Study Of Polarization Characteristics Of Beta Distribution Mode Noise

The Beta distribution can effectively describe the non-Gaussian statistical statistical properties of electromagnetic scattering.Because of its unique interval restriction,Beta distribution can well model the mode noise generated by multimode fiber,which cannot be done by other related distribution models.However,the current studies on the mode noise of Beta distribution are mainly based on random scalar fields,and the properties under random vector fields have not been explored.In this thesis,we focus on the development and evolution of the vector and generated polarization-related mode noise with independent polarization phase quantities whose amplitudes obey the Beta distribution and a finite number,and provide the probability density functions of the Stokes parameters describing the fluctuating polarization in the vector optical field,and explore when the Beta distribution shape parameters are α =2,β =5(Rayleigh-like)and α =5,β =5(Gaussian-like),the two sets of typical Beta The polarization statistical properties of the mode noise modeled by the Beta distribution parameters are investigated when the Beta distribution shape parameters areα =2,β =5 and α =5,β =5.In this thesis,we first introduce the background related to the statistical study of mode noise with Beta distribution and its significance;then we describe the basic concepts related to Beta distribution,including its basic concepts,properties and applications;then we introduce the polarization theory and description methods,including the concept of polarization,various methods to characterize the polarization state and the definition and properties of the Stokes vector;and then we derive in detail the vector light field in Finally,we use two typical Beta-distributed parameters for numerical calculation and plotting to analyze the evolution of polarization characteristics of Beta-distributed mode noise with different polarization states and different contributing phase numbers.The results of this thesis show that the classical statistical theory of scattering intensity always underestimates the possibility of a large scattering noise intensity in real situations when the number of contributions is small.The tails of the probability density function of the Stokes parameters of the mode noise with amplitudes obeying the Beta distribution for both shape parameters are always higher than the tails of the negative exponential density function presented when the number is infinite in the classical theory,in which the Beta distribution mode noise provides excessive fluctuations,and as the number of contributing polarization phase quantities increases,the obtained Stokes parameters decrease in the development of the polarization noise during their fluctuations towards the fully scattered noise.The vector statistics of the amplitude obeying Beta distribution vary slightly for different shape parameter cases,and increasing the value of the shape parameter reduces the tendency of excessive fluctuations caused by Beta distribution.The main contribution of this paper is to investigate and analyze the polarization characteristics of mode noise based on Beta distribution with a new approach and idea to better understand the characteristics and behavior of mode noise,which provides a new theoretical guidance for the optimization of optical and fiber optic communication systems.Also,the vector expansion of a finite number of random wanderings whose amplitudes obey the Beta distribution provides an intuitive explanation for the development of polarization scattering fields and provides a deeper understanding of the evolution of the polarization states of random electromagnetic fields.