English: Electric field distribution from electric line source on dielectric half-space with a relative permittivity of 3. The electric line source is located 1 m above this half-space and has a free-space wavelength of 1 m. The z-oriented electric fields are computed at 10 cm above the half-space. The plot showcases a ${\displaystyle x^{-3/2}}$ dependency at large distances from the sources, which is characteristic of the asymptotic lateral wave behavior for 2D layered media.

This plot is computed using the open-source numerical steepest descent path package ND-SDP for 2D Sommerfeld integrals for half-spaces, published with GNU General Public License. The relevant reference is:

A. Hochman and Y. Leviatan, "A Numerical Methodology for Efficient Evaluation of 2D Sommerfeld Integrals in the Dielectric Half-Space Problem," IEEE Transactions on Antennas and Propagation, vol. 58, no. 2, pp. 413-431, Feb. 2010, doi: 10.1109/TAP.2009.2037761