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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。
Starting from the eigenvalue of optical microsphere cavity resonance mode, an effective method to calculate the size parameter (x) interval between resonance modes by the derivation method is proposed. On the basis of the calculation formula of the dimension parameter obtained by Lam, the quantum number (l) must be an integer and much larger than 1 according to the resonance mode. The dimension parameter interval between adjacent modes (Δl = 1) can be approximated as corresponding The derivative of the size parameter, so that the derivative method can be used to calculate the size parameter spacing between resonance modes. The results show that the relative error between the size parameter of resonant mode with radial quantum number i = 1 and the exact numerical solution obtained by Mie scattering theory is within 0.05%, which is basically consistent with the experimental data. The derivation method does not need to be cumbersome series expansion, thus greatly simplifying the calculation program, which provides theoretical guidance for the experimental study of the optical microsphere cavity.