Hamiltonian analysis of beams in an optical slab guide

The formal analogy between Hamiltonian classical mechanics and quantum mechanics on the one hand and geometrical optics and physical optics on the other hand is systematically presented. When the time is replaced by the axial coordinate of a cylindrically uniform optical system and Hamilton’s principle replaced by Fermat’s principle, classical particle trajectories correspond to rays and quantum-mechanical wave functions to physical-optics fields. The operator formalism of quantum mechanics then provides elegant solutions for problems associated with propagation of beams in a gradient-index multimode optical slab guide.