An investigation of stair mode in optical phased arrays using tiled apertures

With an optical phased array, the individual phases of a multi-fiber laser source can be manipulated by exploiting high-bandwidth phase loops to correct for aero-optical flow over the turret and free-stream atmospheric effects along the line of sight; however, rough surface scatter through laser-target interaction adds the additional constraints of speckle and depolarizing effects. In particular, speckle phenomena can cause unobservable modes to arise in the beam control system of optical phased arrays. One such unobservable mode is termed stair mode and is appropriately identified by a stair-step pattern of piston phase across the individual subapertures that comprise a tiled aperture. This paper investigates the effects of stair mode using wave-optics simulations. To represent different array fill factors in the source plane, both seven and 19 element hexagonal close-packed tiled apertures are used in the simulations along with both Gaussian and flat-top outgoing beamlets. Peak Strehl ratio and power in the bucket are calculated in the target plane for all simulation setups and are then averaged for multiple random realizations of stair mode step sizes. In addition, the stair mode target irradiance patterns are imaged with cameras which have decreasing aperture stop diameters. Initial results show that low resolution imaging conditions, i.e. an aperture stop on the order of a subaperture diameter, makes it difficult to distinguish between different realizations of stair mode using a separate camera sensor.