Performance analysis of the Cassegrain telescope on the QKD with Mathieu-Gauss Beams

Mathieu-Gauss beams (MGBs), a distinctive class of structured light generated by modulating the angular and radial components of Gaussian beams with Mathieu functions, exhibit propagation characteristics that make them promising candidates for free-space optical (FSO) and quantum communication links. In this study, the scintillation behaviour of MGBs under weak atmospheric turbulence is analysed to derive the effective visibility and to quantify its impact on the quantum bit error rate (QBER) and secret key rate (SKR) in quantum key distribution (QKD) systems employing Cassegrain-type transmitters. Numerical simulations are performed using a random phase screen method based on the modified von Kármán spectrum for even and odd MGB modes under various telescope configurations. QBER is modelled as a function of effective visibility derived from the scintillation index. The results demonstrate that the use of a Cassegrain telescope significantly suppresses scintillation-induced degradation, reduces QBER, and enhances SKR, with improvements of up to 80% compared to free-space propagation without telescopic correction. However, the performance enhancement is strongly mode-dependent, with certain MGB orders exhibiting greater turbulence resilience. These findings highlight the importance of transmitter geometry and beam-structure optimisation in improving the robustness and efficiency of structured-light-based FSO-QKD systems.