Optical waveguides (WGs), in the traditional sense, are translucent geometries with a refractive index difference that directs optical beams via total internal reflection [1]. The most well-known illustration is optical fiber, which transmits light signals throughout the world with only a few tenths of a decibel per kilometer loss. Integrated photonic systems, in which optical WGs connect lasers, detectors, power splitters, filters, and modulators, are now the subject of significant study. From communications and information processing to monitoring and medicinal applications, these devices offer a wide range of uses [2]. Planar lightwave circuits are essential for the advancement of photonics current tech. They are two-dimensional photonic devices with numerous optical functionalities on a single chip. Photolithography is a technology for fabricating planar lightwave circuits that has evolved through time in the microelectronics sector [3]. In a cleanroom setting, ultraviolet (UV) radiation, selective etching (chemical or plasma), and doping (ion exchange or diffusion) are all part of the process. Photolithography, despite its benefits in reproducibility and parallel processing, is a time-consuming, stiff multistep operation that can often only generate 2D-optical WG circuits.

A Bragg grating (BG) structure is a regular WG with periodic refractive index (RI) variations running across it ^[4][5][4,5]. These aberrations create a one-dimensional photonic bandgap that reflects only a restricted spectrum of any broadband signal traveling through the WG. BG WGs are conceptually comparable to the well-known fiber Bragg gratings (FBGs) [6]. FBGs, which function as narrowband mirrors integrated into optical fibers and are widespread for wavelength division multiplexing (WDM), tunable filtering, and—when chirped—dispersion compensation in optical communications systems, have been made with lasers for nearly 30 years. Furthermore, because their resonant (reflected) wavelength is very sensitive to external factors such as temperature and strain, these devices are commonly utilized in sensing applications ^[4][7][8][9][4,7,8,9]. Ken Hill discovered FBG in 1978 at the Communication Research Centre in Canada ^[6][10][6,10]. Because of its excellent characteristics, such as its low cost, compact size, real-time response, high precision, high sensitivity, and electromagnetic interference, grating structures have gotten a lot of interest in the field of optical sensing since their invention. Using grating-based devices, it is possible to sense a variety of characteristics such as temperature, pressure, tension, and RI. High-temperature sensors, health and biological devices, structural engineering, industries, biochemical applications, radioactive environments, aerospace, marine, and civil engineering, and many more disciplines use FBGs today [11]. Because most glass materials have an n_eff close to 1.5, Bragg response in the telecom band at 1550 nm requires a short grating period of about ~500 nm [12]. By holographic or phase mask interference, or by point-by-point writing, UV and ultrafast lasers may easily build precisely patterned BGs in optical fibers.

The introduction of arbitrarily shaped optical WGs, many of which are also arbitrarily inhomogeneous, dissipative, anisotropic, and/or nonlinear, has been a significant development in guided-wave optics, including fiber optics and integrated optics. To successfully design, optimize, and realize optical WGs, computational tools for modeling and simulation are crucial. Most of these WG arbitrariness instances do not lend themselves to analytical solutions. Numerous numerical approaches have been developed for this aim, such as the finite difference time domain (FDTD), finite element method (FEM), transfer matrix method (TMM), and coupled-mode theory (CMT). Particularly for the most comprehensive optical WG issue, the finite element method (FEM) is a strong and effective tool. Numerous optical waveguide issues would not be able to be solved without it given how extensively it is used in both industry and research. FEM has been used in the design and analysis of several optical components ^[12][13][14][12,13,14].

2. Fundamentals of Si-Based BG Structures

BGs have developed into key optical devices and have been widely employed in numerous systems since the discovery of Bragg’s law in 1913 ^[15][26]. The desire to investigate on-chip integrated gratings derives from the swift expansion of Si photonics, which is enabling revolutionary applications through small circuits made using CMOS-compatible manufacturing technologies ^{[16][17][18][19][20]}[27,28,29,30,31]. Gratings made of Si ^[21][22][32,33], SiN ^[23][34], and InGaAs/AlInAs ^[24][35] have been proven in a range of shapes, comprising variations and pillars on the strip and ridge formations, with the necessity to adjust attributes for each application driving the variety of techniques ^{[25][26][27][28][29]}[36,37,38,39,40]. The WG core may be reduced to a submicron cross-section while still sustaining single-mode propagation at 1.3–1.5 μm telecommunications wavelengths thanks to the extremely high refractive index difference between the silicon core (n = 3.5) and silica cladding (1.45) [13]. The smallest bending radius can be brought down to the micron range owing to such intense light confinement, providing a path to the realization of very dense photonic integrated circuits on a single silicon chip. Due to the increased contact of the WG mode with the sidewall surface roughness, such high light confinement in submicron SOI strip WGs also produces noticeably increased propagation losses. Surface roughness is the cause of large propagation losses, which might make it impossible to design compact integrated circuits, according to extensive experimental research. High bending losses, usually in the range of 1 dB per 90-degree bend, are also caused by the same surface roughness ^[30][41]. Designing single-mode distributed Bragg reflector (DBR) and distributed feedback (DFB) lasers, for instance, requires the capacity to spatially modulate gratings and apodize their response ^[20][31]. It has been demonstrated that a λ/4 phase shift in DFB lasers increases the mode stability at the center wavelength ^[31][42]. On the AIM Photonics 300 mm Si photonics foundry line, phase-shifted SiN BGs were produced utilizing 193 nm deep ultraviolet lithography (DUVL) ^[32][43].

