中文摘要：

由柱形微腔中回音壁模式满足的本征值方程,得到确定回音壁模式位置和间距的近似解析公式。以此近似解析公式,首次对直径在215-328μm间的5个柱形微腔回音壁激光光谱做了模式标定。在用近似解析公式对柱形微腔激光光谱的数值作拟合的计算中,除了回音壁模的径向模式数（l）和角动量模式数（n）外无需其他拟合参数,解析公式的拟合值和实验激光光谱波长值间的偏差小于0.05 nm,拟合结果精确可靠。柱形微腔回音壁激光光谱模式的精确标定在模式的场分布计算以及频移型微腔生物传感器的研究应用中具有重要作用,文章介绍的方法亦可应用于柱形微腔直径和折射率的精密测量。

英文摘要：

Lasers with spherical or cylindrical dielectric resonators supported by whispering gallery modes（WGM） have attracted much interest due to their microscopic size,high cavity Q factor,and low lasing threshold.Cylindrical microcavity lasers based on the gain only in the evanescent field region of whispering gallery modes have been demonstrated in our recent works.The gain was excited by the evanescent wave of longitudinal optical pumping along the optical fiber.To well understand the obtained lasing spectra,the mode assignment is required.The explicit asymptotic formulas for the position and mode-interval of whispering gallery modes were obtained from the characteristic equation of whispering gallery modes in a cylindrical micro-cavity.The formulas were used to analyze the lasing spectra emitting from cylindrical microcavies which were evanescent-wave-gain pumped.The lasing spectra were found to be transverse magnetic modes（TM）,and then the spectra were mode assigned with two integers,i.e.,radial quantum numbers（l） and angular momentum numbers（n）.Based on the explicit asymptotic formulas,all of the spectra from five optical fibers with a diameter ranging from 215 to 328 mm were well mode assigned.In the match between experimental spectral data and the asymptotic formula,only two matched parameters（l,n） were used,and the wavelength deviation in the match was less than 0.05 nm,which indicated that the mode assignment was reliable and precise.The spectral mode-assignment of cylindrical micro-cavity is important for computing the spatial distribution of mode intensity and is crucial for the applications of frequency-shift biosensor built in cylindrical micro-cavities.The method introduced in this paper can also be used to measure the diameters and refractive indexes of cylindrical micro-cavies precisely.