Racetrack Ring Resonator Integrated with Multimode Interferometer Structure Based on Low-Cost Silica–Titania Platform for Refractive Index Sensing Application

: In this work, a racetrack ring resonator (RTRR) integrated with a multimode interferometer (MMI) structure based on a silica–titania (SiO 2 :TiO 2 ) platform is projected for refractive index sensing application. The typical ring resonator structure requires a gap of ~100 nm to 200 nm between the bus waveguide (WG) and the ring structure which makes it challenging to fabricate a precise device. Thus, the device proposed in this paper can be considered a “gapless” ring resonator structure in which the coupling of light between the ring and bus WG can be achieved via an MMI coupler. A minor change in the refractive index in the vicinity of the MMI structure can trigger a shift in the resonance wavelength of the device. Thus, this simple and fascinating structure can be employed as a refractive index sensor. The device’s sensitivity is ~142.5 nm/RIU in the refractive index range of 1.33 to 1.36 with a ﬁgure of merit (FOM) of 78.3. This simple device structure can potentially be fabricated via a low-cost and highly efﬁcient sol–gel process and dip-coating method combined with the nanoimprint lithography (NIL) method.


Introduction
Multi-mode interference (MMI) structure is based on the 'Talbot effect,' discovered in 1886 by Henry Fox Talbot [1]. It involves self-imaging of injected optical fields in multi-mode WGs, aiding the expansion of compact and efficient photonic devices and components. The fundamental building block of an MMI device is a multimode waveguide (WG) capable of supporting several modes of light propagation. When light travels through this WG, the different guided modes interfere with each other. This interference phenomenon leads to the reconstitution of the input optical field in one or more images at regular intervals along the direction of propagation, depending on the length and width of the WG. This remarkable effect is commonly described as the "self-imaging principle" [2].
Since its initiation in 1975, MMI couplers have seen an instant development [3]. They are generally used in various Planar Lightwave Circuit (PLC) applications, including power splitters, optical switches, and wavelength division multiplexers/demultiplexers. MMI couplers based on different materials, such as LiNBO 3 [4], SOI [5], InP [6], polymer [7], silica-on-silicon (SOS) [8], etc., have been reported. The versatility and efficiency of MMI couplers make them a crucial component in modern integrated photonics devices. The self-imaging principle, based on high-index-contrast WGs, is used to develop MMI devices typically accomplished with InGaAsP/InP [9] and GaAs/AlGaAs [10], but researchers have reported work on low-index-contrast optical WG MMI devices, particularly those based on silica-on-silicon (SOS) WGs [11,12].
Over the past twenty years, there has been a substantial transformation in the field of optical sensors, predominantly driven by advancements in optical device manufacturing and the widespread adoption of various sensing applications [13][14][15][16][17]. This period has seen a revolution, leading to incredible progress in both the development and utilization of photonic sensors based on resonant WG gratings [18], surface plasmon resonance [19][20][21], and guided-mode resonance [22,23]. Researchers have been actively exploring the applications of MMI structures in WG sensor technology [24,25]. These studies have focused on inspecting the potential uses and benefits of MMI devices for sensing purposes. A team of researchers presented a novel approach to microring resonators (MRR) using 4 × 4 MMI couplers for highly sensitive multichannel chemical and biological sensing [26]. The compact design exhibited superior sensitivity compared to existing structures. They optimized and demonstrated the sensor using silicon WGs through numerical simulations and the transfer matrix method (TMM). The sensor successfully detected glucose and ethanol concentrations simultaneously, achieving high sensitivity (9000 nm/RIU) and low detection limits (2 × 10 −4 for glucose and 1.3 × 10 −5 for ethanol) [26].
In a different study [27], researchers fabricated an MRR incorporating a multimode interference coupler on a polymer platform using a UV-based soft nanoimprint technique. The fabrication process involved the use of a special type of fluorinated polymer known as perfluoropolyether (PFPE) for creating a flexible soft mold. Through careful optimization of the proportions between Ormocore and the thinner maT materials, they successfully produced the MRR with minimal residual layer. The proposed device demonstrated a spectrum with an FSR and ER of~335 pm and~11.6 dB, respectively, achieving a high Q factor of 2.3 × 10 4 [27]. In [28], the researchers put forward and designed an innovative S-bend resonator as a RI sensor, utilizing a multi-mode WG. The S-bend resonator was composed of a ridge WG, an MMI coupler, and multiple bend structures. The researchers achieved inspiring results, with a Q-factor of 2.3 × 10 3 and a sensitivity of~52 nm/RIU [28].
