Further generalization of Fermat’ s principle

摘要

From Maxwell’s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introduction of time-averaged energy flow density rays and the definition of new generalized refractive index n_Gl, Fermat’s principle of geometric optics is further generalized and its application conditions are discussed. The generalized Fermat’s principle can be used to describe stable transmission of light in a medium with variable refractive index. The necessary and sufficient conditions of a nondivergent and nonfocusing light beam are derived from this Fermat’s principle.