Ray-wave geometric beam is an exotic kind of structured light with ray-wave duality and coupled diverse degrees of freedom (DoFs), which has attracted intense attention due to its potential applications in theories and applications. This work offers a new insight that the traditional ray-wave geometric beams can be seen as the transverse standing-wave (SW) beams, and can be decomposed into the superposition of transverse traveling-wave (TW) beams. We construct a generalized model for transverse

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... TW and SW ray-wave geometric beams in the wave picture. In experiment, we exploit a digital hologram system with more flexible tunable DoFs to generate the transverse TW and SW beams, inspiring the exploration for the spatial wave structure of more complex structured light.