On the Creation of Optical Bottle Beams

When we create “structured light” with single-frequency (laser) illumination, it is straightforward to use Fourier analysis to describe the result in terms of a superposition of inclined plane waves, each characterized by the same temporal frequency. These simple basis states will have reduced values for the z-component of their propagation vector, kz, which implies a longer spatial frequency along the optic axis. Propagation of a longer spatial frequency at the same temporal frequency implies superluminal phase velocity. Many popular junior-level optics texts fail to mention this phenomenon, and the Gouy Phase Shift that it gives rise to, so it could be of widespread interest to demonstrate how these simple effects can be put to use, e.g., in creating “bottle beams,” where a dark central region is surrounded by an uninterrupted shell of light. In our work, we aim to make use of a different set of basis states, namely propagation-invariant spatial modes, to systematically explore how the Gouy Phase shift varies as we vary the laser modes utilized