Overfelt P L
Research Department, Naval Air Warfare Center Weapons Division, China Lake, California 93555, USA.
J Opt Soc Am A Opt Image Sci Vis. 2001 Aug;18(8):1905-11. doi: 10.1364/josaa.18.001905.
A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.
采用右手螺旋非正交坐标系来确定齐次标量波动方程的螺旋局域波解。在螺旋坐标系中引入特征变量，即(u = \zeta - ct)和(v = \zeta + ct)，其中(\zeta)是沿螺旋轴的坐标，我们可以使用双向行波表示法，并得到波动方程的基本双向螺旋解的集合。这些集合不仅是双向的，即基于平面波的乘积，而且还可以分解为右旋和左旋解。基本螺旋解又可用于创建傅里叶和双向的一般叠加，由此可以合成波动方程的新解。这些基于螺旋双向叠加的新解属于局域波类别。这些新解的例子包括螺旋基高斯聚焦波模式、螺旋贝塞尔 - 高斯脉冲和螺旋声定向能量脉冲序列。其中一些解具有有趣的特性，即它们的形状和局域特性不仅取决于沿纵向轴传播的波数，还取决于归一化螺旋节距。
