Radio Science

Correction to “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers”

Authors

Errata

This article corrects:

  1. Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers Volume 42, Issue 6, Article first published online: 19 December 2007

[1] In the paper “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers” by R. A. Shore and A. D. Yaghjian (Radio Science, 42, RS6S21, doi:10.1029/2007RS003647, 2007), please note the following corrections.

[2] Replace paragraphs 105–107 in section 5 with the single paragraph:

[3] The total fields Ex(z) and Hy(z) to the left of the array (z < 0) can be regarded as the sum of the incident plane wave eikz, a reflected plane wave Re−ikz, and a spectrum of scattered evanescent plane waves from the discrete array elements. Similarly, Ex(z) and Hy(z) to the right of the array (z > Nd) can be regarded as the sum of a transmitted plane wave Teikz, and a spectrum of scattered evanescent plane waves. If z is chosen approximately a wavelength or more from the array boundaries, the evanescent plane waves become negligible and the reflection and transmission coefficients, R and T, are given by

equation image

and

equation image

Even though R and T appear from (126) and (127) to be functions of z (unlike the customary expressions for reflection and transmission coefficients for slabs of continuous material), in fact they are not since the expressions (126) and (127) are given in regions where the evanescent waves are negligible. The coefficients R and T for partially finite arrays of lossless spheres satisfy the energy conservation relation ∣R2 + ∣T2 = 1 as can be numerically verified.

[4] In Appendix B, replace −0.4902 in equation (B7c) by +0.4902.

[5] In equation (B9) of Appendix B, ζ(3) = 1.20205⋯, where ζ is the Riemann zeta function.

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