Superluminal photonic tunneling and quantum electronics

Abstract

Recent experimental studies with microwave and laser pulses have revealed superluminal (faster-than-light) group, signal and energy velocities for the tunneling of electromagnetic wave packets in undersized waveguides and other photonic barriers. First we report on the historic background of tunneling and the problems of the interpretation of electronic tunneling data. The mathematical analogy of the classical tunneling, i.e. the propagation of evanescent modes, described by the Helmholtz equation, and the quantum mechanical tunneling, described by the Schro¨dinger equation, is introduced. In the next sections the experimental data on the tunneling time of electromagnetic wave packets and signals is presented. The interpretation of the experimental observations, particularly the production of superluminal tunneling velocity and its implication for the quantum mechanical electronic tunneling are discussed in the following sections. An introduction to the various theoretical approaches is included. Remarks on superluminal tunneling and on causality conclude the paper.