Self-focusing Effect On The Propagation Characteristics Of Airy Beams

An Airy beam has the non-diffracting,self-healing and self-acceleration characteristics.Due to its characteristics,it can be applied in optical particle manipulation,photon bombs and Airy lasers,etc.When a laser beam propagates in a self-focusing medium,the self-focusing effect on beam propagation characteristics cannot be ignored.Therefore,it is very important to study the self-focusing effect on the propagation characteristics of Airy beams and Airy array beams.The main research results in this thesis are summarized as follows:1.The effect of self-focusing on the propagation characteristics of Airy beams is studied.The air is adopted as the self-focusing medium,and the effects of self-focusing on the self-healing and self-acceleration characteristics of Airy beams are studied numerically.It is found that the self-focusing effect on the self-healing of an Airy beam with the main lobe blocked can be ignored.Due to the self-focusing effect,an Airy beam with main lobe blocked can keep its Airy profile to further propagation distance than a complete Airy beam.This may offer a way to keep the acceleration of an Airy beam under the effect of nonlinear self-focusing.Due to the self-focusing effect,the self-accelerating of Airy beams becomes stronger when the beam power is not very high,which may be applied in practice.In particular,it is found that the resistance of an Airy beam to self-focusing effect is more remarkable than that of a Gaussian one.In addition,the Poynting vector expression in the air is derived in this thesis.When the dielectric constant in vacuum is adopted and the refractive index of the medium is equal to 1,this expression reduces to the Poynting vector expression in vacuum.2.The effect of self-focusing on the propagation characteristics of Airy array beams is studied.The air is adopted as the self-focusing medium,and the effects of self-focusing on the focusing and self-healing characteristics of Airy array beams arestudied numerically.It is found that when the self-focusing effect is strong enough and the sub-beam separate distance is not small,an Airy array beam may focus twice for the coherent combination,while an Airy array beam may not focus for the incoherent combination.These behaviors are quite different from those in vacuum(i.e.,without self-focusing effect),and an Airy array beams only focus once in vacuum.With and without self-focusing effect,the self-healing of Airy array beams with main lobes blocked can achieve,but it is a better reconstruction for the incoherent combination than that for the coherent combination.The propagation distance required for reconstruction of Airy array beams with main lobes blocked decreases due to the self-focusing effect.The reconstruction of an Airy array beam with main lobes blocked may finish before or after focusing,which depends on the intensity distribution and the coherence of the array beam and is independent of the self-focusing effect.