Buried vs. Ridge Optical Waveguide Modeling for Light Trapping into Optical Fiber M.M.Ismail, M.A.Meor Said, M.A.Othman, M.H.Misran, H.A.Sulaiman, F. A. Azmin Abstract This paper presents the investigation on optical propagation characteristic of straight waveguide on light intensity distribution within the structure at 1.55 µm waveguide. The normalized propagation constant b, and effective refractive index neff, has been considered for the straight and single mode propagation waveguide. MATLAB programming has been used as the method of simulation for both propagation characteristics. The characteristic had been analyzed using a numerical method based on finite difference method approach. The results of optimization analysis of waveguide according to a certain parameter may help in application of designed modeling performance of optical waveguide easily. Index Terms Optical Waveguide, Normalized Propagation Constant, Effective Refractive Index. I. INTRODUCTION Optical waveguide had been used widely and gives more advantages than the conventional way. Optical waveguide devices already play important roles in telecommunications systems, and its importance will certainly grow in the future. An optical waveguide is a spatially inhomogeneous structure for guiding light. For example, for restricting the spatial region in which light can propagate. Usually, a waveguide contains a region of increased refractive index, compared with the surrounding medium, called cladding. Optic communication systems widely operate in the wavelength windows at 850 nm, 1300 nm and 1550 nm. For a low loss transmission system, the optical loss due absorption from ultra violet (UV) and infrared (IR) region must minimize at operating wavelength and the system bandwidth will be increase. Thus, operation wavelength at 1550 nm is the best wavelength can maximize the bandwidth system with low attenuating loss. Ideal optical waveguides, such as those illustrated in figure 1 and figure 2, are considered to have dielectric boundaries extending to infinity. They are called open waveguides. Optical waveguides modes are wave trapped in and around the core. They can be excited only by electric fields. Buried type of waveguide is very important and suitable for integrated optical technologies, finding widespread and significant inferometers, splitters, and switches and also as an optical interconnects such as bends and junction. The buried type of channel waveguide has the advantages that the propagation loss in typically lower in 1dBm with smooth surface. It is usually suitable for bend waveguide with small curvature radii due to its characteristic that strongly transverse confinement of scattering loss due to waveguide wall roughness [1]. Fig 1: A Planar Waveguide. The substrate and the film are so wide in the Y direction that W can be approximated by. The substrate thickness is also considered to be in the x direction. Guided-wave modes could propagate in any direction in the YZ plane. Fig 2: A channel waveguide. The high index core ( ) is embedded in the substrate. The core is very long in the z direction with. The guided-wave propagates in the z-direction. The ridge waveguide, as shown in the Figure 3 is a widely used for semiconductor lasers, modulators, switches and semiconductor optical amplifiers as well as some passive devices. This project discusses a number of design considerations for the ridge waveguide including single mode condition. The operation principle of the ridge waveguide is described first in order to provide a context for understanding these design considerations. For single mode condition, it is required for an effective ridge waveguide design. The single mode condition is achieved by carefully controlling the lateral confinement and adjusting the ridge width and etching depth. 273
Now, considering a y-polarized TE mode which propagates in the z-direction and as a propagation constant in longitude direction will then results: Taking as the total propagation constant which combine the horizontal and vertical part, produces: (6) (7) Fig 3: Ridge Waveguide Channel Structure The finite difference method (FDM) is a simple numerical technique used in solving problem that uniquely defined by three things. There are partial differential equation such as Laplace s or Poisson equation, a solution region boundary and/or initial conditions. The basic formulation that governs the propagation of light in the optical waveguide is Maxwell s equations and it derives to obtain E-field. MATLAB software works as a tool to calculate the