How to control single mode emission of VCSEL arrays?

The efficient way to increase the emitted power by VCSEL is to combine several emitters into phase-locked array. There is a strong motivation to develop a design of the VCSEL arrays that will emit in a single and narrow linewidth. In VCSEL arrays one can observe two types of modes. First kind are modes of single emitters, second are the array supermodes formed of the same order of single-emitter modes. The key to narrow the width of emission spectrum is to reduce the number of existing modes down to only one. First kind of modes are known to be governed mainly by the dimension of the single emitter and patterning of optical confinement. The type and number of design parameters that control the second kind of the modes is known much less.