Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) isimportant for tailoring them to experimental needs. Here we report on a novelexperimental mode analysis technique based on the combination of frequencyanalysis and far-field imaging for high mode numbers of large WGMRs. The radialmode numbers q and the angular mode numbers p=$\ell$-m are identified andlabeled via far-field imaging. The polar mode numbers $\ell$ are determinedunambiguously by fitting the frequency differences between individualwhispering gallery modes (WGMs). This allows for the accurate determination ofthe geometry and the refractive index at different temperatures of the WGMR.For future applications in classical and quantum optics, this mode analysisenables one to control the narrow-band phase-matching conditions in nonlinearprocesses such as second-harmonic generation or parametric down-conversion.
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