equation which Graphical User Interface (GUI) was used and make it a friendly user and able to obtain faster and accurate result. A Graphical User Interface (GUI) allows user to perform tasks interactively through controls such as buttons and sliders. II. THEORY AND DESIGN ANALYSIS Some of the most effective methods rely on special geometric features of the waveguides and they may even turn the original linear eignvalue problem to a nonlinear problem for the propagation constant,. Generally, optical waveguides can be analyzed by solving Maxwell s equations, (1) (2) Maxwell s equations in a homogeneous and lossless dielectric medium are written in terms of the electric E and magnetic field H (3) (4) Where E and H are the electric and magnetic fields, B and D are the electric and magnetic flux densities, and J are electric charge and electric current densities, or their reduced form, the electromagnetic wave equation, with appropriate boundary conditions determined by the propertied of the waveguide and cladding materials. The equations provide the mathematical foundation used to model and evaluate the flow of electromagnetic energy in all situations, of which waveguides form a special case. A finite difference solution to Poisson s or Laplace s equation, for example proceeds in three steps. First is dividing the solution region into a grid of nodes. Second, is approximating the differential equation and boundary conditions by a set of linear algebraic equations on grid points within the solution region, and finally, by solving this set of algebraic equations. The wave equation for the electric field can be presented as: (5) Knowing that k is a multiplication of free space propagation constant, and refractive index, n for respective layer, Equation (7) can be written in the form of: (8) Considering that having component in x and y direction E(x,y), numerical approach of Taylor s expansion is applied to Equation (8) where the differential components are obtained as follows: Electric field can be obtained by combining Equation (8) and (9), (9) (10) Where i and j represent the mesh point corresponding to x and y directions respectively. If equation (8) is multiplied with and operating double integration towards x and y, it will result: (11) Due to difficulties in interpreting small differences of effectives index values, a more sensitive comparison is made by introducing a normalized propagation constant, (12) In this analysis, it focused on buried square channel that symmetrical and straight waveguide. is the refractive index upper cladding, is the refractive index core and is the refractive index lower cladding. Meanwhile represent of upper cladding thickness and w for width. Assume that no air at the waveguide, and was fixed at 2µm and assume n upper cladding and lower cladding equal to 3.34. While n core, equal to 3.44, also assume that lambda, is 1.55 µm. 274
Fig 4: Buried Channel Structure The two types of ridge waveguide s parameter will be concerned, which are the total thickness of core layer (t + h) and the ridge width w. The total thickness of core layer is kept constants at 1µm, but varies the value of t. In this particular project, the waveguide is in single mode, so to get this mode, the ridge width must be less than 4.7µm. Fig 5: Ridge Channel Structure III. RESULTS AND DISCUSSIONS For buried optical waveguide analysis, the simulation process is done on the constructed GUI page as in Figure 6. The result output came out as in Figure 7 which consists of Refractive Index Profile, E-field Profile and E-field Contour plot. Table 1 represent nine data samples have been analyse to prove the theory, which are from 3µm to 7µm thickness. Table 1: Data Samples of Multiple Thickness and Result (µm) 3.0 4.0 5.0 6.0 7.0 3.4281 3.4337 3.4365 3.4382 3.4392 b 0.3776 0.1994 0.1089 0.0568 0.0241 A range of 3.4281 3.4392. this shows that the range in between n core and n cladding suitable the theory. As the thickness increase, the effective index, will increase too. The value of β also increases and it make the propagation light within the structure fully trapped into core region, resulting propagation loss to decrease. This is because in order to determine the accuracy light intensity trapped inside the core, the effective index profile should be in range between core refractive index, ( ) and classing refractive index, n cladding ( and ).. of the fundamental mode is related to the propagation constant by.while the range of b from 3µm to 7µm thickness was 0.3776 b 0.0241 as shown in the Table 1 and Figure 9,b