Recognition of fractional orbital angular momentum modes under scattering with transmission matrix

Vortex beams carrying fractional orbital angular momentum (FOAM) mode show great potential in optical encryption, anisotropic edge enhancement, optical communication, etc. However, the small mode interval of FOAM makes it sensitive to transmission scattering, which distorts the helical phase-front and leads to substantial mode crosstalk. Herein we propose a transmission matrix method to recognize FOAM modes under scattering. By constructing the linear relationship between the input and scattering field, a transmission matrix retrieval algorithm was used to recover the helical phase-front of the vortex beam from its intensity distribution, and FOAM mode was recognized via the phase period. We showed that FOAM modes under scattering are successfully recognized with an accuracy of >99.8%. As a proof-of-concept, a 100 × 100 pixel image was transmitted and recovered in a high scattering. Our results indicate that the transmission matrix method presents a new approach to recognize FOAM modes under scattering, which may benefit various FOAM applications.