The topological evolution of classic eigenmodes including Hermite-Laguerre-Gaussian and (helical) InceGaussian modes is exploited to construct coherent state modes, which unifies the representations of travelingwave (TW) and standing-wave (SW) ray-wave structured light for the first time and realizes the TW-SW unified ray-wave geometric beam with topology of raytrajectories splitting effect, breaking the boundary of TW and SW structured light. We experimentally generate these new modes with high purity and dynamic control by digital holography method, revealing potential applications in optical manipulation and communication.
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