二维电磁亥姆霍兹腔中回音壁模式研究

Whispering gallery mode in a two-dimensional electromagnetic Helmholtz cavity

基于严格的广义双级数方法,研究了二维电磁亥姆霍兹腔内回音壁模式的激发;在给出几种回音壁模式的激发波长的同时,探讨了入射角、亥姆霍兹腔开口大小对回音壁模式的影响.结果表明,回音壁模式对入射波长和腔开口大小的改变非常敏感,但相比而言,固定腔的方位角不变时,入射角在较宽范围内的变化并不影响模式的激发.因此,腔的开口大小对亥姆霍兹腔的性能有很大影响,是亥姆霍兹腔设计中需要重点关注的参量.而当这些亥姆霍兹腔用于构建人工电磁材料时,由于回音壁模式可在较宽的入射角下激发,因而不需要严格要求每个腔的开口方向,材料的加工难度也不大.

In this paper, whispering gallery mode(WGM) excited in a two-dimensional electromagnetic Helmholtz cavity are studied using a rigorous, generalized dual series approach. The excitation wavelengths of several whispering gallery modes are given, and the dependence of electromagnetic whispering gallery modes on the angle of incidence and the angular width of opening cavities is investigated. It was found that WGM are very sensitive to slight changes in wavelength or the angular width of the opening;at the same time, WGM can be excited across a wide range of incident angles given a fixed orientation angle of the cavity. This shows that the angular width of the opening has a significant influence on the performance of Helmholtz cavities and hence is a key parameter in their design. On the other hand, given the lack of sensitivity to the incident angle, no particular specification is needed when designing an artificially structured electromagnetic material using these Helmholtz cavities;accordingly, the fabrication difficulty is relatively low.