Intensity Distribution Of Beam Research Articles

Evolution properties of partially coherent radially polarized Laguerre–Gaussian vortex beams in an anisotropic turbulent atmosphere

Analytical formulas for the cross-spectral density matrix of a partially coherent radially polarized Laguerre-Gaussian vortex (PCRPLGV) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution laws of statistical properties of a PCRPLGV beam in turbulence, such as the average intensity, degree of coherence (DOC) and degree of polarization (DOP), are investigated in detail. It is found that the atmospheric turbulence induces degeneration of the intensity distribution of a PCRPLGV beam on propagation, and some new properties, such as self-shaping and self-rotating, will appear on propagation due to vortex phase. In addition, in order to verify our theoretical results, we combined the complex screen method and multi-phase screens method to simulate the propagation of PCRPLGV beam in atmospheric turbulence. And the studies indicate that the simulation results are consistent with the theoretical predictions. Our results will be useful in some potential applications, such lidar detection, remote sensing and free-space optical communications.

Terahertz vortex beam propagation through a magnetized plasma-ferrite structure

Interaction of vortex beams with materials has proven to be a key for controlling and exploiting theirs properties. In this paper, we propose an adjustable stratified structure constructed from plasma and ferrite layers, which greatly manipulates the intensity and phase distributions of incoming terahertz vortex beam (TVB), and demonstrates a considerable amount of Faraday rotation. To obtain the output beam profiles, first using angular spectral expansion technique the incoming TVB is decomposed into a superposition of plane waves, then employing 4×4 matrix formalism total reflection and transmission coefficients are extracted. Numerical analysis reveals that how the variations of external static magnetic field, incident angle, and radial and angular indices of the TVB affect the features of reflected and transmitted beams. It is expected that this investigation will shed new light on the interaction of TVB with anisotropic magnetic materials, and open new possibilities for wavefront engineering and material characterization.

Freeform optical design of beam shaping systems with variable illumination properties.

Freeform optics constitutes a new technology that is currently driving substantial changes in beam shaping. Most of the current beam shaping systems are elaborately tailored for fixed optical properties, which means the output light distribution of a beam shaping system usually cannot be changed. What we present here is a class of beam shaping systems, the optical properties of which can be changed to meet the requirements for different applications. The proposed beam shaping system is composed of a freeform lens and a non-classical zoom system which is designed by ray aiming and the conservation of energy instead of aberration control. The freeform lens includes two elaborately designed freeform optical surfaces, by which both the intensity distribution and wave-front of an incident light beam are manipulated in a desired manner. The light beam after propagating through the non-classical zoom system produces an illumination pattern on a fixed observation plane with a variable pattern size and an unchanged irradiance distribution at different zoom positions. Two design examples are presented to demonstrate the effectiveness of the proposed beam shaping systems.

Investigation on reduction of dross height by analyzing beam intensity distribution in fiber laser cutting

Nowadays, fiber lasers have become a main energy source in laser cutting because of their highly electro-optical conversion efficiency and high beam quality. However, the amount of dross produced by fiber laser cutting is larger than that by CO2 laser cutting, and postprocessing is required to obtain a flat surface without dross, which leads to increasing the processing cost. If fiber laser achieves dross-free cutting of a steel plate, further expansion of cutting applications can be expected. Therefore, in order to achieve further reduction of dross, the influence of beam intensity distribution on dross height was investigated by fiber laser cutting experiments and ray tracing analysis. The laser cutting experiment of steel plate cold commercial with 3.2 mm thickness was carried out by a 3 kW fiber laser with nitrogen assist gas, and a round Gaussian mode of 114 μm spot diameter and a square top-hat mode of 132 μm were used. The square top-hat mode can achieve smaller dross height below 12 μm, which is approximately half of the round Gaussian mode. Ray tracing analysis revealed that the square top-hat mode increased the uniformity of absorbed energy on the cutting front surface, and the more uniform intensity distribution contributed to a small ellipticity of the cutting front shape of the kerf. It was clarified that the shape of the cutting front with a small ellipticity reduced the amount of molten metal ejected from the side of the kerf, which resulted in the reduction of dross height by the fiber laser cutting.

