Limited by the size and weight of prism and optical assembling, Rotational Risley-prism-array system is a simple but effective way to realize high power and superior beam quality of deflecting laser output. In this paper, the propagation of the rotational Risley-prism-array-based Gaussian beam array in atmospheric turbulence is studied in detail. An analytical expression for the average intensity distribution at the receiving plane is derived based on nonparaxial ray tracing method and extended Huygens-Fresnel principle. Power in the diffraction-limited bucket is chosen to evaluate beam quality. The effect of deviation angle, propagation distance and intensity of turbulence on beam quality is studied in detail by quantitative simulation. It reveals that with the propagation distance increasing, the intensity distribution gradually evolves from multiple-petal-like shape into the pattern that contains one main-lobe in the center with multiple side-lobes in weak turbulence. The beam quality of rotational Risley-prism-array-based Gaussian beam array with lower deviation angle is better than its counterpart with higher deviation angle when propagating in weak and medium turbulent (i.e. Cn2 < 10-13m-2/3), the beam quality of higher deviation angle arrays degrades faster as the intensity of turbulence gets stronger. In the case of propagating in strong turbulence, the long propagation distance (i.e. z > 10km ) and deviation angle have no influence on beam quality.
Rotational Risley-prism-array system is an effective way to realize high power and high beam quality of deflecting laser output. In order to reveal the quality performance of deflecting beam, the beam compression in the direction of deflection and far field energy centrality of a hexagonal-distributed 7-Gaussian beam array based on rotational Risley-prism-array were studied in detail in this paper. The analytic formulae of the pointing position for the outgoing beam based on the prisms’ rotational angles are calculated by using nonparaxial ray tracing method. Then, the analytical expression for intensity propagation was derived based on the extended Huygens-Fresnel principle. From the irradiance distribution and PIB curve in the focal plane, the quantitatively simulation shows that the beam compression will be more significant as the deflecting angle of emergent increases. The energy centrality will decrease as the propagation distance increases, the fill factor decreases and the deviation angle increases. The mathematical model and calculation results can offer a reference for optical engineering application.
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