无衍射（局域）波的结构及其应用
Structure of the Nondiffracting (Localized) Waves, and some interesting applications
摘要：
自从早期关于所谓的无衍射波（也称为局部化波）的工作[1-4]以来，从理论和实验的角度来看，已经发表了大量关于这个重要主题的结果。最初，该理论仅考虑自由空间;然而，近年来，它已扩展到表现出色散[5-7]，非线性[8]，各向异性[9]和损耗[10]等效应的更复杂的介质。这种扩展已经随着获得亚光速、光速和超光速状态中的无衍射光束和脉冲的有效方法的发展而进行[11-18]。本文（部分评论）地址的一些理论方法有关的无衍射解的线性波动方程在无界均匀介质中，以及一些有趣的应用，这样的波。在第二节中，我们分析了局域波的一般结构，发展了所谓的广义双向分解，并用它得到了波动方程的几个光和超光速（特别是X形）无衍射解。在第三节中，我们发展了一种通过不同速度的X形脉冲连续叠加的时空聚焦方法。第四节研究了啁啾X形光脉冲在无边界介质中的传播特性。最后，在第五节中，我们将展示如何使用贝塞尔光束的适当叠加来获得具有静态包络和高横向局部化的定常局部化波场，并且其纵向强度图案可以在传播轴的选定间隔内呈现任何所需的形状。
英文摘要：
Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially, the theory was developed taking into account only free space; however, in recent years, it has been extended for more complex media exhibiting effects such as dispersion[5-7], nonlinearity[8], anisotropy[9] and losses[10]. Such extensions have been carried out along with the development of efficient methods for obtaining nondiffracting beams and pulses in the subluminal, luminal and superluminal regimes[11-18]. This paper (partly a review) addresses some theoretical methods related to nondiffracting solutions of the linear wave equation in unbounded homogeneous media, as well as to some interesting applications of such waves. In section II we analyze the general structure of the Localized Waves, develop the so called Generalized Bidirectional Decomposition, and use it to obtain several luminal and superluminal (especially X-shaped) nondiffracting solutions of the wave equation. In section III we develop a space-time focusing method by a continuous superposition of X-Shaped pulses of different velocities. Section IV addresses the properties of chirped optical X-Shaped pulses propagating in material media without boundaries. Finally, in Section V, we show how a suitable superposition of Bessel beams can be used to obtain stationary localized wave fields, with a static envelope and a high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval of the propagation axis.
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