Research On Airy Beam And Optical Airy Transform

Airy beam is widely studied because of its many special properties. Airy beam can be used in many fields such as biomedical, optical tweezers, surface Plasmon and light bullets and so on. Using the auto-acceleration of Airy beam or a sudden self-focusing of circular Airy beam, we can study cells, metal nanoparticles, macromolecular material and so on. That is the reason that people is focused on optical tweezers.In the first chapter in this paper, we introduce the significance of the Airy beam, including many applications of the Airy beam. We also expound the research status of Airy beam and then introduce the main research content of this paper.In the second chapter, firstly, we introduce the electric field distribution and the meaning of every parameter of Airy beam. Secondly, we obtain the relationship between electric field and transmission distance through a paraxial diffraction equation. Therefore, we analyze the properties of non-diffracting and acceleration of Airy beam. Afterwards, we introduce the self-healing property of Airy beam.In the third chapter, which is the most important chapter in the paper, we research on optical Airy transform. At first, we introduce mathematical Airy transform and several important theorems of Airy transform. Then the optics system of the Airy transform is introduced. After that, we research on optical Airy transform of fundamental mode Gaussian beam, limited energy Airy beam and flattened Gaussian beams. The Airy transform can produce Airy beam or modulate Airy beam or produce a new light beam which is similar to Airy beam. For producing Airy beam, optical Airy transform device is better than ever before. However, in some aspect the Airy-related beam is different from the Airy beam.In the fourth chapter, we study Fractional Fourier transform of Airy beam. Then the expression of the electric field is deduced after Fractional Fourier transform. In addition, we analyze that Fractional Fourier order p affects intensity, light spot size and attenuation of Airy beam.