Collision off-axis position dependence of relativistic nonlinear Thomson inverse scattering of an excited electron in a tightly focused circular polarized laser pulse

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron's initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum's harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings,when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

Super-resolution longitudinally polarized light needle achieved by tightly focusing radially polarized beams

Based on the vector diffraction theory, a super-resolution longitudinally polarized optical needle with ultra-long depth of focus(DOF) is generated by tightly focusing a radially polarized beam that is modulated by a self-designed ternary hybrid(phase/amplitude) filter(THF). Both the phase and the amplitude patterns of THF are judiciously optimized by the versatile particle swarm optimization(PSO) searching algorithm. For the focusing configuration with a combination of a high numerical aperture(NA) and the optimized sine-shaped THFs, an optical needle with the full width at half maximum(FWHM) of 0.414λ and the DOF of 7.58λ is accessed, which corresponds to an aspect ratio of 18.3. The demonstrated longitudinally polarized super-resolution light needle with high aspect ratio opens up broad applications in high-density optical data storage, nano-photolithography, super-resolution imaging and high-efficiency particle trapping.

Laser parameters affecting the asymmetric radiation of the electron in tightly focused intense laser pulses

The nonlinear radiation of the electron is a distinctive feature of the action of tightly focused linearly polarized lasers.In this paper,from the perspective of radiation symmetry,the effect of laser parameters on the electron radiation power in the time domain is studied systematically.An asymmetric bimodal structure is found in the time domain in the direction of the maximum radiation.For this special structure,an explanation is given based on the electron dynamics perspective.The structure is compared with the symmetric bimodal structure in the classical theory.The increase in laser intensity,while significantly increasing the radiated power of the electron,exacerbates the asymmetry of the electron radiation.The variation in the initial phase of the laser leads to a periodic variation in the electron motion,which results in a periodic extension of the electron spatial radiation with a period ofπ.Moreover,the existence of jump points with a phase difference ofπin the range of 0-2πis found.The increase in pulse width reduces the radiated power,extends the radiation range,and alleviates the radiation asymmetry.The results in this paper contribute to the study of electron radiation characteristics in intense laser fields.

Influence of acceleration on relativistic nonlinear Thomson scattering in tightly focused linearly polarized laser pulses

The influence of acceleration of electrons on relativistic nonlinear Thomson scattering in tightly focused linearly polarized laser pulses is investigated for the first time. In the framework of classical electrodynamics, it is deduced and found that the more severe the change in the electron transverse acceleration, the stronger the asymmetry of the radiation angle distribution, and the greater the transverse acceleration, the greater the radiation energy. Tightly focused, ultrashort,and high-intensity lasers lead to violent electron acceleration processes, resulting in a bifurcated radiation structure with asymmetry and higher energy. Additionally, a change in the initial phase of the laser brings about periodic change of the acceleration, which in turn makes the radiation change periodically with the initial phase. In other cases, the radiation is in a symmetrical double-peak structure. These phenomena will help us to modulate radiation with more energy collimation.

Tightly focused properties of a partially coherent radially polarized power-exponent-phase vortex beam

A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then,the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.

Optical chirality induced by spin–orbit interaction of light in a tightly focused Laguerre–Gaussian beam

Optical chirality is one of the important and fundamental dynamic properties of light besides energy, momentum,and angular momentum. The quantification of electromagnetic chirality has been conceptualized only recently. Now, it is well known that for paraxial plane waves of light, the optical chirality is proportional to the ellipticity of the polarization ellipse, i.e., completely independent of the phase distribution. Here it is shown that optical vortex and state of polarization of the source paraxial field both have contributions to the optical chirality of the nonparaxial field generated by tightly focused Laguerre–Gaussian(LG) beam, which is in Stark contrast to the paraxial plane wave of light known from classical optics. The physical reason is the redistribution of local electromagnetic polarization in three dimensions associated with spin–orbit interaction.

Tight Focusing Properties of Radially Polarized Gaussian Beams with Pair of Vortices

The tight focusing properties of a radially polarized Gaussian beam with a nested pair of vortices having a radial wave front distribution are investigated theoretically by the vector diffraction theory. The results show that the optical intensity in the focal region can be altered considerably by changing the location of the vortices nested in a radially polarized Gaussian beam. It is noted that focal evolution from one annular focal pattern to a highly confined focal spot in the transverse direction is observed corresponding to the change in the location of the optical vortices in the input plane. It is also observed that the generated focal hole or spot lead to a focal shift along the optical axis remarkably under proper radial phase modulation. Hence the proposed system may be applied to construct tunable optical traps for both high and low refractive index particles.

