Design of generalised negative-refractive-index transmission lines for quad-band applications

A design procedure is presented for synthesising artificial transmission lines (metamaterial lines) that exhibit four alternating backward (left-handed) and forward (right-handed) bands. Specifically, analytic expressions are given that directly yield the loading lumped elements needed for synthesising a desired Bloch phase at four specified frequencies and at a specified Bloch impedance level. This procedure becomes useful for designing structures such as dual-band periodic leaky-wave antennas, dual-band/quad-band negative-index lenses, as well as quad-band microwave passive components and resonant antennas.