Geometric modes outside the multi-bouncing fundamental Gaussian beam model

We demonstrate evidence for geometric modes which cannot be explained by the multi-bouncing fundamental Gaussian beam (MBFGB) model. First, we show that a single-frequency VW mode profile always has a bright-centered interference pattern according to the MBFGB model but becomes a dark-centered profile by varying the off-axial pump position. Second, the multi-frequency geometric modes cannot be interpreted by the MBFGB model but can be explained by wave representation. Third, a knife can break a narrow-N mode even when the knife does not hinder any of its expected multi-bouncing beams, which reveals the existence of higher order modes. Our simulations match very well with experiments.