Abstract
We discuss here under which conditions a periodic line with a twist-symmetric shape can be replaced by an equivalent non-twist symmetric structure having the same dispersive behavior. To this aim, we explain the effect of twist symmetry in terms of coupling among adjacent cells through higher-order waveguide modes. We use several waveguide modes to accurately derive the dispersion diagram of a line through a multimodal transmission matrix. With this method, we can calculate both the phase and attenuation constants of Bloch modes, both in shielded and open structures. In addition, we use the higher symmetry of these structures to further reduce the computational cost by restricting the analysis to a subunit cell of the structure instead of the entire unit cell. We confirm the validity of our analysis by comparing our results with those of a commercial software.
Highlights
A higher symmetric periodic line is characterized by its invariance under a geometrical transformation other than a translation
A periodic structure with an N-fold twist symmetry is invariant under the twist operator S N,pẑ : S N,pẑ : (ρ, φ, z) →
In order to prove this, we present a rigorous multimodal Bloch analysis and we apply it to different twisted lines
Summary
A higher symmetric periodic line is characterized by its invariance under a geometrical transformation other than a translation. Recent studies on higher-symmetric structures have revealed interesting characteristics such as a reduced dispersion and wider and stronger stop bands [5,6,7,8,9,10,11,12] These characteristics have led to numerous applications in different areas such as wideband lens antennas [13], cost-effective gap-waveguide technology [14,15], leaky-wave antennas [16], and leakage reduction in waveguide transitions [17]. We formulate, for the first time, the eigenvalue problem based on a twist symmetry operator [4] by means of a transmission-matrix approach This restricts the problem to a subregion of a unit cell and, reduces the computational cost of the analysis. It helps to explain how the higher-order modes affect the reducibility of the structure
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