轨道角动量指向可控的紧聚焦时空波包(特邀)

Tightly Focused Spatiotemporal Wavepacket with Controllable Orbital Angular Momentum Orientation(Invited)

利用Debye积分,研究了三个相互正交的轨道角动量(包括两个正交的横向轨道角动量以及一个纵向轨道角动量)光场在紧聚焦条件下的复杂耦合现象,并演示了焦场中相位奇点在三维时空间中的演化。此外,还研究了具有不同拓扑荷数的纵向轨道角动量对聚焦波包整体轨道角动量指向的影响。数值结果表明,聚焦波包的整体轨道角动量指向可由纵向轨道角动量的拓扑荷数进行调控,进而实现紧聚焦时空波包的轨道角动量指向可控。这种角动量指向可控的时空波包在光学微操作、微纳加工、自旋-轨道耦合以及量子通信等领域具有潜在的应用价值。

It is well known that photons not only carry linear momentum,but also have spin angular momentum related to polarization and Orbital Angular Momentum(OAM)linked with spiral phase.In addition,Spatiotemporal Optical Vortices(STOVs)carrying transverse OAM bring emerging research interests to the optical field.In this paper,we studied the characteristics of tightly focused scalar STOVs and the controllability of OAM orientation in the focused wavepacket.For an incident spatiotemporal wavepacket,which has three mutually orthogonal OAM,including two transverse OAMs and one longitudinal OAM,the corresponding focused wavepacket on the focal plane will collapse due to the spatiotemporal astigmatic effect of the high numerical aperture lens.Based on the modes conversion principle of the cylindrical lens,the incident spatiotemporal wavepacket is preconditioned.And the preconditioned spatiotemporal wavepacket will produce an intact focused wavepacket with a spiral phase in spatiotemporal plane.Debye integral is used to simulate and analyze the characteristics of tightly focused spatiotemporal wavepackets.The numerical simulation results of the preconditioned incident wavepacket show that it is split into two independent parts,the intensity is mainly distributed in the x-t plane and y-t plane,and both of these two planes exhibit binarized phase distributions.In the x-y plane,the phase abruptness caused by the preconditioning gives rise to discontinuous phase distribution in the range of[-π,π].Here,the tightly focused spatiotemporal wavepackets carrying a single transverse OAM or a purely longitudinal OAM are also presented to facilitate the observation of the mutual coupling phenomena between different OAMs.The tightly focused wavepacket with a single OAM exhibits regular doughnut shape,while the three mutually orthogonal OAMs in the focused wavepacket will produce complex coupling phenomenon,leading to the focal wavepacket having an exotic phase singularity trace.Both the phase distributions on the x-t and y-t plane vary continuously from-πtoπalong the counterclockwise direction,indicating that the topological charge of the transverse OAM in these two planes is+1.In the x-y principle plane,five dark areas appear and each area corresponds to a phase singularity.In the central dark area,the phase varies continuously from-πtoπalong the clockwise direction,while in the other four dark areas,their phases vary continuously from-πtoπalong the counterclockwise direction.Thus,the OAM topological charge of the central vortex is-1 and the OAM topological charge of the four peripheral vortices is+1,which is caused by the spatiotemporal coupling.To further analyze the complex coupling phenomenon,the tightly focusing process can be regarded as a Fourier transform of the incident field.According to the expression of the incident field on the principle plan,it can be divided into three parts.The Fourier transformation of the first part will result in two pulse along the x-axis in the focal region,the Fourier transformation of second part will result in two pulse along the y-axis in the focal region,and the Fourier transformation of third parts will produce a highly confined vortex of topological charge of+1 in the focal region.Based on the principle of Fourier transformation,the Fourier transformation of the product of the above three terms is equal to the convolution of their respective Fourier transformations.The convolution of shifted pulse and highly confined vortex will result in the shift of the vortex.Thus,five phase singularities are generated by the complex coupling during the tightly focusing process.Meanwhile,to demonstrate the three-dimensional spatiotemporal evolution trajectory of the phase singularity,we extract the hollow structure inside the focused wavepacket.From the result,we find that the spatiotemporal coupling in the center of the focused wavepacket is stronger than in the peripheral region.We also calculate the topological charge of the OAM within different slices of the focused wavepacket to quantitatively analyze the effect of the spatiotemporal coupling on each kind of OAM.The numerical results show that,the spatiotemporal coupling has few effects on the longitudinal OAM of the focused wavepacket,which provides the possibility to control the focused wavepacket OAM orientation by adjusting the topological charge of the longitudinal OAM in the incident wavepacket.Different topological charge(l=-2,-1,0,1,2)of the longitudinal OAM in the incident wavepacket is taken,and the overall OAM of each tightly focused wavepacket is estimated.The results show that the overall transverse OAM of the tightly focused wavepacket is kept constant while the topological charge of the longitudinal OAM in the focused wavepacket reveals a linear relationship with the topological charge of the longitudinal OAM in the incident wavepacket.Hence,the overall OAM orientation of the focused wavepacket can be controlled by adjusting the topological charge of the longitudinal OAM in the incident wavepacket.Such tightly focused spatiotemporal wavepackets with controllable OAM orientation may find potential applications such as optical trapping,optical tweezer,spin-orbital coupling,micro-nano fabrication.