This paper (i.e., [1]) extends PTD to an impedance half-plane problem.
2. Hacvelioglu, F., L. Sevgi, and P. Y. Ufimtsev, "On the modified theory of physical optics," IEEE Trans. on Antennas and Propagat., Vol. 61, No. 12, 6115-6119, Dec. 2013.
doi:10.1109/TAP.2013.2280042
3. Umul, Y. Z., "Modified theory of physical optics," Opt. Exp., Vol. 12, 4959-4972, 2004.
doi:10.1364/OPEX.12.004959
4. Ufimtsev, P. Y., Fundamentals of the Physical Theory of Diffraction, Wiley & Sons, Inc., Hoboken, New Jersey, 2007 (translated into Russian, Binom, 2009).
doi:10.1002/0470109017
5. Sommerfeld, A., "Mathematische theorie der diffraction," Ann. Math., Vol. 47, No. 2-3, 317-374, 1896.
doi:10.1007/BF01447273
6. Umul, Y. Z., "The relation between the boundary diffraction wave theory and physical optics," Opt. Commun., Vol. 281, No. 19, 4844-4848, Oct. 2008.
doi:10.1016/j.optcom.2008.06.072
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