BURIED WAVEGUIDE POLYMETHYLMETHACRYLATE MODELING FOR REFRACTIVE INDEX SENSOR APPLICATION USING FINITE ELEMENT METHOD

The purpose of this study is to obtain the optimum buried waveguide structure through modeling for refractive index sensor applications. The waveguide cladding material used as Polymethylmethacrylate (PMMA). The core cross-section size was 1 × 1 mm. The simulation was carried out at a wavelength of 650 nm using the Finite Element Method (FEM). The parameter of the buried waveguide optimized in this model was the core refractive index and the thickness of the upper cladding to obtain a high propagation constant and good sensitivity to refractive index. Modeling was done for various core refractive index values varied in the range of 1.52 to 1.59, which are the refractive index of various types of polymers. To optimize the sensitivity, the thickness of the upper cladding was varied between 0.125 mm to 0.5 mm. Besides, a simulation was also carried out for a waveguide without an upper cladding. The results show that the optimum waveguide is a waveguide without upper cladding using polyester as core material with a refractive index value of 1.57 and a sensitivity of 4.9 × 10rad /m RIU.


INTRODUCTION
Fiber optic sensor technology has attracted much attention in various applications since it was more resistant to extreme weather conditions, anti-electromagnetic interference and it can be used for real-time and remote sensing. The detection principle that is widely used in fiber optic sensors is the detection of refractive index change from fiber optic's material or change of refractive index environment. Silica optical fiber is commonly used in fiber optic-based refractive index sensor [1][2][3]. However, for measurement of refractive index in liquid, optical sensor technology based on silica optical fiber has the disadvantage of causing absorption [4]. To overcome the problem, the light source needs to be replaced with visible light. However, visible light does not make it suitable for silica optical fiber. Fiber optic, which works with visible light is polymer optical fiber. However, the availability of polymer optical fiber, for now, is still limited. As an alternative, polymer optical fiber can be replaced with a waveguide with dimension and material which is suitable for visible light.
An optical waveguide sensor has been developed for the application of temperature sensor and refractive index. These sensors are developed using various technologies such as waveguideprism system [5], Bragg grating [6] dan nano-silica waveguide [7]. However, the light sources used in the technique, as mentioned above, where the light source with a wavelength of 1260 nm -1550 nm. Therefore, it will cause high absorption. Du & Zhao [4] and Hooda & Rastogi [8] have designed a waveguide refractive index sensor by using a visible light source (380 nm-760 nm). Du & Zhao [4] used silica carbide (SiC) as core material and SiO2 as substrate and gold layer (Au) on the upper core.
Meanwhile, Hooda & Rastogi [8] used waveguide with Teflon-Cytop-Teflon material. However, the waveguide fabrications were quite complicated and need equipment with high technology, so the research was only done in simulations. Furthermore, the waveguide dimensions were very small (in nanometer and micrometer order) so that the sensor incompatible with polymer optical fiber with a diameter of 1 mm. This will cause a lot of power loss in connection with the light source.
In this research, we proposed a waveguide design for refractive index sensing for operation in visible light. Polymethylmethacrylate (PMMA) was used as a cladding material since PMMA has high transparency, low cost, and easy to fabricate. Furthermore, PMMA is also the material used in polymer optical fiber so it could minimize power loss when it is connected with polymer optical fiber. The design was optimized in terms of the core refractive index and its sensitivity to refractive index environment. The optimization was done by simulation using the Finite Element Method (FEM).

