/? collinearity in a helical beam: https://www.google.com/search?q=collinearity+in+a+helical+beam https://www.google.com/search?q=collinearity+in+a+helical+be.

/? collinearity in a helical beam: https://www.google.com/search?q=collinearity+in+a+helical+beam https://www.google.com/search?q=collinearity+in+a+helical+be... "Collinear superposition of multiple helical beams generated by a single azimuthally modulated phase-only element" (2005) https://opg.optica.org/ol/abstract.cfm?uri=ol-30-24-3266 https://opg.optica.org/ol/abstract.cfm?uri=ol-30-24-3266 https://scholar.google.com/scholar?cites=4433448650775789641&as_sdt=5,43&sciodt=0,43&hl=en https://scholar.google.com/scholar?cites=4433448650775789641... OAM: Orbital Angular Momentum of Light: https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_li... "Universal orbital angular momentum spectrum analyzer for beams" (2020) https://link.springer.com/article/10.1186/s43074-020-00019-5 https://link.springer.com/article/10.1186/s43074-020-00019-5 https://scholar.google.com/scholar?cites=7156827987133110450&as_sdt=5,43&sciodt=0,43&hl=en https://scholar.google.com/scholar?cites=7156827987133110450... : "Approaching the Fundamental Limit of Orbital Angular Momentum Multiplexing Through a Hologram Metasurface" (2022) https://arxiv.org/abs/2106.15120 https://arxiv.org/abs/2106.15120 > This limit considers only one type of polar- ization, and it should be doubled if dual polarizations are adopted. If more plane-wave modes beyond this limit are added, they will not be distinguishable or angularly re- solved. Evanescent modes are required to support the expanded angular spectrum, which, however, are not suitable for far-field communication. "Phase Singularities to Polarization Singularities" (2020) https://www.hindawi.com/journals/ijo/2020/2812803/ https://www.hindawi.com/journals/ijo/2020/2812803/ : > The phase gradient in a phase singularity and azimuth gradient in a polarization singularity circulate around the respective singularities. "Engineering phase and polarization singularity sheets" (2021) https://www.nature.com/articles/s41467-021-24493-y https://www.nature.com/articles/s41467-021-24493-y : > Optical phase singularities are zeros of a scalar light field. The most systematically studied class of singular fields is vortices: beams with helical wavefronts and a linear (1D) singularity along the optical axis. Beyond these common and stable 1D topologies, we show that a broader family of zero-dimensional (point) and two-dimensional (sheet) singularities can be engineered. We realize sheet singularities by maximizing the field phase gradient at the desired positions. These sheets, owning to their precise alignment requirements, would otherwise only be observed in rare scenarios with high symmetry. Furthermore, by applying an analogous procedure to the full vectorial electric field, we can engineer paraxial transverse polarization singularity sheets. As validation, we experimentally realize phase and polarization singularity sheets with heart-shaped cross-sections using metasurfaces. Singularity engineering of the dark enables new degrees of freedom for light-matter interaction and can inspire similar field topologies beyond optics, from electron beams to acoustics.