The University of Queensland
School of Information Technology & Electrical Engineering COMS7309 Computational Techniques in Electromagnetics Assignment 2, S2 2020
These exercises related to course material in related to the 2D-FDTD method
Introduction:
Dielectric lens, as a well-known concept usually employed in optical applications, is now widely used in the antenna design at millimetre-wave frequencies. As an example, shown in Fig.1a, the antenna integrated with convex dielectric lens structure tends to possess many interesting radiation properties to align with the modern communication and remote sensing systems. As indicated in Fig.1b, one of the most useful features of the convex dielectric lens is to focus the RF energy into a focal point, or in other way, to refract the energy from a point source and generate a planar wavefront. The distance from the focal point to the plate of the lens (𝑓) can be determined via the lens’ geometry (curvature radius 𝑅1 and 𝑅2) and its permittivity value (𝜖𝑟).
1 = (√𝜖
)( 1 + 1 )
𝑟−1
𝑓𝑅 1𝑅
2
Fig.1. (a) Dielectric lens antenna, (b) Biconvex lens geometry and focal point distance
Finite difference time domain (FDTD) technique is a good numerical approach to investigate the electromagnetics propagation/scattering behaviour that interact with the dielectric lens geometry in both 2D and 3D scenarios, it has been widely used in the design and optimization process of the dielectric lens structure. Since most of the lens-integrated antenna structure is of rotational symmetry along its central axis, the 3D electromagnetic problem can be solved by simplified electromagnetic simulations conducted in 2D space.
Task:
In this assignment, a 2D-FDTD simulator based on the dielectric lens geometry is required to be programmed. As shown in Fig.2, a biconvex lens with permittivity value (𝜖𝑟 = 4.0) is positioned in the computational domain, its radius of curvature on both sides are of 𝑅1 = 𝑅2 = 20𝑚𝑚; the diameter of the lens is D=20mm. A point source operates at the frequency range from (40~60 GHz) is located at right side of the lens with a focal distance of 𝑓 = 10𝑚𝑚.
Task1: Please build the code to generate a standard FDTD updating procedure with 𝑇E𝑧 wave within the computational domain surround the lens and point source; apply the Perfect Matching Layer (PML) boundary condition on the edge of the rectangular computation domain. Investigate the wave propagation behaviour while the point source is operating over a series of single frequency at 40 GHz, 50 GHz, and 60 GHz respectively.
Task2: Generate a Gaussian pulse at the point source that covers the whole band over 40~60 GHz, and repeat the FDTD simulation. Investigate the simulated field (H𝑧, E𝑥, E𝑦) in the computation domain and
evaluate the goodness of planar wavefront on the left side of the lens (Hint: select a number of points with equal distance to the lens’ plane and plot the field strength in time domain).
Fig.2. the biconvex lens illuminated by the point source to be simulated by 2D FDTD method
In order to build up the lens’ geometry and place the point source in its focal position, a reference MATLAB code is provided as an example to depict the geometry. As shown in Fig.3, the code would generate a binary-mask matrix indicates the lens geometry (wherein ‘1’ presents the occupation of lens, ‘0’ presents the vacant space), a red star ‘*’ presents the source position is depicted on the right side of the lens.
Fig.3. the binary-mask matrix generates from the provided MATLAB code
Please provide your MATLAB (or any other programming language) code with detailed comments for the above tasks.