Generation and propagation properties of Bessel-Gaussian beams with a rotationally symmetric power-exponent-phase vortex.

In this paper, the generation and propagation properties of Bessel-Gaussian (BG) rotationally symmetric power-exponent-phase vortex beam (RSPEPVBs) were demonstrated and discussed. The results showed that the BG-RSPEPVBs can be directly generated based on the spatial light modulator, of which the phase singularities were verified by the interference patterns with the plane wave. It can be found that the intensity distributions of the BG-RSPEPVBs, with different topological charges (TCs) and power orders, were fan-shaped and polycyclic, which possessed the characteristics of BG beams and RSPEPVBs, simultaneously. Thus, the propagation invariance of the BG-RSPEPVBs is better than that of Laguerre-Gaussian RSPEPVBs and RSPEPVBs. Moreover, the focusing spot of the BG-RSPEPVBs would evolve into a bright ring with the same ring radius at the focal plane, which is independent of the TC and more suitable for the applications of optical coupling, optical communication, optical trapping, and so on.

Accurate method for correcting the translation position error of ptychography based on quantum particle swarm optimization.

In ptychography, the translation position error will cause the periodic grid deviation and tremendously decrease the reconstruction quality. It is crucial to attain the precise translation position of the probe with respect to the object. The current correction methods may fall into a local optimal value, and miss the better results. An accurate method based on the quantum particle swarm optimization is proposed to globally correct the translation position error and add the randomness to avoid trapping in local optimum. In our proposed method, particles in a quantum bound state can appear at any point in the solution space with a certain probability density. In order words, the corrected translation position can be spread over the searching space, which can acquire the possibility of jumping out of the local optimum. Experiments are conducted to verify that our proposed method can be used to enhance the correction accuracy of the translation position error as well as avoid local optimum.

Generation of rotationally symmetric power-exponent-phase vortex beams based on digital micromirror devices.

In this paper, what we believe to be a new method for the generation of rotationally symmetric power-exponent-phase vortex beams (RSPEPVBs) based on digital micromirror devices (DMD) was proposed and demonstrated. Based on the theory of binary amplitude holography and Lee method, the two-dimensional amplitude holograms for the generation of RSPEPVBs were obtained. Then, the experimental setup was established for the generation of RSPEPVBs based on DMD and to verify the phase structure of RSPEPVBs by the Mach-Zehnder interferometer. The experimental results showed that the RSPEPVBs can be generated based on DMD with high beam quality and stability, and the ±1st-order diffracted beams were respectively corresponding to the RSPEPVBs with contrary TCs, which was the first time to report the RSPEPVBs with negative TC. Besides, the overall and ±1st-order diffraction efficiencies of RSPEPVBs generated by DMD were 7.18% and 1.73%, respectively. The method can be applied for the generation of RSPEPVBs with different parameters and quickly achieve mode switching by loading different binary amplitude holograms, which provides a new choice for the generation of new structure beams based on DMD.

Optical trapping of multiple particles based on a rotationally-symmetric power-exponent-phase vortex beam.

In this paper, the optical trapping of multiple particles based on a rotationally-symmetric power-exponent-phase vortex beam (RSPEPVB) was introduced and demonstrated. Based on the theories of tight focusing and optical force, the optical force model of RSPEPVB was established to analyze the optical trapping force of tightly focused RSPEPVB. Then, an experimental setup of optical tweezer, by utilizing the RSPEPVB, was built to demonstrate that the optical tweezer of RSPEPVBs can achieve the optical trapping of multiple particles, and the number of captured particles is equal to the topological charge l of RSPEPVB, which shows that the RSPEPVBs can achieve multi-particles trapping with controllable number. Moreover, compared to vortex beam, the captured particles by RSPEPVB will not rotate around the circular light intensity distribution. The results will provide a new option for optical trapping of multiple particles in biomedicine, laser cooling and so on.

Influences of salinity and temperature on propagation of radially polarized rotationally-symmetric power-exponent-phase vortex beams in oceanic turbulence.

In this paper, the propagation properties of radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in oceanic turbulence were theoretically and experimentally studied. Based on the extended Huygens-Fresnel diffraction integral and vector beams theories, the theoretical propagation model of RP-RSPEPVBs in the oceanic turbulence was established. Then, the numerical simulations were carried out to study the influences of the propagation distance z, the rate of dissipation of turbulence kinetic energy per unit mass of fluid ε, the temperature-salinity contribution ratio ω, and the dissipation rate of the mean-squared temperature χT on the optical intensity, spectral degree of polarization (DOP) and spectral degree of coherence (DOC) of RP-RSPEPVBs. Further, an experiment setup was demonstrated to confirm the influences of salinity and temperature on propagation of RP-RSPEPVBs in oceanic turbulence. The results showed that increasing salinity, propagation distance, and turbulence intensity, will result in beam diffusion and intensity reduction of the RP-RSPEPVBs, as well as depolarization and decoherence. Contrarily, high temperature mitigated the intensity loss of the RP-RSPEPVBs and the spectral DOP and spectral DOC increased when the turbulence tends to be dominated by temperature. As a vector beam, the RP-RSPEPVB shows well anti-turbulence interference characteristics, which provides a new choice for optical underwater communication and imaging.

Controlled generation of mode-switchable nanosecond pulsed vector vortex beams from a Q-switched fiber laser.

