Abstract

This paper examines an extension of the Ewald method for evaluating the periodic free-space Green's function due to an array of point sources, when the wavenumber of the phased sources is allowed to be complex. This makes the Ewald method useful for treating leaky modes on periodic structures.

Highlights

  • The Ewald method that is used in evaluating the freespace periodic Green’s function for an array of point sources is extended here to leaky modes by allowing for complex wavenumbers

  • It is shown that care must be taken when choosing the path of integration in the complex plane that is used to define the exponential integral function that appears in the Ewald method

  • One can obtain a simple rule for how to modify the exponential integral calculation to obtain solutions that correspond to physical leakywave solutions. This extension of the Ewald method to complex wavenumbers allows for the treatment of periodic leaky-wave antennas as well as metamaterial structures such as one-dimensional chains of particles, including plasmonic nanoparticles

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Summary

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Computation of the One-Dimensional Free-Space Periodic Green’s Function for Leaky Waves using the Ewald Method. Abstract − This paper examines an extension of the Ewald method for evaluating the periodic free-space Green’s function due to an array of point sources, when the wavenumber of the phased sources is allowed to be complex. This makes the Ewald method useful for treating leaky modes on periodic structures

INTRODUCTION
Rn erfc
The fundamental exponential integral function is defined as
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