decrease when thickness increase. Fig 6: The Result of Effective Index, Neff and Normalized Propagation, B At 3 X 3 Waveguide Fig 8: Effective Index, graph Structures of five ridge waveguide with different thickness, t were simulated as the total thickness of core remain constant at 1µm. Starting from t = 0 µm and add 0.2 µm for the following structure. Other parameters were set to be constant where ridge width, w = 3 µm, upper cladding refractive index (GaAS) = 3.44, and bottom cladding or substrate refractive index (GaAlAs) = 3.36. Fig 7: The Figure of Refractive Index Profile, E-Field Profile and E-Field Contour Plot Output at Waveguide 3 X3 from Calculation Section Fig 9: Normalized Propagation Constant,b graph 275
Fig 12: Effective Refractive Index, Thickness, T As a Function of Fig 10: The Result of Effective Index, Neff and Normalized Propagation, B at T = 0 µm Fig 11: The Figure of Refractive Index Profile, E-Field Profile and E-Field Contour Plot Output At Waveguide T = 0µm from Calculation Section When t is small, the propagation light intensity within the structure fully trapped into the core active region, so it has strongly confinement and the loss is low. Even though when t is small and it has strongly confinement, it does not mean when t is high the ridge is not good because it depends on the application not the value. Table 2 shows the relationship of thickness, t normalized propagation constant, b and effective refractive index,. Table 2: Comparison with Different Structure When T Varied t(µm) h(µm) b Fig 13: Normalized Propagation Constant, B as A Function of Thickness, T According to the E-field contour plot in Figure 14, it shows that when the width, w is increase, the filed distribution will converge and the electric field energy will radiate into core. Its performance does improve as the ridge width increases, due to stronger lateral confinement. Table 3 below shows the relationship of ridge width, w with effective refractive index, and normalized propagation constant, b. 0.0 1.0 3.39475 0.431529 0.2 0.8 3.39509 0.435701 0.4 0.6 3.39578 0.444378 0.6 0.4 3.39695 0.458951 0.8 0.2 3.39855 0.480146 It was then plotted in Figure 12 and Figure 13 to see how the thickness directly proportional to the effective refractive index and normalized propagation index. Fig 14: The Figure of Refractive Index Profile, E-Field Profile and E-Field Contour Plot Output At Waveguide W = 4.0µm from Calculation Section 276
Table 3: Comparison with Width Difference Width, w b (µm) 2.5 3.39149 0.390790 3.0 3.39488 0.433166 3.5 3.39701 0.459717 4.0 3.39843 0.477431 Fig 15: Effective refractive index, w. as the function of width Mode Solver 2D 0.4408 Mode Solver 3D 0.4421 2D-Beam Propagation Method 0.4317 Finite Difference Method (FD1) 0.4367 Finite Difference Method (FD2) 0.4400 Finite Difference Method (FD3) 0.4406 Finite Difference Method (present) 0.4332 Smaller mesh size will increase the accuracy of the Effective Index and Normalized Propagation Constant. The mesh size also determine the sharpness of the plotting either more accurate or not. But if the mesh size is too small, the simulation process will took longer time. The other factor is where tolerance input may determine the number of iteration that will be process by the program. It is also contributing to the accuracy of the simulation because β used to calculate the value of Effective Index and Normalized Propagation Constant needed to converge. The smaller value of the tolerance will also increase computational time. In order to determine the accuracy of the buried optical waveguide analysis, comparison was made to the existing method, which is Finite Element Method. Fig 16: Normalized Propagation constant,b as the function of width,w. From the plotted graph, it shows that the value of normalized propagation constant, b increase as width, w increase. Same goes to the value of effective refractive index, only that it doesn t affect too much as the value is almost the same for all thickness. Table 4: Comparison of Normalized Propagation Constant, b Result with Other Method Method Normalized Propagation Effective Index Method 0.4404 Mode Matching 0.4390 Function Fitting 0.4332 Beam Propagation Method 0.4280 Variational Method 0.4348 Scalar Finite Difference 0.4369 Constant, b (µm) IV. CONCLUSION In the integrated optical circuit, the optimum design of ridge channel waveguide should support with low loss and strongly optical confinement for practical implementation. While a good design of buried and ridge optical waveguide is intended to limit