3. Recent Advances in Si-Based BG Structures

Flexible spectrum tailoring may be accomplished with BGs. It has been demonstrated that by modulating the coupling coefficient (grating strength) along the grating, a filter ^[33][34][45,46] with any spectral response can be built ^[35][47]. This approach, also known as apodization, has allowed for the creation of adaptable spectrum filters for applications such as WDM ^[36][37][48,49], optical signal processing ^[38][50], optical communications ^[39][51], and astrophotonics ^[40][52], to mention a few. Bragg filters have traditionally been realized in integrated photonic systems using sidewall corrugated gratings, which modulate the WG width. This approach is constrained by the manufacturing process’s minimum corrugation size, which dictates the smallest disruption that can be accomplished, as well as the minimum coupling coefficient and filter bandwidth (BW). Because of the strong RI contrast, this limitation is extremely crucial in the SOI platform, where the filter performance is very responsive to tiny fluctuations in the corrugation width. In a 220 nm-thick SOI platform, for example, sub-nanometer BWs need WG sidewall corrugations of 10 nm or less, which are difficult to produce ^[25][36]. New modulation approaches, such as misaligned sidewall corrugations, grating pitch modulation ^[41][53], and subwavelength-tailored sidewall gratings [12], have been developed to alleviate this restriction. These approaches have been used to demonstrate Photonic Hilbert transformers ^[42][43][54,55] and multi-channel filters ^[39][44][51,56]. Nevertheless, corrugation widths that are difficult to produce in a consistent manner (less than 20 nm) are usually needed ^[39][44][51,56]. Cladding-modulated BGs, or structures with periodic fluctuation physically segregated from the WG core, are an intriguing option for implementing spectrum filters in silicon WGs. On lateral Si strips parallel to the WG, periodic arrays of lateral cylinders ^[45][57] and sidewall corrugations ^[46][58] have been suggested. By carefully arranging the grating in close vicinity to the WG core, these geometries enable the creation of weak BGs with limited spectral characteristics. Concurrently, designs with more relaxed minimum feature sizes can be created. Based on cladding-modulated gratings, Gaussian-apodized BGs ^[47][59] and multi-band filters ^[48][60] have been realized. In Si WGs with laterally connected Bragg loading segments, a unique geometry for designing complicated Bragg filters with an adjustable spectrum response is suggested ^[49][61]. The WG core is built with a delocalized mode field, which minimizes the sensitivity to manufacturing faults and increases the quality of synthesized coupling coefficients and the spectral shape control. The researcheuthors offer an effective design technique for cladding-modulated BGs that uses layer-peeling and layer-adding algorithms to easily synthesize an arbitrary target spectrum. By building and experimentally proving a complex spectrum filter on an SOI platform with 20 non-uniformly spaced spectral notches with a 3 dB linewidth as narrow as 210 pm, the suggested filter idea and design approach are proven ^[49][61]. There is a demonstration of a high-sensitivity SOI WG-based-BG sensor ^[50][62]. The temperature measuring range of the BG sensor was wide, and the accuracy was great. It could monitor temperature changes in the human body by continually measuring temperature variations in the range of 35–42 °C. Biomedical sensing, forensic examination, microbiological research, drug screening, environmental monitoring, chemical synthesis, and other areas might all benefit from the sensor. Unlike FBG, which required photosensitive materials in the fiber to be exposed to UV light, WG BG only required etching periodic geometric shapes on the WG’s surface or side to produce a periodic effective refractive index (n_eff) distribution of the grating, which has the benefit of a small volume and seamless integration.