The use of semiconductor optical amplifiers (SOA) in optical communications networks has so far been limited due to their inherent large noise figure (NF) compared to Erbium Doped Fibre Amplifiers. Therefore improvement of the noise performance of SOAs is critical to their widespread adoption in future networks. We propose to reduce the NF of the SOA by introducing a lasing cavity lateral to the axis of amplification of the device. The carrier density within the cavity is clamped at the lasing threshold. It is thus possible to engineer the carrier density distribution along the active waveguide by controlling the cavity design. According to our simulations, some of the cavity designs lead to a reduction of the noise figure in this novel SOA.