Talbot Effect Between Bend-Localised Modes in Multicore Fibre Array

When coreless photonic crystal fibre is made chiral by drawing from a spinning preform, localised eigenmodes are observed to form, despite the absence of any structural core [1]. In a recent paper an efficient and accurate analytical method, based on a modified coupled-mode theory, was used to show that these modes are exponentially localised [2]. Here we report that a family of similarly localized modes forms in a linear array of coupled cores when the fibre containing them is bent around an axis normal to the plane containing the cores (Fig. 1(a)). Under these circumstances the dephasing rate between adjacent cores is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta\vartheta=\beta_{0}\delta\rho/R$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta_{0}$</tex> is the propagation constant in an isolated core, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\delta\rho$</tex> is the inter-core spacing, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R &gt; &gt; N\delta\rho$</tex> is the radius of curvature of the bend and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> the total number of cores (Fig. 1(a)). The coupled mode equations for the bent array then take the form: