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  • 1
    Electronic Resource
    Electronic Resource
    Lattice sums for gratings and arrays (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 7808-7816 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Lattice sums arising in quasiperiodic Green's functions for the Helmholtz equation, over general two-dimensional arrays are investigated. The array sums are related to those over a single quasiperiodic line of sources, and their difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaining to the case of photonic gap states, associated with complex quasiperiodicity (Bloch) vectors. The accuracy and computational speed of our expressions are illustrated. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1310361
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  • 2
    Electronic Resource
    Electronic Resource
    Analytical results for a class of sums involving Bessel functions and square arrays (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2043-2052 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a class of sums involving Bessel functions summed over the square array. The sums involve the length (ξ) of an arbitrary vector lying within the central unit cell. We establish conditions under which the sums reduce to polynomial forms in ξ (possibly with a single logarithmic term in addition), and show how these polynomials may be conveniently evaluated. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531492
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  • 3
    Electronic Resource
    Electronic Resource
    Static Bloch sums for the square array (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2802-2813 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider sums arising in doubly quasiperiodic Green's functions for the Laplace equation, over the square array. The sums are represented as Fourier series, and it is shown that the coefficients in the series can be obtained as polynomials. We give expressions from which the first six array sums can be evaluated efficiently, and accurate to better than one part in 107, over most of the Brillouin zone. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1467968
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    Paper (German National Licenses)
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