In this study, we present a comprehensive analysis to examine the origin of circular polarization stop bands in a dielectric helix structure. We show that band gaps in a helix structure may result from Bragg resonance or non-Bragg mechanism. The two types of gaps exhibit distinct optical properties and display an opposite dependence with respect to structural periodicity. The interplay of gaps not only gives rise to various operation scenarios, but results in pronounced modifications to dispersion characteristics that lead to abnormal propagation properties of circularly polarized waves. Our findings reveal versatile behaviors of circularly polarized light interacted with a three-dimensional helix medium, which can be of great importance for the design and implementation of circular polarization-dependent devices and applications.

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