Spatially and Temporally Nondiffracting Ultrashort Pulses
Spatially and Temporally Nondiffracting Ultrashort Pulses
复制标题
空间和时间非衍射超短脉冲
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
P. Saari
中科院分区：
文献类型：
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作者：
P. Saari
在过去的十年中，已经发现了三维波动方程的许多新的精确解，其名称本身-“飞溅模式”，“自聚焦波模式”，“定向能量脉冲序列”，“电磁子弹”，“无衍射贝塞尔光束”，“无衍射X波”，“弹弓脉冲”，“等--给出了这些奇异波包的局域化甚至粒子性质的概念（见参考文献1 -4及其参考文献）。不幸的是，到目前为止，它们中的大多数只存在于公式中，即使考虑有限孔径和有限不变传播（“无衍射”）距离的近似。这些解决方案的最有趣和前向传播版本的光学实现方式中的一个严重障碍是时间和空间定位所需的超宽带光谱内容。这就是为什么到目前为止，在这个新兴的前景领域的实验结果已经在射频域和声学成像中获得，后者在医学超声诊断的背景下被非常深入地研究。单色贝塞尔光束是一个显著的例外。轴对称贝塞尔光束的场振幅可以表示为：λ B <$J0（rksin θ）exp[i（zkcos θ - ω t）]，其中J 0表示零阶贝塞尔函数，r是到传播轴z的横向距离，k = ω /c是单色光的波数，θ是平面波分量相对于z轴的倾斜角。作为理想平面波解的柱面对应物，自上个世纪以来，它在数学物理中已经相当有名。然而，直到1987年，人们才证明，即使在物理上可实现的近似版本中，光束也基本上保持了其传播不变性：在横截面中具有中心亮点（例如70 μm半高宽）的光束，在70 cm的距离上没有显示出这个小光斑的扩展。
During the last decade a number of novel exact solutions to the three-dimensional wave equation have been discovered, whose names in themselves — “splash modes,” “self-focus wave modes,” “directed-energy pulse trains,” “electromagnetic bullets,” “nondiffracting Bessel beams,” “nondiffracting X waves,” “slingshot pulses,” etc. — give an idea of localized or even particle-like properties of these exotic wave packets (see Refs.1–4 and references therein). Unfortunately, so far the majority of them exists in formulae only, even if approximations of finite aperture and of finite invariant-propagation (“diffraction-free”) distance are considered. A serious obstacles in the way toward optical implementation of the most interesting and forward-propagating versions of these solutions is an ultra-wide-band spectral content needed for the temporal and spatial localization. This is why the experimental results in this emerging prospective field have been so far obtained in radio-frequency domain and in acoustic imaging, the latter being very intensively studied in the context of medical ultrasound diagnostics. The monochromatic Bessel beam is a remarkable exception. The field amplitude of an axisymmetric Bessel beam can be expressed as ФB ∝ J 0(r k sinθ) exp[i (z k cosθ — ω t)], where J 0 stands for the zeroth-order Bessel function, r is the transversal distance from the propagation axis z, k = ω /c is the wave number of the monochromatic light and θ is the tilt of the plane wave components with respect to the z axis. As a cylindrical counterpart of the ideal plane-wave solution, it has been rather well known in mathematical physics already since the last century. However, as recently as in 1987 it was demonstrated that the beam essentially maintains its propagation invariance property even in its physically realizable approximate versions: the beam possessing a central bright spot, e.g. of 70 μm FWHM, in the cross-section, shows no spread of this small spot over a distance of 70 cm.