In terms of the Gaussian beam parameter and Gouy phase, the parametric equations for geometric rays of periodic orbits in spherical resonators are originally generalized as the real parts of polar forms. The derived polar forms are employed to create an analytical wave-packet representation for unifying the ray and wave. The developed wave-packet representation can concurrently manifest the geometric modes and eigenmodes in the degenerate and nondegenerate cavities. Complete comparisons with experimental data are made not only to verify the derived wave-packet representation, but also to disclose the transition from the eigenmodes to geometric modes by increasing the transverse order in a degenerate cavity.
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17 May 2019: A typographical correction was made to Eq. 9.
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