Ring resonators (RRs) are integrated photonic devices employed to sense changes in the environment, such as variations in refractive index, temperature, pressure, or biological interactions [29,30]. They are established on the principle of optical resonance and are commonly used in a variety of applications due to their numerous advantages and magnitudes. RR sensors offer high sensitivity to small changes in the surrounding environment. When the refractive index of the material around the ring changes, it triggers a shift in the resonant wavelength, which can be accurately determined. This sensitivity is particularly helpful in applications like chemical and biological sensing [13]. In [31], we exhibited a standard RR structure based on the SiO 2 :TiO 2 platform for refractive index sensing applications. The gap between the bus WG and the ring is around 100 nm which is quite challenging to attain by employing a standard lithography process.
In this work, we proposed a novel design of a racetrack ring resonator (RTRR) integrated with an MMI structure based on a low-cost silica-titania (SiO 2 :TiO 2 ) optical platform for refractive index sensing applications. The device design is straightforward and does not need a gap between the bus WG and a ring for evanescent field coupling. Hence, we assume that it can be effectively fabricated via a cost-effective nanoimprint lithography (NIL) method as declared in our previous study [32]. The sol-gel process allows us to manufacture a wide range of materials, including glasses, ceramics, and composites [33]. It offers versatility in tailoring the properties of the final product by varying the precursor materials and process parameters. The sol-gel process can produce thin films with precise control over thickness and composition, making them functional for applications like anti-reflective coatings, protective layers, and optical devices [32][33][34][35].
The dip-coating method is reasonably simple and cost-effective compared to other thin-film deposition techniques [36]. It does not demand complex equipment or elaborate setups [37]. Dip-coating can produce uniform and consistent thin films over large or complex-shaped substrates, ensuring even coverage and thickness distribution [38]. The dip-coating process is greatly reproducible, allowing for consistent results when performed under the same conditions [39]. In our previous work [35], high-quality SiO 2 :TiO 2 thin films are deposited on BK7 glass via a sol-gel process and a dip-coating method. Thus, Photonics 2023, 10, 978 3 of 10 we assume that the proposed sensing device in this paper can be effectively fabricated by employing the NIL method as justified in our previous work [32].

Device Design and Parametric Optimization
The graphical illustration of the RTRR integrated with the MMI structure is exhibited in Figure 1a. The device contains two input and two output ports connected to the MMI segment. The output port 2 is further combined with an RTRR structure which has a radius R and acts as a feedback loop. The width (W) of the input and output WGs are fixed at 1.6 µm which satisfies the single mode condition at the operational wavelength of 1.55 µm. The total height of the device is assumed to be 0.41 µm to support the TE 0 mode having an effective refractive index of 1.4737 as shown in Figure 1b. Later, this effective index is employed in designing the device in a 2D numerical model. The width and length of the MMI structure are denoted as W MMI and L MMI , respectively. The W MMI is fixed at 8 µm which specifies a region where multiple modes can interfere. The light is launched at the input port 1 which couples to the RTRR structure via a MMI coupler. The resonance condition is satisfied at specific operational wavelengths which can be collected at output port 1. The feedback loop contains two semi-circular bend WGs; therefore, it is important to plot the E-field distribution and determine the effective refractive index of the mode propagating in the WGs with a bending radius (R) of 25 µm in the presence of ambient refractive index of 1.0 and 1.33 as shown in Figure 1c,d, respectively. The results suggest that WGs with R = 25 µm can support fundamental mode which stabilizes while propagating in the straight WG. Table 1 describes the geometric parameters used to optimize the device design for sensing applications. dius R and acts as a feedback loop. The width (W) of the input and output WGs are fixed at 1.6 µm which satisfies the single mode condition at the operational wavelength of 1.55 µm. The total height of the device is assumed to be 0.41 µm to support the TE0 mode having an effective refractive index of 1.4737 as shown in Figure 1b. Later, this effective index is employed in