The Influence Of Turbulence On Propagation And Far-field Beam Quality Of Hermite-Gaussian Beams And M×N Cosh-Gaussian Beams

The propagation of light beams in atmospheric turbulence is a topic that has been of considerable theoretical and practical interest. On the one hand, actual laser are often in muti-mode operation. Therefore, the study of the propagation of high-order Gaussian beams in atmospheric turbulence is important. On the other hand, high-power beams can be obtained by technique of beam combination, which may maintain high beam quality. Therefore, the propagation properties of combined beams in atmospheric turbulence are of importance in many practical applications. This paper is divided into three parts:1. Based on the extended Huygens-Fresnel principle, the propagation equation of three-dimensional intensity of Hermite-Gaussian (H-G) beams through the turbulent atmosphere is derived. It is shown that a H-G beam retains its beam character when it propagates in free space; but a H-G beam in turbulence undergoes three stages of evolution with increasing propagation distance, and at last it turns into Gaussian-like profile in the far field. Furthermore, the evolution of the three stages which H-G beams propagate in turbulence accelerates due to increasing turbulence. The turbulence results in a beam spreading and decrease of the maximum intensity. However, H-G beams with higher order numbers m and n are less affected by the turbulence than those with lower m and n.2. The propagation properties of one-dimensional off-axis Gaussian beams through turbulent atmosphere are studied in detail. The propagation equation of intensity is derived. It is shown that one-dimensional off-axis Gaussian beams in turbulent atmosphere undergo three stages of evolution with increasing propagation distance z, i.e., their beam profile with saw tooth is similar to the initial one in the near field, and then it becomes a flat-topped profile with increasing z, at last it turns into Gaussian-like profile in the far field. The turbulence accelerates the evolution of three stages which one-dimensional off-axis Gaussian beams undergo. Furthermore, the normalized intensity distributions of one-dimensional off-axis Gaussian beams with different beam numbers are close to each other due to turbulence. In addition, one-dimensional off-axis Gaussian beams with higher beam numbers are less sensitive to the effects of turbulence than those with lower beam numbers, and one-dimensional off-axis Gaussian beams are less sensitive to the effects of turbulence than Gaussian beams.3. Based on the extended Huygens-Fresnel principle, the propagation equation of three-dimensional intensity of M×N cosh-Gaussian (ChG) beams through atmospheric turbulence is derived by using incoherent combination. The power in the bucket (PIB),β-parameter and Strehl ratio ( S R) are chosen as the parameters characterizing the beam quality in the far field, and the influence of turbulence on the far-field beam quality is studied. It is shown that turbulence accelerates the evolution of three stages. The turbulence results in a spreading and degradation of the maximum intensity in the far field. However,β-parameter decreases with increasing beam numbers M (N), separate distances xd (yd) and beam parameterδ. Furthermore, there exist optimal values of xd (yd) andδ, SR of the corresponding M×N ChG beams reaches its maximum. Therefore, a suitable choice of M (N), xd (yd) andδmay reduce the influence of turbulence on the beam quality in the far field.