Circular-area-equivalence approach for determining propagation constants of a single-mode polygonal nanowire

Abstract

One-dimensional crystalline nanowire structures have been widely used as nano-waveguides in nanophotonics. The propagation constant of a certain waveguiding mode in the nanowire is essential to its optical waveguiding properties. To estimate the propagation constant, commonly the cross section of such a nanowire is treated as a circle with a diameter equal to the longest diagonal of the cross section. However, experimentally, crystalline nanowires (e.g., semiconductor nanowires) are usually polygonal in cross section. The diagonal-circle approximation (DCA) is not accurate enough, especially for polygonal cross sections with fewer sides such as triangles, squares, and hexagons. Here, we propose a circular-area-equivalence (CAE) approach to accurately determine the propagation constants of single-mode polygonal nanowires, while maintaining its convenience and simplicity in practical use. Instead of the diagonal circle, here we use a circle with an area equal to that of a real polygonal cross section. Our results show that, compared with the DCA, the CAE approach can offer much higher accuracy for determining propagation constants of single-mode polygonal nanowires, e.g., a deviation of 20.0% of DCA versus 1.9% CAE for normalized effective index (a direct measure of the propagation constant) in a half-wavelength-diameter triangle nanowire. The effectiveness of the CAE approach for nanowires with material dispersion and supporting substrates is also analyzed and verified.