We reported and demonstrated a ring Q-switched Ytterbium-doped fiber laser that can generate mode-switchable nanosecond pulsed vector vortex beams between two different orders. In the spatial optical path of the fiber laser, several cascaded Q-plates, divided into two Q-plate groups, are applied for intracavity mode conversion between LP01 mode and vector vortex beams. In one Q-plate group, two quarter-wave plates are inserted to achieve the addition and subtraction of the order of Q-plates. By tuning the polarization state in the cavity, mode-switchable vector vortex beams (VVBs), including cylindrical vector beams (CVBs), elliptically polarized cylindrical vector beams (EPCVBs), and vortex beams, of two different orders can be generated on demand. The experimental results show that by using the group of 1st and 3rd orders Q-plates, the 2nd and 4th orders mode-switchable VVBs (vortex beams with topological charges of ±2, ±4, CVBs and EPCVBs of 2nd- and 4th-order) can be obtained from the fiber laser. The slope efficiency, pulse width, and repetition rate are 33.4%, 360 ns, and 241kHz respectively. To the best of our knowledge, this is the first time to realize the direct generation of mode-switchable VVBs on the arbitrary position of the higher-order Poincaré sphere between two different orders from a fiber laser. This work lays the foundation for the flexible generation of arbitrary modes of VVBs with multiple different orders in the laser cavity.

Generalized shift-rotation absolute measurement method for optical surface shapes with polygonal apertures based on migration recognition by Radon transform.

A generalized shift-rotation absolute measurement method for optical surface shapes with polygonal apertures based on migration recognition by Radon transform is proposed. The rotation angles and translation distances of the test surface, measured three times, are calculated through migration recognition. The absolute shape of the test surface with the polygonal aperture is fitted by orthogonal Zernike polynomials. Compared to the existing absolute measurement method for polygonal apertures, our method ensures test surface measurement accuracy without high-precision attitude control and repeated adjustments. The measurement is simple and coherent, which reduces the measurement time and improves the efficiency.

Accelerated convergence extended ptychographical iterative engine using multiple axial intensity constraints.

The extended ptychographical iterative engine (ePIE) is widely applied in the field of ptychographic imaging due to its great flexibility and computational efficiency. A technique of ePIE with multiple axial intensity constraints, which is called MAIC-PIE, is proposed to drastically improve the convergence speed and reduce the calculation time. This technique requires that the diffracted light from the sample is propagated to the multiple individual axial planes, which can be achieved by using the beam splitter and multiple CCDs. In this technique, an additional intensity constraint is involved in the iterative process that makes for building the reasonable guesses of the probe and object in the first few iterations and accelerating the convergence. Simulations and experiments have verified that MAIC-PIE behaves good performance with fast convergence. The great performance and limited computational complexity make it a very attractive and promising technique for ptychographic imaging.

Generalized shift-rotation absolute measurement method for high-numerical-aperture spherical surfaces with global optimized wavefront reconstruction algorithm.

In this paper, a generalized shift-rotation absolute measurement method is proposed to measure the absolute surface shape of high-numerical-aperture spherical surfaces. Based on the wavefront difference method, the high order misalignment aberrations can be removed from the measurements. Our generalized shift-rotation absolute measurement process only needs one rotational measurement position and one translational measurement position. A wavefront reconstruction method based on the self-adaptive differential evolution algorithm is proposed to calculate the Zernike polynomials coefficient ai of the absolute surface shape Wtest(x,y), the rotation angle Δθ, the translation δx along the x axis, and the translation δy along the y axis. The translation error and rotation error in other absolute measurement methods are avoided using our generalized shift-rotation absolute measurement method. Experimental absolute results of the test surface and reference surface are given and the difference of reference surface shapes between two testings in experiments is 0.12 nm root mean square.

Real-time complex amplitude reconstruction method for beam quality M2 factor measurement.

We present a real-time complex amplitude reconstruction method for determining the beam propagation ratio M2 of laser beams based on the transport of intensity equation (TIE). In this work, a synchronous acquisition system consisting of two identical CCDs is established. Once two beam intensity images at different cross-section positions along the optical axis are captured simultaneously by the system, the complex amplitude of the laser beam can be rapidly reconstructed using TIE algorithm. Then the beam intensity distribution at any section position along its propagation direction can be obtained by using angular spectrum (AS) theory. The beam quality M2 factor is therefore calculated utilizing the second-order moments and hyperbola fitting methods, which conform to the ISO standard. The suitability of this method is verified by the numerical analysis and experiments with the He-Ne and high-power fiber laser sources, respectively. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Resolution enhancement of the microscopic imaging by unknown sinusoidal structured illumination with iterative algorithm.

Microscopy by sinusoidal structured illumination is a conventional method to improve resolution, which largely depends on accurate knowledge of the illumination pattern. Two steps are included in the reconstruction process of our proposed technique. The first step solves the parameters of the structured illumination in the spatial domain. Besides the phase-shifting amounts, the period, the modulation factor, and the background intensity of the pattern are extracted from three segmented raw images by the iterative algorithm. The second step is retrieval and synthesis of the low- and high-frequency information of the object in the Fourier space with obtained data. Since the unknown object information is not involved in the pattern parameters' solving process, it is possible to figure out the problem with higher precision and less requirements. We test the performance of this method in the experiments. The resolution is improved with the designed carrier frequency of the illumination pattern.

Focal length measurement based on the wavefront difference method by a Fizeau interferometer.

A method for measuring the focal length of the lens by a Fizeau interferometer is proposed. Based on the Gaussian imaging equation and the longitudinal displacements of the object point and image point, a precise formula for focal length calculation is deduced. The longitudinal displacement of the object points is determined by the wavefront difference method with a subnanometer resolution. An experimental system for focal length measurements is set up to verify the principle. The sources of uncertainty in measurement are discussed. Both the positive and negative lens experimental results indicate that the measurement accuracy is less than 0.16% under normal experimental environment.