Research On Potential Manipulation And Talbot Imaging Of Airy Pulses

Diffraction phenomenon occurs when an optical beam with finite width propagates in free space.How to suppress the diffraction effect and realize the diffraction-free beams is an important research topic in optics.In recent years,Airy beams have drawn considerable interest due to the intriguing properties including transverse self-accelerating,diffraction-free propagating,and self-healing.These features have found wide applications in optical micromanipulation,super-resolution imaging and etc.The spatial paraxial diffraction is analogous to the temporal narrow-band dispersion.Thus the spatial diffraction effect and optical devices can be extended to time domain,such as temporal Talbot effect,time lens,and temporal soliton,which may find applications in ultrahigh-rate optical communication and ultrafast optical signal processing.In optical fiber communication systems,the fiber dispersion can arouse pulse broadening and distortion,which will increase the bit error rate and decrease the communication quality.Hence,it is of great significance to cancel the pulse dispersion.Inspired by the space-time duality,the temporal Airy pulse has also been proposed.Analogously,the Airy pulse manifests the characteristics of dispersion-free,self-accelerating,and self-healing,which have been used in linear light bullets,Raman frequency tunning,and supercontinuum generation.Despite the similar propagation properties of Airy beams and Airy pulses,there is an important physical difference between temporal and spatial accelerations.An accelerating beam bends its propagation trajectory in space,whereas the self-acceleration leads to varying group velocity of Airy pulses during propagation.The dispersion and nonlinearity of optical fiber are controllable.Through the engineering design of dispersion and nonlinearity,Airy pulse shows distinct characteristics during propagation,which can be used to reveal the physical mechanism of interaction between the Airy laser beam and the medium.In addition,in the optical fiber communication system,the information is carried by the optical pulses.In order to control the transmission of information,it is necessary to manipulate the propagation of optical pulses.The temporal and spectral evolution of Airy pulse can be engineered by the time-dependent potential,which can be generated by virtue of the electro-optic effect in the crystal and the nonlinear optical effect in the medium.Furthermore,by combining the propagation properties of Airy pulses with the conventional optical effects,one obtains many interesting physical phenomena,which contribute to extend the application range of Airy pulses.Based on the above arguments,our research contents are as follows.Firstly,we investigate the temporal and spectral evolutions of finite-energy Airy pulses in the time-dependent power-law potentials,which are constructed by the cross-phase modulation between a weak signal and strong pump pulses.By using the linear potential,we can modify the self-acceleration of Airy pulse and realize the unidirectional frequency shift.We also achieve the self-splitting effect of Airy pulse both in temporal and spectral domains by means of the symmetric linear potential.In addition,when a parabolic potential is utilized,The Airy pulse will exhibit the periodic temporal and spectral imaging as well as timefrequency conversion behaviors.Further,we realize the temporal and spectral revival behaviors of Airy pulse by exploiting the higher-order power-law potentials.These results may lead to many applications in pulse reshaping and temporal-spectral imaging for both optical communication and signal processing systems.Secondly,we analyze the propagation dynamics of Airy pulse in time-varying periodic potentials and realize the temporal Airy-Bloch oscillation effects.The oscillation amplitude and period of Airy pulse can be engineered by varying the amplitude and repetition frequency of periodic potential as well as the gradient of linear potential.Furthermore,we theoretically propose an optical fiber loop structure to realize the generalized Wannier-Stark Hamiltonian and accelerated Airy-Bloch oscillation.The study paves a promising approach to manipulate the propagation of Airy pulse and provides a versatile platform for optical simulation of electron motion in periodic lattice and crystal.Then we investigate the temporal accelerating self-imaging effect for a train of Airy pulses propagating in an optical fiber.Due to the self-acceleration of Airy pulse,the selfimaging is along the parabolic trajectory in the parameter space spanned by propagation distance and time.By changing the main lobe width and the time interval of Airy pulses,we can modify the self-imaging distance and trajectory.Under the action of third-order dispersion,we realize the temporal magnified self-imaging effect of Airy pulse trains.For ideal Airy pulses possessing infinite energy,the self-imaging maintains indefinitely.For the truncated Airy pulses,by decreasing the main lobe width and increasing the time interval of Airy pulses,we can also realize the finite-energy Airy-Talbot effect.The study provides a mechanism to achieve the self-imaging of nonperiodic optical field and may find applications in information transmission and processing in optical fibers.Finally,we utilize the time-dependent linear potential to manipulate the Talbot imaging of Airy pulse trains.For the self-accelerating Airy pulses,the parabolic self-imaging trajectory can be tailored by varying the dispersion sign and the linear potential gradient.By imposing linear phase modulations on the Airy pulse trains,we realize the Airy-Talbot effects accompanied with positive and negative refractions.The one-dimensional stationary eigensolution of the Schr?dinger equation with a linear potential is an Airy wave packet.The self-imaging of wave train composed of stationary Airy pulses follows straight lines.The self-imaging distance can be controlled by changing the gradient of linear potential.We also realize the above effects in piecewise linear potential.The study provides opportunities to manipulate the self-imaging of optical pulse trains.