Resonant tunneling of ultrashort electro-magnetic pulses in gradient metamaterials: paradoxes and prospects

摘要

This report is devoted to new effects of wave-pulse tunneling through inhomogeneous media. The concept of tunneling often refers to quantum effects of particle penetration through potential barriers with the heights exceeding the energy of the particles themselves. It is this problem that was first solved by G A Gamow in 1928 [1] when E Rutherford asked him to explain the paradox of the alpha decay of atomic nuclei, in which the energy of an alpha particle leaving a nucleus proved to be lower than the height of a potential barrier surrounding the nucleus. By using the formal analogy between the classical wave equation and the Schroè dinger equation, Gamow managed to show that a partial penetra- tion of de Broglie waves describing an alpha particle through the barrier corresponds to the frustrated total internal reflection effect known in optics. Such a penetration mechan- ism, which is impossible in classical mechanics, was called `tunneling'. By connecting this analogy with the uncertainty in the relation between the momentum and coordinate of a quantum particle, Gamow calculated the exponentially small but finite probability of particle tunneling through the barrier. This was probably the first application of quantum mechanics in nuclear physics, and became for many years an etalon for describing the tunneling of quantum objects in electronics and solid state physics.