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With the increased interest for interstellar exploration after the discovery of exoplanets and the proposal by Breakthrough Starshot, this paper investigates the optimisation of photon-sail trajectories in Alpha Centauri. The prime objective is to find the optimal steering strategy for a photonic sail to get captured around one of the stars after a minimum-time transfer from Earth. By extending the idea of the Breakthrough Starshot project with a deceleration phase upon arrival, the mission’s scientific yield will be increased. As a secondary objective, transfer trajectories between the stars and orbit-raising manoeuvres to explore the habitable zones of the stars are investigated. All trajectories are optimised for minimum time of flight using the trajectory optimisation software InTrance. Depending on the sail technology, interstellar travel times of 77.6-18,790 years can be achieved, which presents an average improvement of 30% with respect to previous work. Still, significant technological development is required to reach and be captured in the Alpha-Centauri system in less than a century. Therefore, a fly-through mission arguably remains the only option for a first exploratory mission to Alpha Centauri, but the enticing results obtained in this work provide perspective for future long-residence missions to our closest neighbouring star system.