Far-field characteristics of coherently combined beams emitted from arrays on multiple polygons

By using Fourier Optics, the general analytical expression of intensity distribution for the coherently combined beams positioned on the X-Y plane, which is applicable to both Gaussian and non-Gaussian beams, can be derived. Considering the fact that in many cases the array configuration can be regarded as composed of several regular polygons with a common center, an explicit analytical expression of the far-field intensity distribution for these cases has been derived. As an example, the above expression has been applied to study a 19 emitter array. Studies have also been done on the dark fringes of the far-field pattern for the specific emitters, whose numbers are 2 and 4, respectively.