designing the device in a 2D numerical model. The width and length of the MMI structure are denoted as WMMI and LMMI, respectively. The WMMI is fixed at 8 µm which specifies a region where multiple modes can interfere. The light is launched at the input port 1 which couples to the RTRR structure via a MMI coupler. The resonance condition is satisfied at specific operational wavelengths which can be collected at output port 1. The feedback loop contains two semi-circular bend WGs; therefore, it is important to plot the E-field distribution and determine the effective refractive index of the mode propagating in the WGs with a bending radius (R) of 25 µm in the presence of ambient refractive index of 1.0 and 1.33 as shown in Figure 1c and Figure 1d, respectively. The results suggest that WGs with R = 25 µm can support fundamental mode which stabilizes while propagating in the straight WG. Table 1 describes the geometric parameters used to optimize the device design for sensing applications.  The transmission and E-field distributions of the sensing device are verified by the finite element method (FEM) by employing commercially available COMSOL Multiphysics software 6.1. Perfect matching layer (PML) and scattering boundary condition (SBC) are applied to simulate the behavior of EM wave propagating in unbound domains as shown in Figure 1e. The numeric ports are also assigned to the bus WG to excite the input of the bus WG (input port) and collect the transmission at the output (output port). PML is an absorbing boundary condition that allows for the reduction of reflection and surplus wave interactions at the boundaries of the simulation domain. Moreover, meshing is a crucial step in the FEM process, and it plays a significant role in the accuracy and efficiency of simulations in COMSOL Multiphysics. Meshing involves dividing the computational Photonics 2023, 10, 978 4 of 10 domain into smaller geometric elements, for instance, triangles or tetrahedra in 2D or 3D, respectively. Each element corresponds to a discrete region where the equations of the physics being simulated can be approximated and solved. For our model, we choose "physics-controlled mesh", which provides an appropriate mesh size to acquire accurate results. To obtain a 3 dB 2 × 2 MMI coupler, the length of the multimode segment can be calculated as [27]: where L π is the beat length of the two lowest-order modes and can be stated as: where n eff is the effective refractive index, λ is the free-space wavelength, W MMI is the width of the MMI segment, which is fixed at 8 µm, and β o and β 1 are the propagation constants of the fundamental and first-order lateral modes, respectively. From Equation (1), the L MMI is calculated as~40.56 µm. The precise length of the MMI segment is attained via FEM as shown in Figure 2. The schematic representation of the 2 × 2 MMI segment is shown in Figure 2a which will be integrated with the final device configuration. The TE polarized light at the operational wavelength of 1.55 µm is launched at input port 1 and the transmission (a.u) spectrum obtained at output port 1 and output port 2 is plotted versus L MMI as shown in Figure 2b. The L MMI is varied from 40 µm to 114 µm, whereas W, W MMI , and g are fixed at 1.6 µm, 8 µm, and 2 µm, respectively. The power ratio (P1/P2) of the output ports is plotted in Figure 2c which indicates several points where equal power distribution can be achieved. However, looking at the maximum power transmission of 0.31 which is obtained at both output ports, L MMI = 44 µm is selected. The normalized E-field distribution in the MMI structure for L MMI = 44 µm (equal power distribution at output ports) and L MMI = 68 µm (unequal power distribution at output ports) is presented in Figure 2d,e, respectively.
The transmission spectrum of the RTRR integrated MMI structure is simulated for R = 25, 30, 35, and 40 µm, while keeping the remaining structural variables such as L MMI , W MMI , L, W, and g at 44 µm, 8 µm, 94 µm, 1.6 µm, and 2 µm, respectively. For the spectral range of 1.548 µm to 1.560 µm, almost three resonance dips appear as shown in Figure 3a. The free spectral range (FSR) of a RR is a key parameter that characterizes its optical behavior. The FSR refers to the spacing between adjacent resonant frequencies or wavelengths at which the RR exhibits constructive interference [40]. In other words, it is the frequency difference between two consecutive resonance peaks of the RR's transmission spectrum [31]. From Figure 3b, it can be seen that the FSR of the device reduces from 4.65 nm to 3.675 nm as R increases from 25 µm to 40 µm. The FSR is a vital parameter in various applications, such as in WDM systems and the design of optical filters and lasers [41,42].
