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Articles

On the Computation of the Free-Space Doubly-Periodic Green's Function of the Three-Dimensional Helmholtz Equation

Pages 457-465 | Published online: 03 Apr 2012

References

  • Guérin , N. , Enoch , S. and Tayeb , G. 2001 . Combined method for the computation of the doubly periodic Green's function . J. Electromagn. Waves Appl. , 15 : 205 – 221 .
  • Kambe , K. 1967 . Theory of electron diffraction by crystals. Green's function and integral equation . Z. Naturforschg. , 22a : 422 – 431 .
  • Kambe , K. 1967 . Theory of low-energy electron diffraction. I. Application of the cellular method to monoatomic layers . Z. Naturforschg. , 22a : 322 – 330 .
  • Segall , B. 1957 . Calculation of the band structure of “complex” crystals . Phys. Rev. , 105 : 108 – 115 .
  • Kambe , K. 1968 . Theory of low-energy electron diffraction. II. Cellular method for complex monolayers and multilayers . Z. Naturforschg. , 23a : 1280 – 1294 .
  • Kohn , W. and Rostoker , N. 1954 . Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium . Phys. Rev. , 94 : 1111 – 1120 .
  • Abramowitch , M. and Stegun , I. A. 1973 . Handbook of Mathematical Functions , Dover Publications .
  • Ozorio de Almeida , A. M. 1975 . Real-space method for interpreting micrographs in cross-grating orientations. I. Exact wave-mechanical formulation . Acta Cryst. A , 31 : 435 – 442 .
  • Berry , M. V. 1981 . Quantizing a classically ergodic system: Sinai's billiard and the KKR method . Ann. Phys. (NY) , 131 : 163 – 216 .
  • Jennings , P. J. and McRae , E. G. 1970 . Electron diffraction at crystal surfaces IV. Computation of LEED intensities for “muffin-tin” models with application to tungsteen (001) . Surf. Sci. , 23 : 363 – 388 .
  • Jepsen , D. W. , Marcus , P. M. and Jona , F. 1971 . Accurate calculation of the low-energy electron-diffraction spectra of Al by the layer-Korringa-Kohn-Rostoker method . Phys. Rev. Lett. , 26 : 1365 – 1368 .
  • Pendry , J. B. 1974 . Low Energy Electron Diffraction , London : Academic Press .
  • Tong , S. Y. 1975 . Theory of low-energy electron diffraction . Prog. Surf. Sci. , 7 : 1 – 48 .
  • Ohtaka , K. 1980 . Scattering theory of low-energy photon diffraction . J. Phys.: Solid State , 13 : 667 – 680 .
  • Modinos , A. 1987 . Scattering of electromagnetic waves by a plane of spheres-formalism . Physica , 141 : 575 – 588 .
  • Stefanou , N. , Karathanos , V. and Modinos , A. 1992 . Scattering of electromagnetic waves by periodic structures . J. Phys.: Condens. Matter , 4 : 7389 – 7400 .
  • Psarobas , I. E. , Stefanou , N. and Modinos , A. 2000 . Scattering of elastic waves by periodic arrays of spherical bodies . Phys. Rev. B , 62 : 278 – 291 .
  • McRae , E. G. 1968 . Electron diffraction at crystal surfaces I. Generalization of Darwin's dynamical theory . Surf. Sci. , 11 : 479 – 491 .
  • Moroz , A. 1995 . Density-of-states calculation and multiple scattering theory for photons . Phys. Rev. B , 51 : 2068 – 2081 .
  • Van der Lem , H. and Moroz , A. 2000 . Towards two-dimensional complete photonic band gap structures below infrared wavelengths . J. Opt. A: Pure Appl. Opt. , 2 : 395 – 399 .
  • Moroz , A. and Sommers , C. 1999 . Photonic band gaps of three-dimensional face-centered cubic lattices . J. Phys.: Condens. Matter , 11 : 997 – 1008 .
  • Press , W. H. , Teukolsky , S. A. , Vetterling , W. T. and Flannery , B. P. 1992 . Numerical Recipes in Fortran , Cambridge : Cambridge University Press .
  • Nussenzveig , H. M. 1992 . Diffraction Effects in Semiclassical Scattering , Cambridge : Cambridge University Press . Sec. 5
  • Moroz , A. 2001 . Exponentially convergent lattice sums . Opt. Lett. , 26 : 1119 – 1121 .
  • Moroz , A. A review of exponentially convergent lattice sums of the free-space periodic Green's functions of the Helmholtz equation . J. Math. Phys. , scheduled for
  • McLaren , J. M. , Crampin , S. , Vvedensky , D. D. , Albers , R. C. and Pendry , J. B. 1990 . Layer KKR electronic structure code for bulk and interface geometries . Comp. Phys. Commun. , 60 : 365 – 389 .
  • Yannopapas , V. , Stefanou , N. and Modinos , A. 1998 . Heterostructures of photonic crystals: frequency bands and transmission coefficients . Comp. Phys. Commun. , 113 : 49 – 77 .

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