Vortex memory effect of light for scattering-assisted massive data transmission

The optical memory effect (ME) is a physical phenomenon that enables imaging through scattering media. Here we report an extended optical ME known as vortex ME (VME) in a continuous orbital angular momentum (OAM) space. When the azimuthal phase mode index $\ell$ carried by a vortex beam shifts slightly with $\mathrm{\Delta }\ell$, the scattering medium (SM)-encoded optical speckles will remain spatially correlated, and the correlation coefficient decays in the form of ${\text{sinc}}^2(\mathrm{\Delta }\ell )$. Even after passing through a strong multilayer SM, the inherent orthogonality among OAM variables will be transferred to the speckle-based correlation spectrum intact. The speckle-encoded OAM fractional spectrum enables high-resolution observations of the angular double-slit interference pattern in a single shot. For a vortex beam with a multiplexed OAM fraction spectrum, a generalized group VME (GVME) can be manifested, and it is confirmed that a strong SM can be an OAM-invariant system. Furthermore, we present a speckle-encoded secure optical communication scheme to reliably transmit color image data under various high-scattering conditions, with no need to measure the complex transmission matrix. The proof-of-principle experiments, with a channel capacity of $>16$ bits or polarization (or wavelength) multiplexing-enabled $\sim 32.1$ bits per shot, achieve a low symbol error rate ($<0.5\mathrm{\%}).$ This work provides an intriguing physical perspective of speckles for understanding continuous fractional OAM and the unerasable orthogonality, as well as promising approaches for diverse optical applications.