Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

By generalizing recently obtained results we calculate the excess noise fac tor (Petermann factor) for a laser system with non-orthogonal eigenmodes. T he quantum consistency of the calculation is shown through the explicit con servation of input-output commutation rules. As a result of the calculation , the excess noise in the lasing mode is shown to depend on the laser gain below threshold, and on the noise analysis frequency below and above thresh old.