Tight focusing of axially symmetric polarized vortex beams

Tight focusing of axially symmetric polarized vortex beams is studied numerically based on vector diffraction theory. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the polarization order and topological charge of the incident beams. Moreover, focal spots with flat-topped or tightly-focused patterns can be flexibly achieved by carefully choosing the polar- ization order and the topological charge, which confirms the potential of such beams in wide applications, such as optical tweezers, laser printing, lithography, and material processing.

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.

Tight focusing of femtosecond elliptically polarised vortex light pulses

This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.

Tight Focusing Properties of Azimuthally Polarized Pair of Vortex Beams through a Dielectric Interface

Tight focusing properties of an azimuthally polarized Gaussian beam with a pair of vortices through a dielectric interface is theoretically investigated by vector diffraction theory. For the incident beam with a pair of vortices of opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane, which results in the generation of many novel focal patterns. The usable focal structures generated through the tight focusing of the double-vortex beams may find applications in micro-particle trapping, manipulation, and material processing, etc.

Tight Focusing Properties of Phase Modulated Radially Polarized Laguerre Bessel Gaussian Beam

We propose a new approach for generating a multiple focal spot segment of subwavelength size, by tight focusing of a phase modulated radially polarized Laguerre Bessel Gaussian beam. The focusing properties are investigated theoretically by .vector diffraction theory. We observe that the focal segment with multiple focal structures is separated with different axial distances and a super long dark channel can be generated by properly tuning the phase of the incident radially polarized Laguerre Bessel Gaussian beam. We presume that such multiple focal patterns and high intense beam may find applications in atom optics, optical manipulations and multiple optical trapping.

Constructing ultra-long focal fields via tightly focused Bessel beams

We numerically demonstrate that the tight focusing of Bessel beams can generate focal fields with an ultra-long depth of focus(DOF).The ultra-long focal field can be controlled by appropriately regulating the order of the Bessel function and the polarization.An optical needle and an optical dark channel with nearly 100λDOF are generated.The optical needle has a DOF of~104.9λand a super-diffraction-limited focal spot with the size of 0.19λ^(2).The dark channel has a full-width at halfmaximum of~0.346λand a DOF of~103.8λ.Furthermore,the oscillating focal field with an ultra-long DOF can be also generated by merely changing the order of the input Bessel beam.Our results are expected to contribute to potential applications in optical tweezers,atom guidance and capture,and laser processing.

Characterization of tightly focused partially coherent radially polarized vortex beams

Tight focusing properties of partially coherent radially polarized vortex beams are studied based on vectorial Debye theory.We focus on the focal properties including the intensity and the partially coherent and polarized properties of such partially coherent vortex beams through a high numerical aperture objective. It is found that the source coherence length and the maximal numerical aperture angle have direct influence on the focal intensity,as well as coherence and polarization properties.This research is important in optical micromanipulation and beam shaping.

Linear and angular momenta in tightly focused vortex segmented beams of light(Invited Paper)

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

Redistributing the energy flow of tightly focused ellipticity-variant vector optical fields

The redistribution of the energy flow of tightly focused ellipticity-variant vector optical fields is presented.We theoretically design and experimentally generate this kind of ellipticity-variant vector optical field, and further explore the redistribution of the energy flow in the focal plane by designing different phase masks including fanlike phase masks and vortex phase masks on them. The flexibly controlled transverse energy flow rings of the tightly focused ellipticity-variant vector optical fields with and without phase masks can be used to transport multiple absorptive particles along certain paths, which may be widely applied in optical trapping and manipulation.

Detecting the vector of nanoscale light field with atomic defect

Modulation of a vector light field has played an important role in the research of nanophotonics.However,it is still a great challenge to accurately measure the three-dimensional vector distribution at nanoscale.Here,based on the interaction between the light field and atomic-sized nitrogen-vacancy(NV)color center in diamonds,we demonstrate an efficient method for vectorial mapping of the light-field distribution at nanoscale.Single NV centers with different but well-defined symmetry axes are selected and then interact with the same tightly focused light field.The excitation of a single NV center is related to the angle between the NV center axis and the polarization of the light field.Then the fluorescence patterns of different NV centers provide the information on the vectorial light field distribution.Subsequently analyzing the fluorescence patterns with the help of a deep neural network,the intensity and phase of the light-field vectorial components are fully reconstructed with nanometer resolution.The experimental results are in agreement with theoretical calculations.It demonstrates that our method can help to study light–matter interaction at nanoscale and extend the application of vector light fields in research on nanophotonics.