Focused interdigital transducers (FIDTs) can generate surface acoustic wave (SAW) with high intensity and high beamwidth compression ratio. Owing to these features, they are very suitable to be used as the sources of microacoustic channels or waveguides in the near future. The focusing properties of FIDTs are dominated solely by their geometric shapes. Therefore, to obtain optimal performance, it is essential to analyze the FIDTs with a variety of geometric shapes. However, among the existing studies concerning the diffraction of FIDTs, a detailed analysis and design of FIDTs is still in paucity. In this paper, we adopted the exact angular spectrum of plane wave theory (ASoW) to calculate the amplitude fields of FIDTs on Y-Z lithium niobate (LiNbO3) with the shape as a concentric circular arc and the concentric wave surface. Based on the calculation results, we discussed the variations of the amplitude fields induced by changing number of pairs, degree of arc, and geometric focal length. In addition, the focusing properties of FIDTs on the (100)-oriented GaAs substrate were also analyzed and discussed. We also summarized the guiderules for designing a FIDT via four important factors. It is worth noting that the results of this study provide an important basis for designing various FIDTs to fit the desired applications.