Figure 1:

Dispersion surfaces calculated for s-polarised radiation in the EMA for grating velocities close to the speed of light as indicated by $\delta$ . We choose $\alpha =0.05$ and the surfaces are singular when $\delta \approx \pm {\alpha }^2=\pm 0.0025$ . k _y lies along the abscissa and k _s , the component parallel to the direction of motion, along the ordinate. Both wave vectors are proportional to $\omega c_1^{-1}$ which we take to be unity. The top row approaches c ₁ from below and the bottom row from above.