The thesis entitled "OPTICAL ANALYSIS OF AN ELECTRO-OPTIC SEMICONDUCTOR MODULATOR WITH MICROSTRIP ELECTRODE", submitted by MAHUB AMIN, Session No Roll: April 2003, has been accepted as satisfactory in partial fulfillment of the requirement of the Master of Science in Electronics for the degree of Electronics. Engineer on June 26, 2010. I am thankful to all the members of the Board of Examiners for their valuable and fruitful suggestion.
Acronyms
Introduction
- Historical Perspective of Fiber Communication System
- Literature Review
- Objective of This Study
- Thesis Organization
Thus, to achieve the fundamental objective, the microwave analysis of the EOM will first be performed using the finite element method in MATLAB PDE toolbox [31]. Due to the presence of microwave fields, the anisotropic change in refractive index of the optical waveguide due to the electro-optic effect will be determined prior to optical analysis.
Basics of Electrooptic Modulator
- Introduction
- Direct Modulation
- Indirect Modulation
- Modulator Characteristics
- Extinction Ratio (ON/ OFF)
- Bias Voltage
- Chirping
- Frequency Modulation
- Bandwidth
- Insertion Loss
- Electrooptic Effect in GaAs Modulators
- Types of Electrooptic Modulator (EOM) .1 Phase Modulators
- Polarization Modulators
- Amplitude Modulators
- Thermally Compensated Devices
- Resonant Versus Broadband Devices
- Traveling-Wave Modulators
- Electro Absorption Modulator (EAM)
- Applications
The role of the optical modulators in the high capacity transmission systems is illustrated in the figure. For the linear electro-optic effect (Pockel's effect), an applied electric field changes each of the coefficients 12.
Concepts of Finite Element Method
- Historical Background
- The Range of Applications
- Primary Steps of a Finite Element Method (FEM)
- Domain Discretization
- Selection of Interpolation Functions
- Formulation of the System of Equations
- Formulation via the Ritz Method
- Formulation via Galerkin’s Method
- Solution of the System of Equations
The main idea behind the method is to represent the domain with smaller subdomains called finite elements. In most finite element solutions, the problem is formulated in terms of the unknown function at the nodes connected to the elements. Domain discretization is usually considered a preprocessing task because it can be completely separated from other steps.
The functional F given in (3.7) can be expressed as 3.9), where M is the number of elements that make up the entire domain and. Finally, we set the boundary conditions to obtain the final form of the system of equations. On the contrary, (3.27) is of the eigenvalue type, which is derived from the homogeneous governing differential equation and homogeneous boundary conditions.
Characterization of Electrooptic Modulator
Microwave Analysis
- Calculation of Electrode Capacitance
- Calculation of Microwave Index and Characteristics Impedance
- Calculation of Microwave Loss
- Calculation of Optical Response and 3-dB Bandwidth
By replacing the dielectric materials with free space, capacitance of the free space line C0 can be calculated using the same equation. Here Ex and Ey are the x-axis and y-axis components of the electric field respectively, Nm is the microwave index, and 0 is the intrinsic impedance of free space. The optical response of a modulator is determined by the microwave propagation properties of the electrode, namely the effective index of the microwave, Nm, the characteristic impedance.
Here Nm is the microwave effective index, N0 is the optical effective index, represents the total microwave and dielectric losses, and c is the speed of light [20]. However, in modulator bandwidth estimation, the critical factor is the speed mismatch, and when this is not achieved, the optical bandwidth Af of 3 dB is approximately determined by [13]. Where c is the conductor loss in decibels per (square root of gigahertz * centimeter), and d is the total dielectric loss in units of decibels per (gigahertz * centimeter).
Optical Analysis
- Fundamental Equations
- Hybrid EDGE/ NODAL Elements
- Finite Element Discretization
- Calculation of Half-Wave Voltage-Length Product V L
For the lowest order element the tangential component t is constant along each side of the triangle, but for higher order element it is approximated to linear order. 4.1, the transverse components x, and the axial component y z of the unknown φ in each element are approximated as. For a better understanding of the shape functions, we first describe the importance of shape functions for a linear nodal triangular element of Fig.
By taking advantage of the sparsity of the finite element matrices in the hybrid element algorithm, it is possible to handle problems involving matrices in the thousands. The term VL is the product of the device half-wave voltage (V) and the interaction length (L), and it is the key parameter of an EOM. This bias can be achieved by applying a voltage, V 12V , where a small sinusoidal modulation voltage will cause an almost sinusoidal modulation of the transmitted intensity as illustrated in fig.
