenwaves of the homogeneous anisotropic medium, which travel in the positive direction.

Ключевые слова: интеграл Релея-Зоммерфельда, анизотропная среда, дифракция, уравнения Максвелла, собственные значения, собственные функции, поверхностные электромагнитные волны, разложение по плоским волнам.

Key words: Rayleigh-Sommerfeld integral, anisotropic medium, gyrotropic medium, diffraction, Maxwell’s equations, surface plasmons, plane waves.

Литература:

  1. Marathey A.S. On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory / A.S. Marathey, J.F. McCalmont // J. Opt. Soc. Am. -2004. -A21, -P.510–516.
  2. Osterberg. H. Closed solutions of Rayleigh’s diffraction integral for axial points / H. Osterberg., L. Smith // J. Opt. Soc. Am. -1961. -A51, -P.1050–1054.
  3. Marathay S. Vector diffraction theory for electromagnetic waves / S.Marathay, J.F. McCalmont // J. Opt. Soc. Am. -2001. -A 18, -P.2585–2593.
  4. Romero J. A. Vectorial approach to Huygens’s principle for plane waves: circular aperture and zone plates / J. A. Romero, L.Hernández, // J. Opt. Soc. Am. -A 23, -P.1141–1145 (2006).
  5. Romero J. A. Diffraction by circular aperture: an application of the vectorial theory of Huygens’s principle in the near field / J. A. Romero, L. Hernández //J. Opt. Soc. Am. -2008. –A. 25, -P.2040–2043.
  6. Kang X. Vectorial nonparaxial flattened gaussian beams and their beam quality in terms of the power in the bucket/ X. Kang, B. Lu // Opt.Comm. -2006. -262, -P.1–7.
  7. Barnes W.L. Surface plasmon subwavelength optics./ W.L. Barnes, F. Dereux., T.W.Ebbesen // Nature. -2003. –P.424-830.
  8. Berini P. Long range surface plasmons on ultrathin membranes/ P. Berini, R Charbonneau., N. Lohaud //. Nano Lett. -2007. -7 -P.1376-80.
  9. Lee I. M. Dispersion characterictics of channell plasmon polariton waveguides with block-trench-type groves./ I. M. Lee, J .Jang, J. H .Park,Kim, B.Lee // Opt Express. -2007 -Dec 10;15(25):-P.16596-603.
  10. Hohenau. A. Dielectric optical element for surface plasmons./ A.Hohenau, J.R. Krenn, A.L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A.L Leitner, F.R. Authenegg // Opt Lett. -2005 Apr 15;30(8):893-5.
  11. Radko I.P.. Surface plasmon polariton beam focusing with parabolic nanoparticle chains. / I.P. Radko, S.I. Bozhevalnyi, // Optics express -2007. -15(11):-6576-82.
  12. Fan X.. Nanoscale metal waveguide arrays as plasmon lenses/ X. Fan, G.P. Wang // Opt. Lett. 31, -2006. –P.1332-4.
  13. Steele J.M. Resonant and non-resonant generation and focusing of surface plasmons with circular gratting ./ J.M. Steele, Z. Liu, Y. Wang, X. Zhang // Opt. Express -2006. -14, -P.5664-70.
  14. Soifer V.A. Method for computer design of difractive optical elements / V.A. Soifer. - New York Willey, -2002
  15. Besus E.A. Design of diffractive lenses for focusing surface plasmons / E.A. Besus, L.L. Doskolovich. N.L. Kazansky. V.A. Soifer, S.I. Kharitonov // Jornal of Optics -2010. -01501.

References:

  1. Marathey A.S. On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory / A.S. Marathey, J.F. McCalmont // J. Opt. Soc. Am. -2004. -A21, -P.510–516.
  2. Osterberg. H. Closed solutions of Rayleigh’s diffraction integral for axial points / H. Osterberg., L. Smith // J. Opt. Soc. Am. -1961. -A51, -P.1050–1054.
  3. Marathay S. Vector diffraction theory for electromagnetic waves / S.Marathay, J.F. McCalmont // J. Opt. Soc. Am. -2001. -A 18, -P.2585–2593.
  4. Romero J. A. Vectorial approach to Huygens’s principle for plane waves: circular aperture and zone plates / J. A. Romero, L.Hernández, // J. Opt. Soc. Am. -A 23, -P.1141–1145 (2006).
  5. Romero J. A. Diffraction by circular aperture: an application of the vectorial theory of Huygens’s principle in the near field / J. A. Romero, L. Hernández //J. Opt. Soc. Am. -2008. –A. 25, -P.2040–2043.
  6. Kang X. Vectorial nonparaxial flattened gaussian beams and their beam quality in terms of the power in the bucket/ X. Kang, B. Lu // Opt.Comm. -2006. -262, -P.1–7.
  7. Barnes W.L. Surface plasmon subwavelength optics./ W.L. Barnes, F. Dereux., T.W.Ebbesen // Nature. -2003. –P.424-830.
  8. Berini P. Long range surface plasmons on ultrathin membranes/ P. Berini, R Charbonneau., N. Lohaud //. Nano Lett. -2007. -7 -P.1376-80.
  9. Lee I. M. Dispersion characterictics of channell plasmon polariton waveguides with block-trench-type groves./ I. M. Lee, J .Jang, J. H .Park,Kim, B.Lee // Opt Express. -2007 -Dec 10;15(25):-P.16596-603.
  10. Hohenau. A. Dielectric optical element for surface plasmons./ A.Hohenau, J.R. Krenn, A.L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A.L Leitner, F.R. Authenegg // Opt Lett. -2005 Apr 15;30(8):893-5.
  11. Radko I.P.. Surface plasmon polariton beam focusing with parabolic nanoparticle chains. / I.P. Radko, S.I. Bozhevalnyi, // Optics express -2007. -15(11):-6576-82.
  12. Fan X.. Nanoscale metal waveguide arrays as plasmon lenses/ X. Fan, G.P. Wang // Opt. Lett. 31, -2006. –P.1332-4.
  13. Steele J.M. Resonant and non-resonant generation and focusing of surface plasmons with circular gratting ./ J.M. Steele, Z. Liu, Y. Wang, X. Zhang // Opt. Express -2006. -14, -P.5664-70.
  14. Soifer V.A. Method for computer design of difractive optical elements / V.A. Soifer. - New York Willey, -2002
  15. Besus E.A. Design of diffractive lenses for focusing surface plasmons / E.A. Besus, L.L. Doskolovich. N.L. Kazansky. V.A. Soifer, S.I. Kharitonov // Jornal of Optics -2010. -01501.

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