Abstract
An epsilon-near-zero graded-index converging lens with planar faces is proposed and analyzed. Each perfectly-electric conducting (PEC) waveguide comprising the lens operates slightly above its cut-off frequency and has the same length but different cross-sectional dimensions. This allows controlling individually the propagation constant and the normalized characteristic impedance of each waveguide for the desired phase front at the lens output while Fresnel reflection losses are minimized. A complete theoretical analysis based on the waveguide theory and Fermat's principle is provided. This is complemented with numerical simulation results of two-dimensional and three-dimensional lenses, made of PEC and aluminum, respectively, and working in the terahertz regime, which show good agreement with the analytical work.
Highlights
The challenge of engineering and controlling the electromagnetic properties of materials is on the forefront of basic materials science and engineering
At the plasma frequency of a Drude medium the real part of the permittivity effectively goes to zero and at the resonance of a Lorentzian medium, the permittivity may become very large. This behavior is usually found at mid infrared frequencies for polar dielectrics and lightly-doped semiconductors [9], and in the visible and ultraviolet for noble metals [10]
As we will discuss below, here we use one dimension of the cross section of the hollow waveguide made of perfectly-electric conducting (PEC) walls to adapt the phase delay and the other one to effectively match our lens to the incoming plane-wave propagating in free-space
Summary
The challenge of engineering and controlling the electromagnetic properties of materials is on the forefront of basic materials science and engineering. The dimensions of each waveguide is designed independently in order to have the desired propagation constant and phase delay inside each waveguide for achieving a flat convergent lens while each waveguide remains approximately impedance matched to free-space. With this approach Fresnel reflection is significantly reduced. As we will discuss below, here we use one dimension of the cross section of the hollow waveguide made of PEC walls to adapt the phase delay and the other one to effectively match our lens to the incoming plane-wave propagating in free-space
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