Analysis of coupling coefficient between two vertical cavity surface emitting lasers for two-dimensional phase-locked array

The coupling coefficient between two adjacent circular vertical cavity surface emitting lasers having an InGaAs strained quantum well active region ( lambda _g=1 mu m) and a GaAs cavity has been analysed. The analysis was performed for Al_0.3Ga_0.7As cladding (n=3.325) and air (n=1). In order to obtain a coupling coefficient of 10^-3, which is known for the stable phase locking of array, the laser separation must be less than 0.25 mu m for the lasers of radius 0.4 mu m with air cladding and be less than 0.72 mu m for the lasers of radius 1.2 mu m and Al_0.3Ga_0.7As cladding. Various structures of two-dimensional phase-locked arrays, such as periodic, circular and concentric circular arrays, can be realised by bringing lasers into close proximity, the separation value of which can be obtained from the analysis.