Citation: Praena, J.Á.; Carballar, A. Chirped Integrated Bragg Grating Design. Photonics 2024, 11, 476. https://doi.org/10.3390/ photonics11050476 Received: 11 April 2024 Revised: 13 May 2024 Accepted: 16 May 2024 Published: 19 May 2024 Copyright: © 2024 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/). photonics hv Article Chirped Integrated Bragg Grating Design JoséÁngel Praena 1, * and Alejandro Carballar 2 1 Ingeniería de Sistemas y Automática, Escuela Politécnica Superior, Universidad Pablo de Olavide, Ctra. Utrera km 1, 41013 Sevilla, Spain 2 Departamento de Ingeniería Electrónica, E.T.S. de Ingeniería, Universidad de Sevilla, C/Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain; carballar@us.es * Correspondence: japrarod@upo.es Abstract: We analyze the two classic methods for chirped Integrated Bragg Gratings (IBGs) in Silicon- on-Insulator technology using the transfer matrix method based on the effective refractive index (n eff ) technique, which translates the geometry of an IBG into a matrix of n eff depending on the wavelength. We also implement a procedure that allows engineering of the chirped IBG parameters, given a required bandwidth (BW) and group delay (GD). Finally, a complementary method for designing chirped IBG is proposed, showing a significant improvement in the bandwidth of the device or a moderation in the variation of the geometrical parameters of the grating. Keywords: Integrated Bragg Grating; silicon photonics; chirp function; group delay; effective refractive index 1. Introduction Integrated Bragg Gratings (IBGs) in Silicon-on-Insulator (SOI) technology are optical structures that implement a periodic modulation of the effective refractive index through a defined variation in the geometry of an integrated silicon waveguide [1]. They have the important advantage of being compatible with CMOS (complementary metal-oxide- semiconductor) technology manufacturing [1,2], which allows photonic and electronic circuits to be integrated into the same chip. They are very frequency-selective and have a high extinction ratio, as well as low insertion loss. IBGs are used in many photonic devices, such as sensors [3], communications [4], photonic signal processing [5], microwave photonic signal processing [6], active photonic devices, slow-light EOM (electro-optic modulators) [7,8] and dispersion control applications [9]. The latter have been especially important in recent years due to the advancement in ultrafast lasers. To achieve this purpose, apodized chirped Bragg Gratings are being developed [10]. In relation to Fiber Bragg Gratings (FBGs), chirped gratings have been widely used to address two traditional challenges: the need to broaden the bandwidth coupled by a uniform grating, and the demand for a passive device that exhibits a linear group delay as a function of wavelength that allows for chromatic dispersion compensation [11]. These two issues have been translated into IBG technology, where the design of integrated chirped gratings must take into account the wavelength dependence of the effective refractive index, as well as its geometric dependence. Compared to FBGs, these dependances constitute a setback in the design method for chirped IBGs that can be leveraged to enable new ways of designing chirped IBGs. Due to this double dependance, which can be formulated as n eff (λ,W), the traditional Coupled Mode Theory (CMT), which leaves out the physical structure of the grating and hence its variation with the effective refractive index, should not be used to analyze IBGs, as any tiny variation in the geometry has to be considered. In this work, we propose an approach for the design of chirped IBGs based on the transfer matrix method (TMM) of electromagnetic waves in multilayer media, characterized by their effective refractive index (ERI) [12–14]. On the basis of this ERI–TMM approach, Photonics 2024, 11, 476. https://doi.org/10.3390/photonics11050476 https://www.mdpi.com/journal/photonics