Resolving the wave-vector in negative refractive media: The sign of   $\sqrt{Z}$
  We address the general issue of resolving the wave-vector in complex electromagnetic media including negative refractive media. This requires us to make a physical choice for the sign of a square-root imposed merely by conditions of causality. By considering the analytic behaviour of the wave-vector in the complex plane, it is shown that there are a total of eight physically distinct cases in the four quadrants of two Riemann sheets. 
S. Anantha Ramakrishna and Olivier J.F. Martin