When the photon is emitted, can you change the angular speed? This has been experimented with vortex beams but I don’t quite understand how it works. Also, an optional follow up question, would a photon’s angular speed have to be greater then it’s original speed in order to be linearly polarized or move in a curve.
What you are looking for is a photon OAM switch.
The OAM of light is the component of angular momentum of a light beam that is dependent on the field spatial distribution and not the polarization.
It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum.
The photon OAM is a discrete degree of freedom that characterizes the topological charge (winding of the azimuthal phase) of a photon field with cylindrical symmetry.
Therefore a natural question is whether a topological process can be designed to create a robust photonic OAM switching device with high performance. Recently, the study of topological photonics has become one frontier direction in optical physics with the major focus on modulating photon propagation through topological edge states [29–35], while practical topological photonic devices for on-demand switching of photon internal degrees of freedom are still largely lacking. Conventional spatial light modulator  and digital micro-mirror device  are limited by the switching rates of ∼kHz. Higher switching rates can be achieved by combing acousto-optic (electro-optic) modulator with SLMs (q-plate) [25, 28], or using on-chip resonators . However, the acousto-optic modulator would induce unwanted change in wavelength, and the on-chip switching has a very low efficiency. Moreover, all these approaches require precise control of experimental parameters and the number of usable OAM modes is usually very limited. In contrast, our scheme is robust against perturbations due to its topological feature, and also able to rapidly switch to high OAM modes with high efficiency. Our results of single-photon pumping can be generalized to multi-photon states or even classic coherent states. Since the system is linear with no interaction, every photon is pumped independently.