Graded-index antiresonant reflecting optical waveguides
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Graded‑index antiresonant reflecting optical waveguides Jacek M. Kubica1 Received: 7 June 2020 / Accepted: 8 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper is devoted to the theoretical analysis of planar antiresonant reflecting optical waveguides (ARROW’s) with graded-index core layers. It presents results of numerical calculations involving relevant iteration procedure aimed at proper design of antiresonant claddings and illustrates modal properties of graded-index ARROWs for various waveguide parameters. Keywords Optical waveguides · Antiresonant reflecting optical waveguides · Planar waveguides · Guided waves · Leaky waves
1 Introduction Antiresonant reflecting optical waveguides (ARROW’s) exhibit a large number of interesting properties that found numerous applications in recent years. In particular, they can form a basis of various sensing devices such as biosensors (Haji et al. 2012; Hiraoui et al. 2012), integrated refractometers for chemical applications (Bernini et al. 2002, 2003) or fluorescent nanoparticle detectors (Parks et al. 2016). On the other hand, sensitivity mechanism of ARROW geometry to refractive index changes has been analyzed (Kubica 1995, 2002). However, all theoretical research devoted to the planar ARROW configuration was restricted to the waveguides with homogeneous cores separated from the substrate by several antiresonant cladding layers. In that case, the antiresonant parameters of the cladding resonators are given by simple analytical formulas (Duguay et al. 1986). The aim of this paper is to provide for the first time an analysis of planar ARROW waveguides with inhomogeneous cores, where analytical formulas cannot be applied. The calculations are based on the relevant iteration procedure that involves multiple numerical solution of the complex dispersion equation (Kubica 1994). The numerical analysis is focused on the design issues corresponding to the graded index core of different profile parameters. It provides optimization clues for low-loss operation and high refractive index sensitivity.
* Jacek M. Kubica [email protected]; [email protected] 1
Industrial Lab Consulting, Bełdan 1/33, 02‑695 Warsaw, Poland
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2 Design and calculation method The typical ARROW geometry is illustrated in Fig. 1. The core layer of thickness d1 and refractive index n1 (x) is separated from the high-index substrate by the interference cladding system formed by the high-index cladding layer ( d2 , n2 ) and the second cladding layer ( d3 , n3 ). The cladding layers are designed to form antiresonant Fabry–Perot resonators which reduce the radiation loss into the substrate from the leaky ARROW mode and lead to specific modal properties of the structure. Antiresonant reflecting optical waveguides with homogeneous cores can be simply designed by choosing cladding layer thicknesses di to meet the antiresonant conditions (Duguay et al. 1986):
( ( )2 ( )2 )−1∕2 n1 𝜆 𝜆 (2N + 1), 1− + di =
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