  We theoretically and numerically study the design of optical 'lumped'
nanofiltering devices in the framework of our recently proposed paradigm for
optical nanocircuits. In particular, we present the design of basic filtering
elements, such as low-pass, band-pass, stop-band and high-pass 'lumped'
nanofilters, for use in optical nanocircuits together with more complex
designs, such as multi-zero or multi-pole nanofilters, to work at THz, infrared
and optical frequencies. Following the nanocircuit theory, we show how it is
possible to design such complex frequency responses by simple rules, similar to
RF circuit design, and we compare the frequency response of these optical
nanofilters with classic filters in RF circuits. These results may provide a
theoretical foundation for fabricating nanofilters in optical lumped
nanocircuit devices.