Solving the Problem Using MATLAB
- An Overview of the PDE Toolbox
- The Type of Problems that can be solved by PDE Toolbox
- Areas in which PDE Toolbox can be used
- Defining a PDE Problem
- Solving a PDE Problem
- Adaptive Mesh Refinement
- Microwave Analysis of EOM Using PDE Toolbox
- Application Mode
- Geometrical Description
- Applying Boundary Conditions
- PDE Mode
- Mesh Refinement
- Finding and Plotting the Solutions
- Further Processing of the Results
- Data Processing for Optical Analysis
The accuracy of the numerical solution can be evaluated by comparing the results from a sequence of sequentially refined grids. The PDE Toolbox can be applied to a large number of problems in engineering and science. Using the “Electrostatics” mode of the PDE Toolbox, electrostatic problems can be modeled using the above equation [33].
The set formula option was used to obtain a 100 μm by 100 μm cross section of the modulator structure. Using the boundary condition mode, boundary conditions were applied to the various boundaries of the structures. The PDE mode view of the PDE toolbox for an unetched structure is shown in Fig.
Simulation Results and Discussion
Microwave Characteristics
- Capacitance per unit Length
The arrows point away from the hot electrode, which is essentially the direction of the electric field. The contour plots show that the maximum electric field occurs at the edge of the electrodes and here of course the field points from the hot electrode to the ground electrode (which in this case is a highly doped region) except at the edge of the metal conductor. To find the microwave properties of the structure, it is necessary to find the first capacitance.
We see that there is a decrease in capacitance with the increase in the thickness of the buffer layer. But an important issue is that there is no variation in the capacitance when the electrode thickness changes. So for all three electrode thicknesses the capacitance curve overlaps and appears to be a single curve.
Buffer layer thickness, B( m)
Microwave Index and Characteristic Impedance
With the help of C and C0, we can easily calculate the microwave index Nm and the characteristic impedance Zc. First, we show the variation of the microwave index, Nm, and the microwave characteristic impedance, Zc, with the interlayer thickness, B, for two different values of the core height, H, given in Figure 6.8. As shown in the figure, the microwave index Nm decreases almost linearly, while the microwave characteristic impedance Zc.
The variation of the microwave index, Nm and the microwave characteristic impedance Zc with the thickness of the buffer layer, B for three different values of the electrode thickness T is given in figure. From the figure we see that with the increase in the thickness of the buffer layer, the values of Nm. In the case of characteristic impedance Zc, we find that the values of Zc increase with the variation of the thickness of the buffer layer.
Dependence on Atomic percentage of Buffer layer
Atomic percentage of the buffer layer
Atomic percentage of the buffer layerEffective index,Nm
Microwave Loss Characteristics
Here we can see that the attenuation constant decreases with increasing thickness of the interlayer. But as the thickness of the electrode increases, the attenuation constant decreases for a given thickness of the interlayer. However, the rate of decrease of the attenuation constant with B at different T is very slow.
Buffer layer thickness, B( m)Conductor loss,c (dB/GHz0.5cm)
Optical Bandwidth Estimation
The bandwidth of an optical modulator depends mainly on the phase mismatch between the optical and microwave phase velocities. However, when matched, a maximum optical bandwidth is achieved, and this value is limited by the total microwave loss. Variation of the optical bandwidth of 3 dB with the thickness of the buffer layer for different metal electrode losses is considered, but the effect of impedance mismatch is neglected.
When only the conductor loss is considered and the dielectric loss is neglected, the bandwidths calculated by equation (4.24) are shown by the solid lines in the figure. However, this maximum value of 124.5 GHz is larger than that of 1 µm, since the microwave loss is greater in this case.
Optical Mode Fields
As mentioned in section 2.3, the optical analysis should be performed after taking the electro-optical effect into account. This new refractive index is calculated using the procedure of Section 2.3 and then optical analysis is performed using the FEM as described in Section 4.2. And that the index change in the dominant x and z components should be significant in this case.
Half-wave voltage length product of the EOM
Next, we show the variations of VπL with H for different aluminum concentrations of the buffer layer in fig. Since the increase of aluminum concentration leads to an increase in the refractive index difference between the core and the buffer layer in such a way that the optical field of the E11y mode will be pushed slightly downward and away from the hot electrode, this would lead to a slightly lower interaction between the electric field and the optical field, giving rise to the small increase in VπL with the increase in aluminum concentration. 6.21, the variations of VπL with the electrode width Wel at different values of the waveguide width and the core height are shown.
Thus, the width of the electrode should not be narrower than the width of the waveguide, but could be equal to the width of the waveguide in order to improve performance and also facilitate its manufacture. When the electrode width is small compared to the waveguide width, the electric field profile spreads less in the horizontal direction compared to the case when it is wider, giving less overlap with the optical field profile. The figure also shows that for the same core height H, the value of VπL remains the same as long as the width of the electrode and the width of the waveguide are almost similar.
This reduction in VπL as H is reduced is a direct consequence of the increased electric field intensity, and thus lower voltages are required to maintain the 180° phase difference at the output ports of the MZ structure.
Conclusions and Suggestions for Future Work
Scope of future work
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