A new look at the modified Fermat’s principle: nonlinear optics through the prism of thermodynamics of light trajectories

The paper presents a new approach to the description of light paths in nonlinear optical media based on a modified Fermat's principle using concepts of thermodynamics. The traditional Fermat's principle, formulating the light path as an extremum of optical time, is extended to take into account nonlinear interactions and dissipative processes. The formalization of light paths through the minimization of a functional that takes into account not only the optical path length, but also the entropic and energy characteristics of the medium is proposed. The basic equations revealing the connection between nonlinear optics and thermodynamic laws are given, and the prospects of application of this approach in light control and development of new optical devices are discussed.