Defining speckle-based spectral metric from a linear array detector for characterizing the laser focusing spot

Speckle modulation in the laser beam projection scenarios such as adaptive optics, remote sensing, and active imaging has been a long-standing challenge that causes intensity fluctuation and further degrades the performance of the system. Speckle statistical characteristics coupled with the feature of the laser beam intensity distribution can be obtained by analyzing the speckle variation through a single point detector or an image sensor. A single point detector has the advantage in high sampling rate but may lose speckle spatial information, while the image sensor has a high spatial resolution but slow sampling rate. In this paper, we defined a dynamic speckle metric based on a linear array detector to estimate the encircled energy of the far-field spot on the diffuse target, which well balanced the trade-off between sampling rate and spatial resolution. The potential of the metric is analyzed using a physics-based speckle simulation and experimental verification. Both results agree with each other, showing that the metrics based on the speckle-field spatiotemporal spectrum analysis are monotonically dependent on the target focused-spot size.

Multi-degree-of-freedom beam rotation based on multi-beam vector superposition

A method for the generation of tunable multi-degree-of-freedom rotations of vector beams on demand along a propagation direction is theoretically proposed. This generation can be achieved by a suitable vector superposition of three monochromatic non-coplanar beams, including a plane wave with elliptical polarization and two Bessel–Hermite–Gauss (BHG) beams with orthogonal polarization, the parameters of which were systematically chosen to obtain the different longitudinal characteristics of the field, i.e., the state of polarization (SoP), phase, and intensity. On one hand, both the incidence angles of the two BHG beams and the additional phase of the plane wave affect the rotation of the beam intensity and phase, but the incidence angle does not affect the rotation of the SoP. Moreover, the additional phase can lead to a change of the rotation angle of the SoP. On the other hand, the weight coefficients of the two BHG beams periodically change the beam intensity distribution along the propagation direction. Interestingly, the beam is non-diffracting, which means that energy is only exchanged internally and is conserved as a whole. This approach may find applications in dynamic multi-beam optical tweezers, atom guiding, materials processing, microscopy, and optical communications.

Optical vortices with an infinite number of screw dislocations

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

Generation of hollow laser beam with adjustable profile distribution by using tapered fiber

We present a method to produce a hollow laser beam with adjustable profile distribution using a tapered optical fiber. The dependence of the dark spot size (DSS), hollow beam width (HBW), and transverse field intensity distribution of the hollow beam on the incidence angle of the laser beam, cone angle of the tapered fiber, and working distance are analyzed theoretically and experimentally. The study shows that a high-power hollow laser beam with excellent propagation properties can be achieved by using a tapered fiber with certain parameters. The proposed technique is simple, flexible, and easy to control and operate.

Creation of Hollow-Gaussian Beam for Optical Trap by Dual-beam Nonliear Fabry-perot Interferometer

In this paper, a model of dual-beam nonlinear Fabry-Perot interferometer (DBNFPI) for creation laser hollow-Gaussian beam (HGB) is investigated. It includes a thin film of organic dye sandwiched between two optical mirrors, and irradiated by two signal and pump laser Gaussian beams. Based on the equation describing the output-input relation of intensities concerning pump intensity and the expression of the spatial intensity distribution of output signal beam (OSB), the range of pump intensity and collection of designed parameters are numerically calculated and discussed for HGB creation. These results give us the opportunity to use DBNFPI for optical trap of low-index dielectric particles.

Optical vortices with an infinite number of screw dislocations

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

Experimental study on compensation of beam distortion caused by turbulence using a phase conjugate beam

The distortion of the laser beam caused by atmospheric turbulence has always been a major impediment in free space optical communication (FSOC) system. The atmospheric turbulence is mainly from the changes of the random refractive index in the atmosphere and leads to the random distribution of beam intensity. A phase-conjugate beam can effectively correct this type of deformation. In our research, by degenerate four-wave mixing (DFWM) method, a phase-conjugate beam is generated through a methyl orange doped polyvinyl alcohol solution to correct the mirror-reflected beam through a turbulence promoter. In comparison with the mirror-reflected beam, the phase-conjugate beam has a better near-Gaussian intensity distribution. The results show that the phase-conjugate beam has a positive effect on the correction of distortion caused by turbulence.

Wavefront Restoration Technology of Dynamic Non-Uniform Intensity Distribution Based on Extreme Learning Machine.

Non-uniform intensity distribution of laser near-field beam results in the irregular shape of the spot in the wavefront sensor. The intensity of some sub-aperture spots may be too weak to be detected, and the accuracy of wavefront restoration is seriously affected. Therefore, an extreme learning machine method is proposed to realize high precision wavefront restoration under dynamic non-uniform intensity distribution. The simulation results show that this method has better accuracy of wavefront restoration than the classical modal algorithm under dynamic non-uniform intensity distribution. The root mean square error of the residual wavefront for the proposed method is only 2.9% of the initial value.

