Effect of curvature of the boundary on the modal dispersion of a single-mode dielectric waveguide of core cross-section bounded by involuted spirals

In this paper, we are presenting an analytical study of the effect of curvature of the spiral shape on the modal dispersion characteristics of the waveguide whose core cross-section is bounded by two involuted spirals of the form 1/r=ξθ, where ξ is a constant and represents the curvature of the spiral taken to design the waveguide into consideration. This study has been done under the weak guidance approximation. Analyzing the dispersion curves for different curvature we found that this waveguide supports only the single mode, and their cutoff value decreases as the the curvature of the spiral increases.