Propagation Properties Of Self-focusing And Frequency Conversion Of Circular Airy Beams

The radially symmetric Airy beam,also known as the circular Airy(CA)beam,features unique properties such as the ability to auto-focus without a reliance on any external system.This unique propagation properties means that it has valuable applications in many fields such as laser surgery,optical particle manipulation,and laser-induced terahertz radiation.In the above applications,the low control efficiency of single CA scalar beam and the problems of single control degree of freedom and small wavelength tuning range are still important factors that limit the development of CA beam application technology.Therefore,to solve the above-mentioned problems,it takes the propagation properties of CA beam as the starting point in this paper,the self-focusing propagation properties of CA vector light field and CA beam array and the propagation properties of CA beam frequency conversion are systematically studied theoretically and experimentally,which lays a foundation for the design of optical tweezers,CA beam frequency converter and other instruments.First,the self-focusing propagation properties of CA beams with different topological charges and initial launch angles are studied.Beginning with theory on Airy and CA beams,the basic characteristics of the Airy beam and the CA beam such as self-acceleration,self-healing,and self-focusing are studied.On this basis,the effects of parameters such as the topological charge,initial launch angle,distribution factor,and main ring radius on the self-focusing propagation properties of the CA beams are demonstrated.The results show that,by changing these parameters,the self-focusing focal length and light intensity distribution of the beam are controllable.A method of adjusting the concurrence and polarization distribution of CA vector light field by using the initial launch angle parameter is proposed.The characterization method of CA vector light field is studied theoretically,using spatial light modulator,CA vector light field is produced in experiment,the characterization of any vector mode on the high-order Poincarésphere can be performed.When the initial launch angle parameters of the orthonormal basis vector of the synthetic vector light field are 0 and 1,respectively,the concurrence is at a maximum at z=0.Here,the value C=1.00 gradually decreases to C=0.36 at z=800 mm,while the polarization distribution also changes with transmission of the beam,the flexible control of CA vector light field is realized.The CA beam array is generated experimentally and its propagation properties are studied,which realize the generation and regulation of CA beam array with independent parameters.Bases on Fourier conjugate symmetric extended computed holography method,CA beam array is generated.Five topological charges were selected for the CA vortex beam(n=0,1,2,3,4,5),and it is found that the CA beams in the array focus simultaneously near z=30 mm,while the hollow radius of the beams at the focusing position increases with an increase in the value of n.Similarly,five CA vortex beams with different initial launch angles(v=0,0.5,-0.5,1,-1)are selected to form an array,the CA beams are focused at different positions such as z=20 mm,z=25 mm,and z=30 mm,respectively.The results show that the CA beam array generated by this method can independently control the beam parameters in the array.Compared with the existing beam array research,the generation technology of CA beam array in this thesis can achieve more flexibly the beam array arrangement,it achieve the purpose of simultaneous control of multiple particles in optical tweezers.Finally,the frequency conversion and nonlinear transmission transformation mechanism of CA beam are studied.Based on the second-order nonlinear theory of CA beam,the frequency conversion of CA beam under the control of signal light and pump light is carried out,respectively.The input signal is focused at the propagation distance z=169.8mm,while the frequency-doubled beam more slowly auto-focuses at z=339.5mm,twice the focus position as the signal.It is verified that the self-focusing focal length of CA beam is inversely proportional to the wavelength.The high fidelity frequency conversion of CA beam is realized by using a flat-top beam as the pump light,and the beam inherits all key focusing characteristics of the input signal after frequency conversion.By studying the propagation properties of CA beam after frequency conversion under Gaussian pump with different waist radius,it is found that when the waist radius of Gaussian pump beam is more than 3times of the peak intensity radius of CA beam main ring(R_HM(28)3R₀),self-focusing characteristics similar to those of flat-top pumps can be obtained.The propagation properties of CA beam after frequency conversion are studied on three different nonlinear regions of CA beam:starting point,self-focusing and Fourier plane.The transformation rules of spatial spectrum and intensity contrast of CA beam is revealed,which provides a reference for constructing CA beam frequency converter and adjusting its transmission characteristics on demand.