Corrections to “Relativistic Aspects of Plane Wave Scattering by a Perfectly Conducting Half-Plane With Uniform Velocity Along an Arbitrary Direction” [Sep 17 4759-4767]

摘要

In a recent paper [1], there was a typo in (13), which should read as a scalar equation for the $ {z}$ -component of $tilde {mathbf {E}}{tilde {mathbf {H}}}$ in the form begin{equation*} tilde {E}_{ {z}} {tilde {H}_{ {z}}} = F(tilde {xi }^{i}) , tilde {E}_{ {z}}^{i} {tilde {H}_{ {z}}^{i}} + F(tilde {xi }^{r}) tilde {E}_{ {z}}^{r} {tilde {H}_{ {z}}^{r}} end{equation*} from which the remaining field components may be obtained. The full vector equation for the electric field is then given by begin{align*} tilde {mathbf {E}}=&F(tilde {xi }^{i}) tilde {mathbf {E}}^{i} + F(tilde {xi }^{r}) tilde {mathbf {E}}^{r} + frac {e^{i pi /4}}{sqrt { 2 pi tilde {k} tilde {rho } sin tilde {theta }_{0} }} e^{i tilde {k} (tilde {rho } sin tilde {theta }_{0} -tilde { {z}} cos tilde {theta }_{0})} [3pt]× bigg { cos frac {tilde {phi }-tilde {phi }_{0}}{2} left [{ left ({ tilde {mathbf {E}}^{i}_{0} cdot hat {tilde { {z}}} }right) hat {tilde { {z}}} - tilde {mathbf {E}}^{i}_{0} }right ] +sin frac {tilde {phi }-tilde {phi }_{0}}{2} , hat {tilde { {z}}} times tilde {mathbf {E}}^{i}_{0} [4pt]&+,cos frac {tilde {phi }+tilde {phi }_{0}}{2} left [{ left ({ tilde {mathbf {E}}^{r}_{0} cdot hat {tilde { {z}}} }right) hat {tilde { {z}}} - tilde {mathbf {E}}^{r}_{0} }right ] +sin frac {tilde {phi }+tilde {phi }_{0}}{2} , hat {tilde { {z}}} times tilde {mathbf {E}}^{r}_{0} bigg } end{align*} where $tilde {mathbf {E}}^{i,r}_{0}$ denotes the incident (reflected) electric field amplitude at the edge of the half-plane in frame $tilde {S}$ . In addition, $Z tilde {B}_{h}$ in (24) should read as $tilde {B}_{h}$ , yielding begin{align*} tilde {bar {bar {F}}}_{re}=&dfrac {tilde {Q}}{c} × ! begin{bmatrix}! 0 !&quad ! -!tilde {B}_{e} sin dfrac {tilde {phi }}{2} !&quad ! tilde {B}_{e} cos dfrac {tilde {phi }}{2} !&quad ! 0 tilde {B}_{e} sin dfrac {tilde {phi }}{2} !&quad ! 0 !&quad ! 0 !&quad ! -tilde {B}_{h} sin dfrac {tilde {phi }}{2} -tilde {B}_{e} cos dfrac {tilde {phi }}{2} !&quad ! 0 !&quad ! 0 !&quad ! tilde {B}_{h} cos dfrac {tilde {phi }}{2} 0 !&quad ! tilde {B}_{h} sin dfrac {tilde {phi }}{2} !&quad ! -tilde {B}_{h} cos dfrac {tilde {phi }}{2} !&quad ! 0 end{bmatrix}!. end{align*} None of the above-mentioned remarks affect the calculations and results presented in [1].