On the Counterpropagation of Waves

Abstract This work analyses the counterpropagation of transversal plane waves in a linear, homogeneous, nondispersive, and isotropic medium. Although this is a traditional subject in disciplines associated with wave phenomena, a propagation analysis is not found in the literature. With this purpose, the resultant wave and consecutively its phase velocity in such system are obtained analytically. Instead of what happens with the individual waves, the analytical results demonstrate that the phase velocity of the resultant wave actually is not a constant and depends explicitly of the time or the spatial coordinates, and principally depends of the amplitudes of the individual waves. This last remarkable feature, when considering as example electromagnetic systems, can be used to adequately control and accelerate particles in a charged medium. Full agreement between the analytical and numerical results is found.

摘要 本研究针对线性、均匀、无色散且各向同性介质中横向平面波的对向传播展开分析。尽管该主题属于波动现象相关学科中的经典议题，但现有文献中尚未见针对其传播特性的系统分析。基于此研究目标，本文通过解析方法推导得到该系统中的合成波及其相速度。与单一平面波的传播特性不同，解析结果表明，合成波的相速度并非恒定值，其显式依赖于时间或空间坐标，且主要由单一入射波的振幅所决定。若以电磁系统为例，这一显著特性可用于实现带电介质中粒子的有效调控与加速。解析结果与数值模拟结果完全吻合。