On the use of a digital twin to enhance femtosecond laser inscription of arbitrary phase patterns

Thanks to the non-linear nature of laser-matter interaction, the use of femtosecond lasers offers a versatile method for encoding information and modifying transparent materials in their volumes and this, with sub-micron resolution. The underlying physical process is a succession of intricate and complex nonlinear phenomena that are sensitive to multiple and multidimensional parameters, such as beam intensity distribution, exposure dose homogeneity and pulse-overlapping sequences as well as propagating wavefront angular orientations and temporal distortions. As a consequence to this inherent and often overwhelming complexity, obtaining a repeatable and accurate result relies strongly on time-consuming machine-specific calibration and experiment-specific fine-tuning attempts until the desired result is reached. Here, we present a digital twin of the processed specimen that not only accurately predicts the exposure outcome in terms of introduced retardance, but also offers a pathway for designing feedforward schemes that compensate for known inaccuracies. We demonstrate the merit of this approach through illustrative examples of arbitrary phase patterns, forming waveplates and images, based on refractive index modulation induced during laser exposure.

The effect of laser beam intensity distribution on weld characteristics in laser welded aluminum alloy (AA5052)

The distribution of laser beam intensity can play a key role in laser welding, since it is deeply related to the temperature gradient and cooling rate of the melt pool. In this study, aluminum alloy butt welding was conducted using a normal Gaussian beam and modulated beams with various intensity profiles, produced with a diffractive optical element (DOE). Their effect on the weld characteristics was investigated. Welding with the modulated beams generally required larger heat input for full penetration compared with the Gaussian beam welding (GBW) since laser energy was spread by the core and ring beam combination. This laser energy spreading reduced weld defects and produced a funnel-shaped weld cross-section in the modulated beam welding (MBW). Microstructure analyses found that the GBW and MBW had different grain growth behaviors based on the shape of the melt zone boundary. A straight melt zone boundary formed along the vertical direction induced columnar grain growth along the horizontal direction in the GBW. For the MBW, it grew along the diagonal direction, because the melt zone boundary had a slanted shape. The highest tensile strength (208.2 MPa, which corresponded to ~ 91% of the tensile strength of the base material) was obtained with the MBW, owing to reduced average grain size. It was found that the re-crystallization process induced by laser welding significantly increased the grain size of the original material.

Spatial modulation of Gaussian beam by dual-beam nonlinear Fabry-Perot interferometer

In this paper, a model of dual-beam nonlinear Fabry-Perot interferometer (DBNFPI) for laser Gaussian beam’s spatial modulation is proposed. It includes a thin film of oil red O sandwiched between two optical mirrors and is irradiated by two signal and pump laser Gaussian beams. The equation describing the output-input relation of intensities concerning pump intensity and the expression describing the spatial intensity distribution of output signal beam (OSB) are derived. The optical bistability of DBNFPI is numerically calculated with different pump intensities as well as the capability to spatially modulate the Gaussian beam is discussed. The different shapes of the OSB as: Gaussian, flat-top-Gaussian, ring-Gaussian, hollow-Gaussian, and multi-hollow-Gaussian are shown. The suitable range of pump intensity for particular shape of OSB is discussed, especially the hollow-Gaussian shape requirement for optically trapping microspheres having reflective index to be lower than that of embedding fluid.

Intensity and beam widths of a four-petal Lorentz-Gauss vortex beam propagating in turbulent atmosphere

The equations of average intensity and beam widths of a four-petal Lorentz-Gauss vortex (FPLGV) beam propagating in turbulent atmosphere have been derived, and the evolutions of average intensity and beam widths of a FPLGV beam in turbulent atmosphere are discussed using numerical examples. It is found that intensity distribution of a FPLGV beam at the short distance can be controlled by modulating topological chargeM and beam order N, and the FPLGV beam will translate into Gaussian beam due to the actions of atmospheric turbulence at longer distance. It is also found that the beam widths of a FPLGV beam will increase as the distance increases, and the beam propagating in stronger atmospheric turbulence will have a larger beam width at the same propagation distance.

Unified Model for Laser Doping of Silicon from Precursors.