propagation loss and the transition losses. For buried optical waveguide the core thickness and core width influence the value of E-field, effective index and normalized propagation constant. While the parameters that affect the performance of ridge waveguide are core thickness and ridge width. These parameters will affect the value of normalized propagation constant and also effective refractive index. The finite difference method is one of the methods that can used to study about electric field distribution. ACKNOWLEDGMENT Authors would like to thanks UniversitiTeknikal Malaysia Melaka for financing this project and this journal. REFERENCES [1] Koshiba, M, Optical Waveguide Analysis, McGraw Hill, New York, 1992. [2] N. MohdKassim, A. B. Mohammad, A. S. MohdSupa at, M. H. Ibrahim, and S.Y. Gand, Single Mode Rib Optical Waveguide Modeling Techniques, RF and Microwave Conference, October 2004, pp.272-276. [3] Kassim, N., Mohammad, A.B., Ibrahim, M.H., 2005. Optical waveguide modeling based on scalar finite difference scheme. Journal Teknologi, 42(D) 41-54 UniversitiTeknologi Malaysia. [4] M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric rectangular waveguide, (in Japanese) Trans. Ins. 277
Electron. Commun. Eng.Japan, vol. J64-C, pp. 674-681, October 198. [5] F. Anibal Fernandez, Yilong Lu.1996 Microwave and optical waveguide analysis. Research studies press LTD, Somerset, England. Author s Biography MohdMuzafar Ismail was born on 5 August 1985, Raub, Pahang, Malaysia. He received his first degree Bachelor of Engineering (Electrical-Telecommunications) at UniversitiTeknologi Malaysia (UTM) on 2008. He got his Master s Degree, Master of Engineering (Electronic and Telecommunications) at UTM, 2010. Previously he worked as an Electrical Engineer at Venture Technocom System Singapore before joining UniversitiTeknikal Malaysia Melaka as a lecturer on 2010 at FakultiKej. ElektronikdanKej.Komputer. His research currently focus on Electromagnetic, Acoustic Engineering, Optical communication, and Optimization. Maizatul Alice Meor Said was born on 26 Oktober 1982, Taiping,Perak, Malaysia. She received Bachelor of Engineering (Electronics) at University of Surreyon 2006. She received her Master of Engineering (Telecommunication) at University of Wollongong, 2009 and she joined Universiti Teknikal Malaysia Melaka as a lecturer on 2009 at Fakulti Kej. Elektronik dan Kej. Komputer. Currently she is working on RF & Microwave and Antenna propagation. MohdAzlishah Othman was born on 21 st October 1980 at Johor Bahru, Johor, Malaysia. He received Degree Bachelor of Engineering in Electrical Engineering (Telecommunication) from UniversitiTeknologi Malaysia (UTM) on 2003. In September 2005 he joined UniversitiTeknikal Malaysia Melaka (UTeM) as a Lecturer at FakultiKej. ElektronikdanKej.Komputer (FKEKK). He received his Master s Degree in Computer and Communication Engineering from University of Nottingham, UK on 2005 and continues his PhD in Electrical and Electronic Engineering in University of Nottingham, UK from 2006 till now. His PhD thesis on the field of Terahertz circuits and devices. Currently he is working on RF and Microwave circuits and devices. Mohammad Harris Misran was born on 29 February 1980, Kluang, Johor, Malaysia. He received his first Degree Bachelor of Engineering (Electronics) at University of Surrey, 2006. Then he continued his Master s Degree on Master of Engineering (Telecommunication) at University of Wollongong, 2008. Then he joined UniversitiTeknikal Malaysia Melaka as a lecturer on 2008 at FakultiKej. ElektronikdanKej.Komputer. Currently his research on RF and Microwave circuits and Antenna Propagation. HamzahAsyraniSulaiman was born on 28 Januari 1985, Jitra, Kedah, Malaysia. He received his first degree Bachelor of Engineering (Computer) at UniversitiTeknologi Malaysia (UTM) on 2008. He got his Master s Degree, Master of Science (Computer Science) at UTM, 2010. He joined UniversitiTeknikal Malaysia Melaka as a lecturer on 2010 at FakultiKej. ElektronikdanKej.Komputer. His research currently focus on Computer Graphics and Visualization/ Data Computation and Algorithm with Graphics Processing Unit (GPU). F.A. Azmin was born on 29 Mac 1986, Kuala Lumpur, Malaysia. She received her first Degree Bachelor of Electronic Engineering (Wireless) at UniversitiTeknikal Malaysia Melaka on 2012. Currently she continued her study on Masters of Electronic Engineering (Telecommunication System) at UniversitiTeknikal Malaysia Melaka and her research on RF and Microwave circuits and Antenna Propagation. 278