Rapid tunneling transit times for electrons and photons through periodic fragments

Abstract

The complex band-structure method is used to examine tunneling transit times and velocities through periodic fragments. The analysis applies equally well to both electron tunneling through chainlike molecules and evanescent light passing through periodic dielectric photonic crystals. Analytic properties of the complex band structure produce branch points where the speed of (nonrelativistic Schrodinger) electron tunneling is unbounded, and evanescent light travels faster than c. The analysis is general, can be applied to very complex periodic systems, and produces a simple result for the tunneling transit time τ for both electrons and photons. In the limit of a very thick periodic tunneling region of thickness L, the transit time for electrons is τ =L/ν* g , where v* g is the generalized complex band-structure transmission group velocity, 1/v* g = ∞‖∂β/∂E‖, where β is the imaginary part of the complex wave vector. The derivative ∂β/∂E vanishes at the branch point of the complex band structure producing unbounded (or ultrafast) speeds. Analogous results are also found for photons.