The Kramers-Kronig relations for light moving backwards in time
  The recent discovery of light moving backwards in time, when it propagates in a suitable dispersive medium, obliges us to reexamine the Kramers-Kronig relations. In their usual form, they are dealing with usual light (moving forward in time), and they are a consequence of causality. In a similar fashion, we derive the appropriate form of these relations for light moving backwards in time, starting, instead of causality, from a principle of anti-causality, appropriate to such a light. 
Evangelos Chaliasos