Besieris Ioannis M, Shaarawi Amr M
The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24060, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 2):056612. doi: 10.1103/PhysRevE.72.056612. Epub 2005 Nov 29.
A hybrid spectral superposition method is presented that allows a smooth transition between two seemingly distinct classes of localized wave solutions to the homogeneous scalar wave equation in free space; specifically, luminal or focus wave modes, and superluminal or X waves. This representation, which is based on superpositions of products of forward plane waves moving at a fixed speed v>c and backward plane waves moving at the speed c, is used to construct a large class of finite-energy superluminal-type X-shaped localized waves. The latter are characterized by arbitrarily high-frequency bands and are suitable for applications in the microwave and optical regime. In the limiting case v-->c, one recaptures the well-known focus wave mode-type localized wave solutions. A modified hybrid spectral representation, based on superpositions of products of forward plane waves moving at a fixed speed c and backward plane waves moving at the speed v>c, allows in the limit v-->c a smooth transition from superluminal localized waves to paraxial luminal pulsed beams. Although the proposed methods are applicable to a (n+1)-dimensional, n> or =2, scalar wave equation, the discussion will be limited to the case n=2 for simplicity; also, so that comparisons can be made to related recent results in the literature.
提出了一种混合谱叠加方法，该方法允许在自由空间中齐次标量波动方程的两类看似不同的局域波解之间进行平滑过渡；具体而言，是腔内或聚焦波模式以及超光速或X波。这种表示基于以固定速度v>c传播的正向平面波与以速度c传播的反向平面波的乘积的叠加，用于构建一大类有限能量的超光速型X形局域波。后者的特征在于具有任意高的频带，适用于微波和光学领域。在极限情况v→c时，可以得到众所周知的聚焦波模式型局域波解。一种基于以固定速度c传播的正向平面波与以速度v>c传播的反向平面波的乘积的叠加的改进混合谱表示，在极限v→c时允许从超光速局域波到傍轴腔内脉冲光束的平滑过渡。尽管所提出的方法适用于(n + 1)维（n≥2）标量波动方程，但为简单起见，讨论将限于n = 2的情况；此外，以便能够与文献中相关的最新结果进行比较。
