THE THEORETICAL ANALYSIS AND EXPERIMENTAL INVESTIGATION OF SUB-WAVELENGTH FOCUSING VIA CONCAVE LENS
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摘要:为了提升传统平面透镜的聚焦效果, 增加焦点处的能量, 缩小焦斑尺寸, 实现亚波长聚焦, 文章基于厚度变化设计了用于聚焦平面弯曲波的凹透镜. 首先, 基于Timoshenko梁理论求解了弯曲波在经历厚度变化后的透射系数及相位变化, 并基于此完成了凹透镜的结构设计; 其次, 应用有限元软件COMSOL Multiphysics的结构力学模块开展了该透镜频域内的工作性能分析, 包括聚焦位置及焦点处能量、焦斑尺寸等, 并与传统平面透镜的情况进行对比; 最后, 实验验证了凹透镜设计的合理性和正确性. 研究结果表明: 文章所设计的凹透镜使平面入射的弯曲波聚焦在预先设定位置, 且其性能优于传统的平面透镜, 焦点处的能量更高、焦斑尺寸更小; 凹透镜的焦斑尺寸小于工作波长的0.5倍, 属于亚波长聚焦; 此外, 该透镜还具有一定的工作频率带宽, 在结构参数不变的情况下能够在设计频率附近正常工作. 提出的透镜设计方法易于工程实现, 且聚焦性能优越, 设计思想也能为声波、光波等领域相关透镜的设计提供借鉴.Abstract:In order to improve working performance of traditional plane lens, i.e., increase energy at focal point, reduce focusing size, and achieve subwavelength focusing, a concave lens for focusing incident flexural wave is designed based on the plate thickness variation. Firstly, the transmission coefficient and phase variation are obtained by utilizing the Timoshenko beam theory, based on which the lens design is performed. After that, the working performance of concave lens designed is simulated via the frequency analysis in structural mechanics module of COMSOL multiphysics software, including the focal position, energy distribution, focusing size, and so forth, which are further compared with the traditional plane lens. Finally, the experimental measurements are carried out to further validate and conform the design scheme. It is demonstrated that the concave lens can focus the incident flexural wave at the specific position, with its performance better than the plane lens, because energy concentrated is higher and the focusing size is smaller. Specifically, it exhibits subwavelength focusing phenomenon with the focusing size smaller than half wavelength. Additionally, the concave lens is broadband, which can work at a frequency region centered at designed frequency even if the whole structure is maintained. The present design scheme is easy realized for engineering application, and the concave lens exhibits better performance, which can also provide guidance for the lens design in acoustics and optics.
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Key words:
- focusing lens/
- flexural wave/
- subwavelength focusing
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图 4工作频率f= 20 kHz情况下相位、透射系数和反射系数随厚度的变化趋势
Figure 4.Variations of phase and transmission coefficient versus thickness whenf= 20 kHz
图 5透镜各通道的相位及厚度
Figure 5.Phase and thickness values of individual elements of the curving lens designed
图 8实验结果: (a) 凹透镜(左)和平面透镜(右)在焦点附近电压平方的云图; (b) 电压平方沿x轴(左)和y轴(右)的分布
Figure 8.Results from experimental measurement: (a) The contour distributions of voltage square near the concave lens (left) and plane lens (right); (b) The distributions of voltage square alongx(left) andy(right) directions, respectively
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