Enhanced radiation amplitude by current-driven diffusing-growing mechanism of electromagnetic field near cutoff in a waveguide

Abstract

The cut-off condition in the waveguide is usually avoided in general waveguide circuits since the power transmission is significantly deteriorated by radiation reflection near the boundary. However it is possible to get an alternative, non-stationary mode of power transmission near cut-off: the diffusion-growing of the locally-energy-fed electromagnetic field. Such a temporally evolving mode can be modeled by a driven-diffusion equation of the electromagnetic field with complex diffusion coefficient. The diffusion equation of the field can be obtained starting from the general wave equation of the field, where the field is decomposed into a temporally slow amplitude and fast oscillating eikonal parts. Some interesting solutions of the diffusion equation indicate that the electromagnetic field grows as a function of time by sqrt(t), and the growing field slowly diffuses outward from the current source. As the diffusing-growing field comes across the tapered section of the waveguide, it can be effectively converted into a free space radiation with significantly higher amplitude than in the case of direct coupling between radiating antenna and free space or coupling via a waveguide but high above the cut-off. In terms of circuit, the enhanced radiation amplitude can be interpreted as an increased radiation impedance for the current source, or reduced one for a voltage-driven source, where in any case the power transmission from the radiation source to the free space increases.