Strong coupling of the whispering gallery modes with bulk excitons in semiconductor cylinders is demonstrated theoretically. The strong-coupling threshold is governed by the radiative decay rate of optical modes, which we analyze as a function of the radius of the cylinder. Interestingly, the value of the Rabi splitting is found to be almost independent of the radius of the cylinder in the large limit. This is a consequence of the strong confinement of the whispering gallery modes.\u
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