Differences between the geometric phase and propagation phase: clarifying the boundedness problem

We show white light interferometer experiments that clearly demonstrate the basic differences between geometric and propagation phases. These experimental results also suggest a way to answer the "boundedness problem" in geometric phase-whether geometric phase is unbounded (i.e., can take on any values without limit) or bounded (i.e., limited to values between -π and +π). We show why the answer to this question is not as easy as it seems, from both a theoretical and an experimental perspective, and explain how the answer depends on one's choice of phase convention. We also hope that the videos provided will be pedagogically useful for explaining geometric phase.