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

In this paper,an effective derivative method has been presented to calculate the size parameter(x) separation of adjacent resonant modes(Δl=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.