Investigation On The Construction And Propagation Properties Of Optical Fields Related To The Airy Beams

Apart from the broadening of diffraction and the relativistic effects, light beams tend to propagate along a straight path in vacuum. In 2007, light beams that can bend themselves along a curved path in vacuum was found by D. N. Christodoulides and his collaborators. Later, this beam is called self-accelerating Airy beams. Existing research show that the self-accelerating Airy beams have the properties of propagation-invariant, self-healing and self-accelerating, which make them very useful in the field of the optically clearing, curved plasma channels generation, light bullet, electron acceleration, particle manipulation, optical routing and optical imaging and so on.With the development of the laser technology, the propagation and transformation of laser beams in optical system and turbulent atmosphere have attracted much attention in applications of laser. Therefore, the appearance of new laser beams made it urgent to study their propagation and transformation in order to meet the requirements in practical applications.In this thesis, we mainly plan to carry out the construction and propagation properties of optical fields related to the Airy beams. Some optical fields which related to the Airy beams are introduced first. Their propagation characteristics are also investigated. The characteristic of the Airy beams’ wander in atmospheric turbulence is revealed and some means that can reduce the beam wander of Airy beams are found. At last, the ability to a Bessel-Gaussian beam and an Airy beam have been studied and compared based on similarity between two infinite-dimensional complex vectors in Hilbert space.In chapter 1, we have introduced the background of the generation, characteristic, application and propagation properties of Airy beams. The main content and originality of this thesis are also presented.In chapter 2, we have introduced the light propagation theory and the mathematical theory related to Airy function.In chapter 3, we have proposed some theoretical model that related to the Airy beams and have studied their propagation properties. First, A new form of laser beam called finite energy Airy-Hermite-Gaussian beam is introduced to solve the integral divergence of the Airy-Hermite-Gaussian beam. The new beam can describe the out mode of the metal strip waveguide and the views of previous literature are clarified by our work. Second, the composed of two Airy beam is concerned for its position of the hot spot can be controlled. We introduce a convenient mathematical model which describes a composed symmetric dual Airy beam with a tunable parameter. The advantage of our mathematical model is to facilitate study the propagation characteristics of dual Airy beam. Third, A new method to generate a high-power Airy beam of large scale by using coherent combining technology is proposed and the propagation of high-power Airy beam in a turbulent atmosphere has been analytically studied. At last, the propagation properties of Airy beam passing through the misaligned optical system with hard aperture are illustrated.In chapter 4, we have investigated the beam wander of Airy beam in a turbulent atmosphere. We found that the beam wander of an Airy beam has a maximum when kurtosis is 4.3 regardless of the variation of propagation distance, characteristic scales of Airy beam, inner scales of turbulence and wave length. Simultaneously, we find that decreasing the coherent length of a partially coherent Airy beam and increasing the topological charge of an Airy beam with a spiral phase can be used to decrease the wander effect. We also find that the beam wander of array beams is smaller than that of a single beam and Gaussian beam arrays with the same arrays order under the condition of each coherence length significantly. We think these results indicate that the Airy beam have potential applications in atmosphere optical communications.In chapter 5, we have quantitative investigated the self-healing ability of Airy beams. Generally, the self-healing ability of nondiffracting beam is strong. However, the comparison of the self-healing ability between different beams has not been made until now. In this chapter, we have introduced the quantitative description of a laser beam’s self-healing ability. As describing the similarity by using the angle of two infinitedimensional complex vectors in Hilbert space, the similarity is proposed to quantitatively describe the self-healing ability of different beams. Based on this theory, the ability to a Bessel-Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel-Gaussian beam with Airy beam under the same conditions, we find that Airy beam has stronger self-healing ability than that of Bessel-Gaussian beam in a short length.In chapter 6, the conclusion of this thesis is drawn and some prospects are illustrated.