Propagation Properties Of Laser Beams Through A Turbulent Atmoshere And Paraxial Optical Systems

Generation and application of laser beams have induced rapid development of modern science and technology, resulted in emerging some new disciplines and cross-disciplines, and promoted the development of laser material processing, optical communication and remote sensing in atmosphere. The propagation and transformation of laser beams through various media and optical system play an important role in laser physics and laser applications. Due to their important practical applications, propagation properties of various laser beams in turbulent atmosphere or through truncated optical system have been investigated in detail. This thesis consists of following three topics(1) Based on extended Huygens-Fresnel principle and the Wigner distribution function of the second-order moment in a turbulent atmosphere, the propagation factors (i.e., M~2-factors) of some laser beams, such as dark hollow beam, laser array beam and standard Hermite-Gaussian beam, are studied; (2) Based on extended Huygens-Fresnel principle and the Rytov approximation in a turbulent atmosphere, the average intensity distributions and effective beam sizes of some laser beams such as standard and elegant Hermite-Gaussian beams are examined; (3) Focusing properties of a laser beam named four-petal Gaussian beam through an apertured optical system are investigated.First, we introduce the basic theory of propagation of laser beam in free space and in turbulent atmosphere, the definition of propagation factors, and some related theory on focal shift and focal switch theory of laser beam propagating through paraxial apertured optical system. Second, we derive the analytical formulae for the propagation factors of coherent and partially coherent dark hollow Gaussian beam and laser array beams in a turbulent atmosphere, and studied their evolution properties. Numerical examples show that: in free space, the propagation factor of a laser beam depends on the beam parameters but remain invariant on propagation. In turbulent atmosphere, the M~2-factors increases upon propagation, and the evolution properties are determined by the beams parameters, transmission distance, structure constant and inner scale of the turbulence; The M~2-factors of a rectangular laser array beam with different orders in x and y directions becomes equivalent to each other in the far field of turbulent atmosphere, although they different in the source plane. Furthermore, we study the average intensity and spreading of elegant Hermite-Gaussian beams (EHGBs) and standard Hermite-Gaussian beams (SHGBs), and the M~2-factors of coherent and partially coherent one-dimensional SHGBs. Our results show that the EGHB transforms to a laser with four-petals in the far field of free space, while EHGB and SHGB becomes Gaussian beams in the far field of turbulent atmosphere. The EHGB with higher beam order is less affected by the turbulence. The EHGB spreads slower than a SHGB. The evolution properties of the M~2-factor of coherent and partially coherent Hermite-Gaussian beam are similar to those of dark hollow beam and laser array beam, and are closely related to the beam parameters. At last, we study the focal shift and focal switch of four-petal Gaussian beams through an apertured ABCD optical system. Our numerical results show that focusing properties of the four-petal Gaussian beams are closely determined by the Fresnel number and the beam orders. A summary is given and some prospects are illustrated at the end of this paper.The theoretical results of this thesis will be useful for application of laser beams in free space optical communication and remote sensing.