近几十年来，人们已经对介电和金属材料的非线性散射和倍频效应作了很多的研究，得到了很多有意义的结果。最近左手材料在实验上被成功制备出来，人们也对这种新兴材料的性质作了许多的研究和讨论，发现这种材料与一般材料有着完全不同的新的特性，诸如负折射率、逆多普勒频移、负切连科夫效应等等。但是在柱状左手材料中非线性倍频效应会是怎样呢？本文对这个问题做了详细的研究。本文利用解析和数值计算相结合的方法，对柱状左手材料的非线性散射和倍频效应作了详细的讨论，分别对散射强度的角分布、散射交叉截面等不同情况进行了讨论和计算，我们发现由于左手材料特有的介电常数和磁导率，改变了介电材料原有的激发模式，由于介电常数和磁导率均为负值，使得电磁波可以在左手材料中传播，使得原来的高度局域化表面模不能存在，从而使得非线性散射在大部分左手区域中得到了抑制；但同时在某些频率下，介质表面会形成新的表面模，形成共振，从而极大地增强非线性散射，可以将散射强度提高2个量级。

In the recent decades, non-linear scattering and second harmonic generation (SHG) was fully discussed in metallic and dielectric materials, many significant results have been obtained. While on the other hand, the left-handed materials have been successfully man-made in recent years, people have also done some researches on these kinds of new materials, and found that the left-handed materials posses many unusual properties in comparing with the normal materials.In this paper, we have investigated the non-linear scattering and second harmonic generation of the infinite cylinder particles consisting of the left-handed materials by using both of the analytic and the numerical methods. The scattering cross section and angular distribution of the SHG intensity of the left-handed cylinder have been calculated respectively. Our results show that SHG can be surprised in the two-dimensional cylinder particles within the left-handed material under large frequency region in comparing with normal cylinder. This is because the left-handed material is transparent; the highly localized surface mode cannot be sustained. In contras in another frequency regions the SHG can also be improved about 2 orders, which is due to the appearance of the new surface modes.