Characterizing propagation-dependent spatial entanglement for structured laser beams generated by an astigmatic mode converter

The propagation-dependent spatial entanglement for the structured laser beams generated by an arbitrary incident Hermite–Gaussian (HG) mode passing through an astigmatic mode converter (AMC) is theoretically explored. The structured output beams are analytically decomposed into the expansion of HG modes for any given rotation angle of the AMC. Based on the Schmidt decomposition, the propagation-dependent spatial entanglements of the structured output modes are quantified with the von Neumann entropy. To manifest the propagation-dependent entropy, the probability distribution of the expanded HG modes in the structured output beam is quantitatively analyzed.