METHODOLOGICAL NOTES: Formulating Fermat's principle for light traveling in negative refraction materials

The formulation of Fermat's principle for electromagnetic waves traveling in materials with a negative refractive index is refined. It is shown that a formulation in terms of the minimum (or extremum) of wave travel time between two points is not correct in general. The correct formulation involves the extremum of the total optical length, with the optical length for the wave propagation through left-handed materials taken to be negative.