1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 47 Number 6, June 1999

Efficient Calculation of Lattice Sums for Free-Space Periodic Green's Function

Page 1050.

Abstract:

An efficient method to calculate the lattice sums is presented for a one-dimensional (1-D) periodic array of line sources. The method is based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function. The lattice sums of arbitrary high order are then expressed by an integral of elementary functions, which is easily computed using a simple scheme of numerical integration. The calculated lattice sums are used to evaluate the free-space periodic Green's function. The numerical results show that the proposed method provides a highly accurate evaluation of the Green's function with far less computation time, even when the observation point is located near the plane of the array.

References

1. R. Lampe, P. Klock, and P. Mayes, "Integral transforms useful for the accelerated summation of periodic, free-space Green's functions," IEEE Trans. Microwave Theory Tech., vol. MTT-33, pp. 734-736, Aug. 1985.
2. K. R. Demarest, E. K. Miller, K. Kalbasi, and L. K. Wu, "A computationally efficient method of evaluating Green's functions for 1-, 2-, and 3-D enclosures," IEEE Trans. Magn., vol. 25, pp. 2878-2880, July 1989.
3. R. E. Jorgenson and R. Mittra, "Efficient calculations of the free-space periodic Green's function," IEEE Trans. Antennas Propagat., vol. 38, pp. 633-642, May 1990.
4. S. Singh and R. Singh, "Application of transforms to accelerate the summation of periodic free-space Green's functions," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1746-1748, Nov. 1990.
5. S. Singh, W. F. Richards, J. R. Zinecker, and D. R. Wilton, "Accelerating the convergence of series representing the free space periodic Green's function," IEEE Trans. Antennas Propagat., vol. 38, pp. 1958-1962, Dec. 1990.
6. S. Singh and R. Singh, "On the use of \rho-algorithm in series acceleration," IEEE Trans. Antennas Propagat., vol. 39, pp. 1514-1517, Oct. 1991.
7. N. A. Nicorovici, R. C. McPhedran, and R. Petit, "Efficient calculation of the Green's function for electromagnetic scattering by gratings," Phys. Rev. E, vol. 49, no. 5, pp. 4563-4577, May 1994.
8. J. P. Skinner and P. J. Collins, "A one-sided version of the Poisson sum formula for semi-infinite array Green's functions," IEEE Trans. Antennas Propagat., vol. 45, pp. 601-607, Apr. 1997.
9. N. A. Nicorovici and R. C. McPhedran, "Lattice sums for off-axis electromagnetic scattering by grating," Phys. Rev. E, vol. 50, no. 4, pp. 3143-3160, Oct. 1994.
10. H. Roussel, W. C. Chew, F. Jouvie, and W. Tabbara, "Electromagnetic scattering from dielectric and magnetic gratings of fibers--A T-matrix solution," J. Electromagn. Waves Applicat., vol. 10, no. 1, pp. 109-121, Jan. 1996.
11. C. W. Chew, Waves and Fields in Inhomogeneous Media.New York: Van Nostrand Reinhold, 1990.