  Citation: Meudt, M.; Henkel, A.; Buchmüller, M.; Görrn, P. A Theoretical Description of Node-Aligned Resonant Waveguide Gratings. Optics 2022, 3, 60–69. https://doi.org/10.3390/ opt3010008 Academic Editor: Ángel S. Sanz Received: 27 January 2022 Accepted: 3 March 2022 Published: 4 March 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article A Theoretical Description of Node-Aligned Resonant Waveguide Gratings Maik Meudt 1,2 , Andreas Henkel 1,2 , Maximilian Buchmüller 1,2 and Patrick Görrn 1,2, * 1 Chair of Large Area Optoelectronics, University of Wuppertal, Rainer-Gruenter-Str. 21, 42119 Wuppertal, Germany; mmeudt@uni-wuppertal.de (M.M.); henkel@uni-wuppertal.de (A.H.); buchmueller@uni-wuppertal.de (M.B.) 2 Wuppertal Center for Smart Materials & Systems, University of Wuppertal, Rainer-Gruenter-Str. 21, 42119 Wuppertal, Germany * Correspondence: goerrn@uni-wuppertal.de; Tel.: +49-202-439-1424 Abstract: Waveguide gratings are used for applications such as guided-mode resonance filters and fiber-to-chip couplers. A waveguide grating typically consists of a stack of a single-mode slab waveguide and a grating. The filling factor of the grating with respect to the mode intensity profile can be altered via changing the waveguide’s refractive index. As a result, the propagation length of the mode is slightly sensitive to refractive index changes. Here, we theoretically investigate whether this sensitivity can be increased by using alternative waveguide grating geometries. Using rigorous coupled-wave analysis (RCWA), the filling factors of the modes of waveguide gratings supporting more than one mode are simulated. It is observed that both long propagation lengths and large sensitivities with respect to refractive index changes can be achieved by using the intensity nodes of higher-order modes. Keywords: waveguide gratings; guided modes; sensitivity; propagation length; symmetry 1. Introduction Passive and low-loss planar optical waveguides can transport light over large areas [1–4]. When they are combined with optical elements such as diffraction gratings (termed waveg- uide gratings), they can be used for applications such as optical filters [5–10] and sen- sors [11–17] via exploiting guided mode resonances. Commonly, only the spectral positions of resonance are sensitive to refractive index changes, while the corresponding propagation length L prop remains almost constant. This circumstance indicates the necessity of spectrom- eters for such devices based on waveguide gratings. With a large sensitivity of L prop , small refractive index changes could be directly translated into a spatial variation in the outcoupled guided light. This can be detected by an array of simple broadband photodetectors. Beyond passive refractive index sensors, a large sensitivity would allow for electrical control of L prop , which opens up new possibilities such as active beam deflectors or mod- ulators. To meet the requirement of long propagation lengths, it is desirable to use fast and loss-free effects such as the electro-optic Pockels or Kerr effect. However, those effects enable small refractive index tuning in the order of Δn ≈ 10 −4 ... 10 −3 [18–20] only, which requires large sensitivities of L prop . Thus, it is of no surprise that reports about electrooptic detuning of waveguide gratings can only rarely be found in the literature to date and rather show the control of the spectral positions of resonances than the control of the propagation length [21,22]. In fact, there is a way to overcome these limits. It has been shown that intensity nodes of TE modes (s-polarized modes with a transversal electric field node) can be used to maxi- mize the propagation length [23–25] by placing a lossy, diffractive, or scattering structure at the node position. This way, spectrally narrow resonances can also be obtained [26]. Conceptually, it has been estimated that such node modes should provide high sensitivities, Optics 2022, 3, 60–69. https://doi.org/10.3390/opt3010008 https://www.mdpi.com/journal/optics