Arnold F. Mckinley

Theory of the circular closed loop antenna in the terahertz, infrared, and optical regions

Modern antenna theory forms the bulwark of our knowledge of how radiation and metallic structures interact in the radio frequency (RF) and microwave (MW) regions. The theory has not yet penetrated the terahertz, infrared, and optical regions to the same degree. In this paper, we provide a rigorous analysis of closed circular loop antennas from first principles. Using antenna theory, we tie together their long wavelength behavior with their behavior at short wavelengths through the visible region. We provide analytic forms for the input impedance, current, quality factor, radiation resistance, ohmic loss, and radiation efficiency. We provide an exact circuit model for the closed loop in the RF and MW regions, and extend it through the optical region. We also provide an implicit analytic form for the determination of all modal resonances, allowing prediction of the resonance saturation wavelength for loops. Through simulations, we find that this behavior extends to hexagonal and square loops. All results are applicable to loop circumferences as short as 350 nm. Finally, we provide a precise analytic model of the index of refraction, as a tool in these computations, which works equally well for metals and semi-conductors.

The analytical basis for the resonances and anti-resonances of loop antennas and meta-material ring resonators

Interest in the electromagnetic properties of loop structures has surged with the recent appearance of split-ring resonator meta-materials (SRRs) and nano-antennas. Understanding the resonances, anti-resonances, and harmonics of these loops is key to understanding their response to a wide range of excitation wavelengths. We present the classical analytical solution for the input impedance of a loop structure with circumference on the order of the wavelength, and we show how to identify these resonances from the function. We transform the classical solution into a new RLC formulation and show that each natural mode of the loop can be represented as a series resonant circuit, such that the full response function can be resolved by placing all of these circuits in parallel. We show how this formulation applies to SRRs.

Designing Nano-loop antenna arrays for light-trapping in solar cells

Many types of wavelength-scale optical structures have been investigated for light trapping in solar cells. Nano-loops have not yet been studied on solar cells, even though they play a central role in arrays for meta-materials in the microwave (MW) region. In this paper, we use standard antenna theory to provide a rigorous analysis of closed circular metallic loops as antennas in the infrared (IR) and optical region (OR), the regions of solar activity. We provide an exact impedance model for closed loops and an approximate RLC model from which we determine key design factors (resonances, quality factors and radiation efficiencies). Using numerical simulations, we find that these results extend to hexagons and to squares. The principle differences between loops in the radio frequency region (RF) and in the IR/OR are due to dispersion in the loop material. This causes a scaling such that resonances eventually reach saturation; that is, closed loops made of the noble metals will not have their first fundamental resonance at frequencies above the IR. Closed loops, though, do have strong higher harmonic resonances with quality factors on the order of 2 to 5, and these can appear in the OR depending on the loop circumference. Such higher order resonances may be promising for light trapping in solar cells.