Non - Paraxial Partially Coherent Beam

With the development of laser technology, the tightly focused beams and diode laser beams with large divergence angle and non-paraxial resonator eigen-modes, the paraxial approximation fails. People began to research the transmission of the non - paraxial beam. However, in the high-power laser technology, it is difficult to encounter fully spatially coherent Die-Gaussian beam, most of them are partially coherent multi-Gaussian beam, description of Gaussian–Schell-model (GSM) is better than multi-mode laser beam under certain conditions.In recent years, concept of partially coherent non-paraxial beams is proposed and researched for transmission characteristic (scalar, vector) by using the generalized Rayleigh–Sommerfeld diffraction integral in free space, such as Gauss– Schell model (GSM) beams, non-paraxial partially coherent vector hyperbolic - cosine, non-paraxial beam (scalar) of coherent TEM11 Hermite-Gaussian( HG )beams. Then, the Wigner distribution function method was introduced to solve non-paraxial beams, and established basic theory of the Wigner distribution function.In this paper, comparison of the two methods was done and found that Wigner distribution function describing the space domain and frequency domain space at the same time. It has a wide range of application and can be used for the transmission characteristics of non-paraxial (scalar, vector) partially coherent beams, and can also be used to study the transmission characteristics of high Non-paraxial (scalar, vector) fully coherent beam. It will simplify the complex computing algebra. So, the Wigner distribution function method was chose for non-paraxial partially beams.The main works of this paper follows as:1. Based on the far-field approximation, the far-field vectorial theory of Wigner distribution function about the non-paraxial partially coherent beams in free space was expanded. Thus, far-field transmission element of the Wigner distribution function is established.2. To illustrate the correctness of the new theory, a special (GSM) beam is discussed and treated as some interesting cases. 3. The non-paraxial partially coherent TEM11 Hermite - Gaussian (HG) beams have been raised, and researched with scalar diffraction integration. But their far-field characteristics and the vectorial properties are still not solved. Therefore, this paper makes a deep study of non-paraxial (vector) partially coherent TEM11 Hermite– Gaussian (HG) beams.