On scattering of waves by the infinite grating of circular cylinders
On scattering of waves by the infinite grating of circular cylinders
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DOI：
10.1109/tap.1962.1137940
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发表时间：
1962-11
影响因子：
5.7
通讯作者：
V. Twersky
中科院分区：
文献类型：
--
作者：
V. Twersky
本文将以前得到的任意单元的新函数方程特殊化，处理无限长圆柱光栅的边值问题。这指定的一组代数方程，其中只涉及一个孤立的圆柱体的散射系数的问题，和某些系列的基本功能。法向入射的特殊结果是相同的最初获得的Ignatowsky谁的分离变量的解决方案，作为检查，我们也延长他的程序到任意角度，并表明，结果可以转化为我们获得的绿色函数的方法。该方程用于构造系列和封闭形式的近似两个极化，导电和介电圆柱体，对于任意角度的入射。结果被施加到考虑多个散射或耦合效应的模式附近放牧（木材异常），并为紧密间隔的散射体（包装效果）。例如，我们表明，一级近似的包装效果E垂直于轴仅仅增加了孤立的圆柱体的偶极矩;在这个范围内，光栅内的圆柱体相当于一个孤立的椭圆形柱体的大小和形状是独立的入射角。我们还得到了简单的封闭形式的低频显式考虑耦合效应的2^{5}阶多极等。
The boundary value problem of the infinite grating of circular cylinders is treated by specializing the new functional equation obtained previously for arbitrary elements. This specifies the problem in terms of a set of algebraic equations which involves only the known scattering coefficients of an isolated cylinder, and certain series of elementary functions. The special results for normal incidence are identically those obtained originally by Ignatowsky who worked with the separation-of-variables solution; as a check we also extend his procedure to arbitrary angles and show that the results can be transformed to those we obtain by the Green's function approach. The equations are used to construct series and closed form approximations for both polarizations, for conducting and dielectric cylinders, for arbitrary angles of incidence. The results are applied to consider multiple scattering or coupling effects for a mode near grazing (Wood anomalies), and for closely spaced scatterers (packing effects). For example, we show that to a first approximation the packing effects for E perpendicular to the axes merely increase the dipole moment of the isolated cylinder; in this range, the circular cylinder within the grating is equivalent to an isolated elliptic cylinder whose size and shape are independent of angle of incidence. We also obtain simple closed forms for low frequencies which take explicit account of coupling effects up to multipoles of order 2^{5} , etc.