By controlling the FSR, the operating frequencies of the RR can be determined, and tailor its performance to specific applications. The E-field distribution at the resonance wavelength where a sharp dip in the transmission spectrum takes place and the wavelength at which light transmits at output port 1 is shown in Figure 3c,d, respectively. The transmission spectrum of the RTRR integrated MMI structure is simulated for R = 25, 30, 35, and 40 µm, while keeping the remaining structural variables such as LMMI, WMMI, L, W, and g at 44 µm, 8 µm, 94 µm, 1.6 µm, and 2 µm, respectively. For the spectral range of 1.548 µm to 1.560 µm, almost three resonance dips appear as shown in Figure 3a. The free spectral range (FSR) of a RR is a key parameter that characterizes its optical behavior. The FSR refers to the spacing between adjacent resonant frequencies or wavelengths at which the RR exhibits constructive interference [40]. In other words, it is the frequency difference between two consecutive resonance peaks of the RR's transmission spectrum [31]. From Figure 3b, it can be seen that the FSR of the device reduces from 4.65 nm to 3.675 nm as R increases from 25 µm to 40 µm. The FSR is a vital parameter in various applications, such as in WDM systems and the design of optical filters and lasers [41,42]. By controlling the FSR, the operating frequencies of the RR can be determined, and tailor its performance to specific applications. The E-field distribution at the resonance wavelength where a sharp dip in the transmission spectrum takes place and the wavelength at which light transmits at output port 1 is shown in Figure 3c and Figure 3d, respectively.

Refractive Index Sensing Operation
The basic principle of refractive index sensing operation involves exploiting the interaction of light with the material under investigation. Refractive index sensing devices are used in biosensors to detect biomolecules and analytes or monitor chemical reactions [43]. The refractive index is an essential property in the context of bioanalytes, as it can provide valuable information about their composition and concentration. Bioanalytes refer to various biomolecules, cells, or biological substances that are of interest for analysis in biological and biomedical research. Some common bioanalytes include proteins, nucleic acids (DNA and RNA), peptides, antibodies, antigens, cells, and small molecules like glu-

Refractive Index Sensing Operation
The basic principle of refractive index sensing operation involves exploiting the interaction of light with the material under investigation. Refractive index sensing devices are used in biosensors to detect biomolecules and analytes or monitor chemical reactions [43]. The refractive index is an essential property in the context of bioanalytes, as it can pro- vide valuable information about their composition and concentration. Bioanalytes refer to various biomolecules, cells, or biological substances that are of interest for analysis in biological and biomedical research. Some common bioanalytes include proteins, nucleic acids (DNA and RNA), peptides, antibodies, antigens, cells, and small molecules like glucose and ions [44]. The refractive index of a bioanalyte depends on its chemical composition, concentration, temperature, and wavelength of light used for measurement. One significant advantage of refractive index sensors in bioanalyte analysis is that they enable label-free detection. This indicates that the analytes do not require any specific labels or tags, reducing the complexity and cost of the analysis [45].
The RTRR-integrated MMI structure is immersed in a sensing medium (see Figure 4), where the change in the refractive index of the medium can influence the interference pattern of the propagating modes in the MMI structure resulting in the shift in the resonance dip. The sensitivity of the photonic sensor is typically quantified in terms of the smallest detectable change in the measured quantity that can be reliably sensed by the device. Highly sensitive photonic sensors authorize precise and accurate measurements of small changes in physical quantities for instance temperature, pressure, strain, displacement, or chemical concentrations [29,30]. This level of precision is crucial in applications where even petite variations can have substantial implications. The sensitivity of the refractive index sensor based on RTRR-integrated MMI structure is evaluated as: where ∆λ res and ∆n are the variation in resonance wavelength and change in the refractive index of the ambient medium, respectively.  The normalized transmission spectrum of the RTRR-integrated MMI structure in the presence of different ambient refractive indices varied between 1.33 and 1.36 with a step size of 0.05 is shown in Figure 5a. The resonance wavelength performs a redshift as the ambient index increases due to a change in the effective refractive index of the modes interfering in the MMI structure. The change in resonance wavelength shift concerning the variation in ambient refractive index is plotted in Figure 5b (black dotted line). A common method for determining the relationship between two variables is to fit a straight line to a collection of data points using linear regression (red line in Figure 5b). One of the most notable results of this method is the slope of the line, which shows how quickly the dependent variable