无衍射加速波：韦伯波和抛物线动量
Nondiffracting Accelerating Waves: Weber waves and parabolic momentum
摘要：
衍射是物理学的普遍现象之一，如何克服它一直是物理学家的挑战。为了控制绕射，结构波的研究已成为决定性的。在这里，我们提出了一类特殊的无衍射空间加速解的麦克斯韦方程组：韦伯波。这些非傍轴波沿着抛物线轨迹传播，同时近似保持其形状。它们以解析的封闭形式表示，并且在向前和向后传播中自然分离。我们表明，韦伯波是自我修复，可以形成周期性呼吸波，并有一个定义良好的守恒量：抛物线动量。我们发现，我们的韦伯波中到大值的抛物动量可以描述的调制艾里函数。由于韦伯波是波动方程的精确时谐解，它们对自然界中的许多线性波系统都有影响，从声波、电磁波和弹性波到流体和膜中的表面波。
英文摘要：
Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a specific class of nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape. They are expressed in an analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solutions of the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic, electromagnetic and elastic waves to surface waves in fluids and membranes.
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