Husimi functions at dielectric interfaces: Inside-outside duality for   optical systems and beyond
  We introduce generalized Husimi functions at the interfaces of dielectric systems. Four different functions can be defined, corresponding to the incident and departing wave on both sides of the interface. These functions allow to identify mechanisms of wave confinement and escape directions in optical microresonators, and give insight into the structure of resonance wave functions. Off resonance, where systematic interference can be neglected, the Husimi functions are related by Snell's law and Fresnel's coefficients. 
Martina Hentschel, Henning Schomerus, Roman Schubert