changes for each unit increase in the independent variable. The resonant wavelength versus RIU graph can be fitted linearly to get a slope of about 142.5 nm/RIU. The sensitivity obtained with the RTRR integrated with the MMI structure resembles our previous results on the SiO2:TiO2 platform-based standard RR structure [31]. However, we believe that the proposed structure is much simpler and more flexible in fabrication. The figure of merit (FOM) of the sensing device is expressed in terms of: where S is the device's sensitivity and FWHM is the full width at half maximum of the Substrate Sensing medium (n=1.33-1.36) The normalized transmission spectrum of the RTRR-integrated MMI structure in the presence of different ambient refractive indices varied between 1.33 and 1.36 with a step size of 0.05 is shown in Figure 5a. The resonance wavelength performs a redshift as the ambient index increases due to a change in the effective refractive index of the modes interfering in the MMI structure. The change in resonance wavelength shift concerning the variation in ambient refractive index is plotted in Figure 5b (black dotted line). A common method for determining the relationship between two variables is to fit a straight line to a collection of data points using linear regression (red line in Figure 5b). One of the most notable results of this method is the slope of the line, which shows how quickly the dependent variable changes for each unit increase in the independent variable. The resonant wavelength versus RIU graph can be fitted linearly to get a slope of about 142.5 nm/RIU. The sensitivity obtained with the RTRR integrated with the MMI structure resembles our previous results on the SiO 2 :TiO 2 platform-based standard RR structure [31]. However, we believe that the where S is the device's sensitivity and FWHM is the full width at half maximum of the resonant dip, which is~1.82 nm, and, correspondingly, the FOM of the device is~78.3.
the variation in ambient refractive index is plotted in Figure 5b (black dotted line). A common method for determining the relationship between two variables is to fit a straight line to a collection of data points using linear regression (red line in Figure 5b). One of the most notable results of this method is the slope of the line, which shows how quickly the dependent variable changes for each unit increase in the independent variable. The resonant wavelength versus RIU graph can be fitted linearly to get a slope of about 142.5 nm/RIU. The sensitivity obtained with the RTRR integrated with the MMI structure resembles our previous results on the SiO2:TiO2 platform-based standard RR structure [31]. However, we believe that the proposed structure is much simpler and more flexible in fabrication. The figure of merit (FOM) of the sensing device is expressed in terms of: where S is the device's sensitivity and FWHM is the full width at half maximum of the resonant dip, which is ~1.82 nm, and, correspondingly, the FOM of the device is ~78.3. In [46], the authors presented a chip-scale photonic system in their study, aimed at detecting gas composition and pressure at room temperature. This system relied on a slotted Si MRR for its operation. In [47], the researchers documented the development of a In [46], the authors presented a chip-scale photonic system in their study, aimed at detecting gas composition and pressure at room temperature. This system relied on a slotted Si MRR for its operation. In [47], the researchers documented the development of a liquid sensing device that utilized a Ge-Sb-Se MRR operating at a wavelength of 1550 nm. In the study [48], a label-free optical biosensor employing a microring resonator, which utilized lithium niobate-on-insulator (LNOI) technology, was conceptualized and simulated for applications in biosensing. Another study introduced a design guideline for an MZI sensor utilizing SOI nanowires [49]. This guideline enabled the adjustment of sensitivity through the strategic selection of MZI arm lengths, as outlined by the provided data within the research paper. Recently, a unique sensor designed for MIR biochemistry applications was introduced [50]. This sensor employed a configuration featuring two suspended GaAs WGs within an asymmetric MZI setup. The device performance is compared with several other novel designs, as shown in Table 2.

Concluding Statements
A multimode interferometer (MMI) is an optical device used in integrated photonics for various applications, including optical communications and sensors. It is based on the principle of interference, where light waves from different modes interact constructively or destructively to produce an output pattern. In this work, a numerical study on RTRR integrated with MMI structure is aimed at refractive index sensing application. The structure is based on a low-cost SiO 2 :TiO 2 material platform where high-quality thin films are obtained via the sol-gel process and a dip-coating method. The sensitivity and FOM of the proposed device are~142.5 nm/RIU and 78.3, respectively. The cost of the photonic sensor is an important factor, especially for commercial and mass-market applications, as it affects the feasibility of operating the sensor in various scenarios. We consider that this device can be realized via a low-cost NIL method which overall cut down the cost of production of this photonic sensing device.