Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes

Following our recent theoretical development of the concepts of nanoinductors, nanocapacitors, and nanoresistors at optical frequencies and the possibility of synthesizing more complex nanoscale circuits, we theoretically investigate in detail the problem of optical nanotransmission lines (NTLs) that can be envisioned by properly joining together arrays of these basic nanoscale circuit elements. We show how, in the limit in which these basic circuit elements are closely packed together, NTLs can be regarded as stacks of plasmonic and nonplasmonic planar slabs, which may be designed to effectively exhibit the properties of planar metamaterials with forward (right-handed) or backward (left-handed) operation. With the proper design, negative refraction and left-handed propagation are shown to be possible in these planar plasmonic guided-wave structures, providing possibilities for subwavelength focusing and imaging in planar optics and laterally confined waveguiding at IR and visible frequencies. The effective material parameters for such NTLs are derived, and the connection and analogy between these optical NTLs and the double-negative and double-positive metamaterials are also explored. Physical insights and justification for the results are also presented.