Design of filters in a one-dimensional tight-binding system - art. no. 056606

We show how to design one-dimensional systems that in the transmission thro ugh a finite potential barrier, in a predetermined way, discriminate betwee n monochromatic waves depending on their wave number. These systems, descri bed by the on-site tight-binding equation, act as filters of different type s, with adjustable pass and stop bands. The use of these filters for discri mination of linear wave packets depending on their different velocities is illustrated, and we also comment on the influence of an added nonlinearity.