Incidence angles for optimized ATR excitation of surface plasmons

By quantitatively examining dispersion curves of surface plasmons along Ag, Al, Ni, and Fe films, we find that the incidence angle theta(o) that produces a reflection minimum in a variety of ATR geometries is actually different from the angle theta(p) that corresponds to the phase-matching condition. The difference between theta(p) and theta(o) is most significant in the Otto and Kretschmann geometries using metal films with large damping loss, such as Ni or Fe. In addition, we determine the angle theta(m) at which maximum power density is coupled into the metal surface and show that in general the value of theta(m) is also different from both theta(o) and theta(p), the difference being again largest in the Otto or Kretschmann geometries. The differences between theta(o), theta(p), and theta(m) are much smaller, but still detectable, in long-range surface plasmon and extended-range surface plasmon geometries. In all cases, the preferred incidence angle depends on whether one needs to optimize either the plasmon field composition or the power density in the metal.