Study of the Dimensionality Reduction Approach for the Efficient Simulation and Optimization Design of Terahertz Lens with Electrically-large Dimension

Dielectric lenses are widely used in terahertz imaging and communication systems to focus or collimate the Gaussian beam by adjusting the phase distribution of wave front. However, due to the high frequency and short wavelength of the terahertz band, the focusing lenses used in the application systems are usually electrically large, which bring the extremely difficulty to carry out efficient electromagnetic (EM) simulation and optimization design. In this paper, a dimensionality reduction concept was introduced to achieve efficient design and optimization of electrically-large terahertz lenses, which have symmetric structures and are commonly used in quasi-optical systems, such as circular lenses and cylindrical lenses. To precisely solve the EM problem with reduced dimension, a two-dimensional moment method (2D-MOM) for homogeneous dielectric targets was studied and successfully developed by solving the surface coupled integral equation discretized with appropriate basis and test functions. Then, the dimensionality reduction approach with the combination of the ray-tracing method (RTM) and the 2D-MOM was developed for the shaped design of terahertz lens with high efficiency. A 0.3THz lens with diameter 10cm was designed with the proposed approach as an example, with its pattern measured by a terahertz field scanning platform. It's found that, with the dimensional reduction, the unknowns can be reduced more than 1500 times and the memory required can be reduced more than 2.5 million times, as compared to the traditional 3D-MOM simulation. And the simulation results agree well with the experiments, which both demonstrate the greatly improved performance of the lens designed by the proposed approach, as compared to the standard lens.