On a Local Concept of Wave Velocities

The classical far field concept of wave velocities has its merits while exibiting intrinsic difficulties. A general local approach for the definition of velocities and especially phase velocities for waves avoiding these difficulties is proposed. It includes the classical definitions as particular cases and can be applied to waves of an arbitrary structure, and to arbitrary propagation media as well. Applications of the formalism are elucidated and some basic properties of the local concept defined here are discussed. 1 Some remarks on wave velocities Waves are conventionally described via propagating harmonic functions containing a periodic factor of the form e. The argument of these periodic functions , interpreted as the ”phase”, is usually identified with (t− x/c) via the free wave equation, where c is the ”phase velocity” [1]. This canonical approach originates from classical wave optics and analyzes ordinary light waves propagating in the ”far field”, where the wave is far away from the source. Such a light wave is a solution of a source free wave equation described by the periodic function mentioned above. The Ansatz earned his own merits in the context of several wave phenomena and in particular classical wave optics [2]. e-mail: [email protected] e-mail: [email protected]