Numerical Analysis of Sound Pressure Fields Focused by Phase Continuous Fresnel Lens Using Finite Difference Time Domain Method

A convex lens using room temperature vulcanization (RTV) silicone rubber, whose acoustic impedance matches well with that of water, is a typical acoustic lens. However, some considerations are required to reduce the thickness of the lens because attenuation is very large in the RTV silicone rubber. Therefore, we have proposed a phase continuous Fresnel lens, which has some devices to keep the phase continuous in the entire lens aperture without an unequal phase on the exit side. This lens is fabricated by removing its thickness in a staircase shape in which the difference between each step is an integer multiple of wavelength. In this study, the sound fields focused by the phase continuous Fresnel lens are analyzed using a finite difference time domain (FDTD) method. Using a two-dimensional (2-D) FDTD method, we surveyed the sound pressure field of the focal region by changing the burst pulse length, angle of incidence, and frequency. Results show that the lens gain of the phase continuous Fresnel lens is greater than that of the convex lens, that focusing characteristics depend on the burst pulse length of sound source signal, and also that focal points strongly depend on frequency. In another analysis using a three-dimensional FDTD method, we found that the main lobe is the same as that indicated by 2-D analysis results and that the level outer of the main lobe is lower than that in the 2-D analysis results.