METHOD
The waveguide parameter was optimized to get the optimal parameter to be used as a refractive index sensor. Optimization was performed by varying the core refractive index value to get high propagation constant. The higher the value of propagation constant, then lower the waveguide power loss. After the optimum core refractive index was obtained, the next steps were performing a simulation of the effect of environment refractive index value on the | 135

SPEKTRA: Jurnal Fisika dan Aplikasinya Volume 4 Issue 3, December 2019
propagation constant for various upper cladding thicknesses. The purpose of this simulation is to obtain an optimum upper cladding thickness, which results in high sensitivity. The waveguide structure used was buried waveguide structure as shown in FIGURE 1. The simulation was performed using a wavelength of 650 nm. The cladding material used in this simulation was PMMA with a refractive index value of 1.49, while the core material was polymer material with a refractive index value range between 1.52 to 1.59. The sensor sensitivity was determined by plotting refractive index vs. propagation constant. Waveguide propagation constant () was simulated by solving the following Maxwell equations where E(x,y) is the electric field, ko is propagation constant in a vacuum, and n(x,y) is the waveguide material refractive index. Maxwell equations were solved by using numerical method FEM.

Program Validation
Before the simulation, the first steps were program validation. Program validation is required to show that the program and the steps were valid. The validation was done by performing simulation for waveguide structure which has been done by the researcher which was ridge waveguide structure [9]. In [9], the simulation was performed by using Finite Different Method (FDM). The simulation results obtained by FEM were compared with those obtained by FDM. The ridge waveguide which was simulated has core width and thickness of 10 μm and 50 μm, respectively.
Meanwhile, the core refractive index was 2.65, and the substrate thickness was 30 μm. for other waveguide structure simulation, in this case, it was the buried waveguide structure as shown in FIGURE 1.

Mesh grid Study
Before core refractive index optimization performed, the next step after program validation was mesh grid study. The size of the mesh grid is very important in modeling. The mesh grid that was used in this research was free triangular. It was selected since the free triangular provide fast computation [10]. The steps to obtained optimum mesh grid size were done by performing simulation using a large mesh size and decreased it until it reaches convergent propagation constant. The constant propagation value obtained from the variation of the mesh grid as shown in TABLE 1. From TABLE 1, the mesh grid size which was considered as the most convergent was a mesh grid with a size of 0.44 mm. Besides its convergence, the meh grid size was selected by considering the computer memory specification. The smaller the mesh grid, the more memory needed and the longer the computation time will be. Therefore, although reducing mesh grid size smaller from 0.44 mm still changes the propagation of constant value, but the change was very small (in the order of 10 -11 ). Therefore, the mesh grid of 0.44 mm was selected to be used in the simulation. The form and mesh grid size used in the simulation is shown in FIGURE 2.

Waveguide Parameter Optimization
The buried waveguide that was used has a cross-sectional core of 1×1 mm, cladding width of 4 cm, cladding height of 2 mm, and cladding length of 5 cm.

Core Refractive Index Optimization
The value of the core refractive index determines the light propagation constant guided in the waveguide. The simulation was performed for various core refractive index values as shown in TABLE 2. PMMA selected because they have high transparency and low density [11].  where n0 is the refractive index of the medium around the waveguide, which is close to 1 in case of air, ni core refractive index of waveguide, ncl cladding refractive index of waveguide, λ is the light wavelength and a is the radius of the waveguide.  Based on the optimization of the core refractive index, the core materials that were selected were benzocyclobutene which has a refractive index of 1.54 and polyester, which has a refractive index of 1.57. The materials were selected since they were compatible with PMMA, have high transparency, simple fabrication, and low price [14,16].

Upper Cladding Optimization
The last step in parameter optimization was performing upper cladding optimization. It can be seen that the waveguide sensitivity to the refractive index was in the order of 10 -10 rad/m.RIU for waveguide without upper cladding and in the order of 10 -12 rad/m.RIU for a waveguide with upper cladding. For waveguide with the same cladding thickness, the sensitivity of waveguide with Benzocyclobutene material is higher than that of Polyester material. However, Polyester has a lower price and a more simple fabrication process than Benzocyclobutene [14]. Therefore, waveguide without upper cladding with Polyester material is more optimum than waveguide with Benzocyclobutene material.

CONCLUSION
Buried waveguide PMMA simulations have been performed. The optimum waveguide for refractive index sensor application is waveguide without upper cladding with a core material of polyester with a refractive index of 1.57. The refractive index sensitivity was 4.9 × 10 -10 rad/m.RIU.