## 2 Materials and Methods
### Diabetes Detection by FDTD Approach  
The investigation of MRR-based sensors for diabetes detection has been carried out by 3D FDTD using Lumerical FDTD Solutions. The FDTD method in Lumerical FDTD Solutions was used because of its ability to perform good and accurate analyses of light propagating in MRR waveguides. The dimensions of the MRR in this simulation were based on the proposed design of MRRs based on SOI, as shown in Table 2.  
Figure 2: Three steps of the device fabrication process as follows: (**a**) resist spinning, (**b**) Electron Beam Lithography (EBL) patterning and development, and (**c**) silicon etching. In order to obtain the desired results that are near the experimental results, we have optimized several parameters in this simulation. The simulation time was set to 50,000 fs, which is 10 times higher than the initial simulation time, to obtain a more detailed calculation from the FDTD method. The mesh type was set to the automesh feature with the configuration of the mesh being nonuniform to minimize the effect of numerical dispersion. The mesh accuracy was set to 3 in order to get a good trade-off between accuracy, memory requirements, and the total time needed. As for the perfectly matched layer boundary condition, the standard profile was chosen as it will produce a good overall light absorption with a relatively small number of layers so that the required simulation time can be reduced. As a start, the simulation was run for the index background of 1 (air) in the environment temperature of 295 K. This condition was chosen to imitate the real conditions of the experimental work for quality factor measurement. Figure 4 shows the computer-aided design of the MRR device from Lumerical FDTD Solutions. Figure 5 shows a schematic on how the occurrence of the glucose analyte will cause a resonance shift to the MRR-based sensor. The addition of glucose in the environment around the MRR waveguide triggers an increase in the environmental refractive index due to the appearance of glucose analytes. The presence of glucose analytes interferes with the evanescent field, as they will absorb energy initially possessed by the field [28]. If the evanescent field experiences loss of energy due to being absorbed by the glucose analyte, then the total energy of the light traveling on the waveguide will  
Figure 4: The geometry of the designed MRR in this simulation work from (**a**) top view and (**b**) bird’s-eye view. Figure 3: Experimental setup for quality factor characterization in MRR waveguides by through-port power transmission measurements using an optical spectrum analyzer (OSA) and tunable light source (TLS) as a light source. decrease. This is caused by the evanescent field, which is part of the light propagation mode on the MRR waveguide. The energy loss will also decrease the speed of the light phase to propagate on the waveguide. By slowing down the phase and speed of light, the effective waveguide index is affected, as the effective refractive index of the waveguide itself can be defined as the ratio between the speed of the light phase in the vacuum and the speed of the light phase in the waveguide [29]. Based on these definitions, it can be concluded that the decrease in phase velocity will result in an increase in the effective refractive index of the waveguide, thus enabling the resonance shift. Next, to predict the ability of the MRR-based sensor to detect diabetes, the resonance shift that occurs due to changes in glucose concentration in the environment around the MRR were observed. The glucose concentration in the MRR environment will be varied based on glucose levels in people with diabetes. It can be done using Lumerical FDTD Solutions by changing the index background of the simulation to the reference refractive index of certain glucose concentrations. Based on experimental data obtained through a study done by [PERSON] et al.