光学微球腔谐振模式间隔参数的一种简便计算方法  

A simple calculation method for resonant mode separation parameters of optical microsphere cavities

作　　者：顾国强[1] 蔡志平[1] 许惠英[1] 王金章[1] 徐斌[1] 闫宇[1] 

机构地区：[1]厦门大学电子工程系,福建厦门361005

出　　处：《光电子．激光》2012年第12期2267-2272,共6页Journal of Optoelectronics·Laser

基　　金：国家自然科学基金(61275050);厦门市科技项目(3502Z20113004)资助课题

摘　　要：从光学微球腔谐振模式的本征方程出发,提出了一种利用求导法计算谐振模式间尺寸参数(x)间隔的有效方法。在Lam求得的尺寸参数计算公式基础上,依据谐振模式角量子数(l)必须为整数且远远大于1的性质,相邻模式(Δl=1)间的尺寸参数间隔可近似表示为相应尺寸参数的导数,从而可利用求导法计算谐振模式之间的尺寸参数间隔。研究表明,径向量子数i=1的谐振模式的尺寸参数间隔与Mie散射理论求得的精确数值解之间的相对误差在0.05%以内,并且与实验测量数据基本一致。求导法因不需要进行繁琐的级数展开,从而大大简化了计算程序,为光学微球腔的实验研究提供了理论指导。In this paper, an effective derivative method has been presented to calculate the size parameter （x） separation of adjacent resonant modes （△l= 1） based on the eigenvalue equation of the resonant modes of optical microsphere. Starting from Lam＇s formula of size parameter, the angular mode number （l） must be integer and far larger than 1 ,and we deduce that the size parameter separation of adjacent resonant modes can be approximated to the derivative of the corresponding size parameter. The researches show that the relative error of size parameter separation between the derivative method and the exact value from Mie scattering theory for radial order of i= 1 is less than 0.05 %, which is also consistent with the experimental data. Because the derivative method does not require cumbersome series expansion, it greatly simplifies the calculation procedure, and can provide important theoretical guidance for the experimental studies of optical microsphere cavities.

关 键 词：光学微腔 求导法 尺寸参数间隔 微球 

分 类 号：O433.4[机械工程—光学工程] TN248.1[理学—光学]