Propagation of Waves Through one-Dimensional Cantor-Like Fractal Media¹

We consider the resonant tunneling of electrons through one-dimensional Cantor-like fractal barriers. By means of a transfer matrix method, we present a general formalism to calculate the transmission and give some numerical examples. It is found that the transmission spectrum shows rich fractal patterns due to the self-similar geometry of the Cantor set. The scaling behaviour of the transmission spectrum is explored. By plotting the amplitudes of the wave functions, we also investigate the quasi-localization properties of the electrons.