Propagation And Modulation Of Airy Beams

This article mainly introduces Airy beam’s unique properties like exhibiting diffraction-free over long distance and tending to freely accelerate during propagation. In this paper, we express the mathematical properties of the Airy function, and prove the solution of Schrodinger’s equation which is satisfied with the Airy function. Based on the deduction, the Airy beam angular spectrum is obtained. In the propagation and modulation of Airy beam, we investigate the evolution of the beam in homogeneous medium, chiral material, biological tissue, and EIT medium. By using the matrix optics theory and the diffraction integral theory, we deduce the Airy beam’s analytic expression of evolution. On the other hand, in the experiment, we use the space phase modulator (SLM) to produce the Airy beam, and study the self-healing phenomenon of the Airy function, by proposing the self-healing quantitative calculation Q factor for the first time. In this study, we adopt mathematical application software MATLAB to simulate Airy beam, and by changing Airy beams’ input plane parameters (light source parameters) and the propagation medium parameters.Then, we observe its variation law with optical parameters in the medium, and fulfill propagation and modulation of Airy beams.Airy beam’s propagation is a hot spot, and has many novel applications, such as its passing through chiral material which is a kind of artificial composite material. When partial polarized light comes into this medium, it will be separated into left-hand circularly polarized light and right-handed circularly polarized light. The two kinds of light has different speed, which means that they have different refraction phenomenon, and the change of chiral parameters changes the propagation of these two prevalent beams. In addition, the chiral material can achieve negative refraction, which is prevailed in researching area nowadays. In recent years, people has paid more attention to the transmission of these beams in turbulent atmosphere, water, biological tissue and the propagation medium has a trend of diversity. Otherwise, considering the closely connection between propagation of Airy beam and medium refraction, we can use EIT as a special medium in which has a quality of modulating gas refractive index by using rabi frequency to control its refractive index. What’s more, such a research achievement has a very important and application value in medicine science.Another important part of this thesis is the research of Airy beam’s self-healing phenomenon theoretically and experimentally. Firstly, we use mathematical simulation to do the research on theory. And then, we use the space phase modulator (SLM) to realize the Airy beam in experiment and contrast it with theoretically simulation, making a sturdy foundation for the potential application of Bio-medical Photonics in the future.The content of this thesis chapters is arranged as following:The first chapter is the introduction part in which we express the thesis research background and current development, research purpose, content and methods simply.The second chapter talks about some basic theoretical knowledge of Airy functions, such as the basic nature of the Airy function, integral, the spread near zero, and Airy function’s relationship with Bessel function.The third chapter roughly describes the nature of the Airy beam, and then has a modulation on a few light sources character parameters of Airy beam, such as convergence parameters, beam width and wavelength.The fourth chapter is a theoretical study of Airy beam’s transmission in all kinds of medium, using METLAB to modulate Airy beam in some mediums, such as the homogeneous medium, chiral materials, biological tissue, and electromagnetically induced transparency (EIT) medium.The fifth chapter is about the Airy beam’s self-healing phenomenon. Firstly, we have a simple introduction to self-healing theory and property of Airy beam. Secondly we study the application of the Airy beam’s self-healing theory used in the experiment, comparing with numerical simulation theoretically.The sixth chapter is the summary of the full text, giving the main conclusions.