The Mathieu beam is a typical nondiffracting beam characterized by its propagation invariance and self-reconstruction.These extraordinary properties have given rise to potentialities for applications such as optical c...The Mathieu beam is a typical nondiffracting beam characterized by its propagation invariance and self-reconstruction.These extraordinary properties have given rise to potentialities for applications such as optical communications,optical trapping,and material processing.However,the experimental generation of Mathieu–Gauss beams possessing high quality and compactness is still challenging.In this work,even and helical Mathieu phase plates with different orders m and ellipticity parameters q are fabricated by femtosecond laser two-photon polymerization.The experimentally generated nondiffracting beams are propagationinvariant in several hundred millimeters,which agree with numerical simulations.This work may promote the miniaturization of the application of nondiffracting beams in micronanooptics.展开更多
以含分数阶微分项的van der Pol-Mathieu方程为对象,研究了谐波激励作用下主共振的动力学行为和稳定性。采用平均法得到了方程近似解析解,通过数值方法验证了解析结果的准确性。建立了系统稳态响应的幅频方程,利用Lyapunov第一方法得到...以含分数阶微分项的van der Pol-Mathieu方程为对象,研究了谐波激励作用下主共振的动力学行为和稳定性。采用平均法得到了方程近似解析解,通过数值方法验证了解析结果的准确性。建立了系统稳态响应的幅频方程,利用Lyapunov第一方法得到定常解的稳定条件,确定解的稳定性。在此基础上,分析了参激项、自激项以及分数阶微分项参数对系统幅频特性的影响。结果表明:改变参激项系数主要影响系统的响应幅值和共振频率范围;改变自激项系数主要影响系统响应幅值和多值性;改变分数阶微分项系数和阶次对系统的动力学行为具有双重调节的作用。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62125503 and 62261160388)the Key R&D Program of Hubei Province of China(Grant Nos.2020BAB001 and 2021BAA024)+3 种基金the Key R&D Program of Guangdong Province(Grant No.2018B030325002)the Science and Technology Innovation Commission of Shenzhen(Grant No.JCYJ20200109114018750)the Innovation Project of Optics Valley Laboratory(Grant No.OVL2021BG004)the Fundamental Research Funds for the Central Universities(Grant No.2019kfyRCPY037).
文摘The Mathieu beam is a typical nondiffracting beam characterized by its propagation invariance and self-reconstruction.These extraordinary properties have given rise to potentialities for applications such as optical communications,optical trapping,and material processing.However,the experimental generation of Mathieu–Gauss beams possessing high quality and compactness is still challenging.In this work,even and helical Mathieu phase plates with different orders m and ellipticity parameters q are fabricated by femtosecond laser two-photon polymerization.The experimentally generated nondiffracting beams are propagationinvariant in several hundred millimeters,which agree with numerical simulations.This work may promote the miniaturization of the application of nondiffracting beams in micronanooptics.
文摘以含分数阶微分项的van der Pol-Mathieu方程为对象,研究了谐波激励作用下主共振的动力学行为和稳定性。采用平均法得到了方程近似解析解,通过数值方法验证了解析结果的准确性。建立了系统稳态响应的幅频方程,利用Lyapunov第一方法得到定常解的稳定条件,确定解的稳定性。在此基础上,分析了参激项、自激项以及分数阶微分项参数对系统幅频特性的影响。结果表明:改变参激项系数主要影响系统的响应幅值和共振频率范围;改变自激项系数主要影响系统响应幅值和多值性;改变分数阶微分项系数和阶次对系统的动力学行为具有双重调节的作用。