Laser doping of silicon with the help of precursors is well established in photovoltaics. Upon illumination with the constant or pulsed laser beam, the silicon melts and doping atoms from the doping precursor diffuse into the melted silicon. With the proper laser parameters, after resolidification, the silicon is doped without any lattice defects. Depending on laser energy and on the kind of precursor, the precursor either melts or evaporates during the laser process. For high enough laser energies, even parts of the silicon’s surface evaporate. Here, we present a unified model and simulation program, which considers all these cases. We exemplify our model with experiments and simulations of laser doping from a boron oxide precursor layer. In contrast to previous models, we are able to predict not only the width and depth of the patterns on the deformed silicon surface but also the doping profiles over a wide range of laser energies. In addition, we also show that the diffusion of the boron atoms in the molten Si is boosted by a thermally induced convection in the silicon melt: the Gaussian intensity distribution of the laser beam increases the temperature-gradient-induced surface tension gradient, causing the molten Si to circulate by Marangoni convection. Laser pulse energy densities above H > 2.8 J/cm2 lead not only to evaporation of the precursor, but also to a partial evaporation of the molten silicon. Without considering the evaporation of Si, it is not possible to correctly predict the doping profiles for high laser energies. About 50% of the evaporated materials recondense and resolidify on the wafer surface. The recondensed material from each laser pulse forms a dopant source for the subsequent laser pulses.

Optimized Design of a Pump Laser System for a Spin Exchange Relaxation Free Inertial Measurement Device.

In order to improve the precision and beam quality of a pump laser for a spin exchange relaxation free inertial measurement device, we applied one scheme to achieve the square wave modulation and power stability control of the pump laser and another one to obtain the uniform intensity distribution of the laser beam, in which the acousto-optic modulator (AOM) and proportion integration differentiation (PID) controller were used to achieve the former, and the freeform surface lens was designed and optimized to achieve the latter based on the TracePro software. In experiments, the first-order diffraction light beam coming through the AOM had a spot size of about 1.1 × 0.7 mm2, and a spherical vapor cell with a radius of 7 mm was placed behind the freeform surface lens. Results show that the uniformity of the reshaped intensity distribution is higher than 90% within the target area with a radius of 7 mm both in the simulation and the experiment, which ensure that the uniform laser beam covers the area of cell. On the other hand, the power stability of the pump laser is controlled to be less than 0.05%. Compared with traditional methods, the complicated calculation process in optical design is better solved, and a higher uniformity with slight energy loss is achieved.

A crossed focused vortex beam with application to cold molecules* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11834003 and 91836103).

We report the generation of a crossed, focused, optical vortex beam by using a pair of hybrid holograms, which combine the vortex phase and lens phase onto a spatial light modulator. We study the intensity distributions of the vortex beam in free propagation space, and the relationship of its dark spot size with the incident Gaussian beam’s waist, the lens’s focal length, and its orbital angular momentum. Our results show that the crossed, focused, vortex beam’s dark spot size can be as small as 16.3 μm and adjustable by the quantum number of the orbital angular momentum, and can be used to increase the density of trapped molecules. Furthermore, we calculate the optical potential of the blue-detuned, crossed vortex beam for MgF molecules. It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling, as the intensity gradient of such vortex beam is extremely high near the focal point.

Laser-Material Interactions of High-Quality Ultrashort Pulsed Vector Vortex Beams.

Diffractive multi-beams based on 1 × 5 and 2 × 2 binary Dammann gratings applied to a spatial light modulator (SLM) combined with a nanostructured S-wave plate have been used to generate uniform multiple cylindrical vector beams with radial and azimuthal polarizations. The vector quality factor (concurrence) of the single vector vortex beam was found to be C = 0.95 ± 0.02, hence showing a high degree of vector purity. The multi-beams have been used to ablate polished metal samples (Ti-6Al-4V) with laser-induced periodic surface structures (LIPSS), which confirm the polarization states unambiguously. The measured ablation thresholds of the ring mode radial and azimuthal polarizations are close to those of a Gaussian mode when allowance is made for the expected absolute intensity distribution of a ring beam generated from a Gaussian. In addition, ring mode vortex beams with varying orbital angular momentum (OAM) exhibit the same ablation threshold on titanium alloy. Beam scanning with ring modes for surface LIPSS formation can increase micro-structuring throughput by optimizing fluence over a larger effective beam diameter. The comparison of each machined spot was analysed with a machine learning method—cosine similarity—which confirmed the degree of spatial uniformity achieved, reaching cosθ > 0.96 and 0.92 for the 1 × 5 and 2 × 2 arrays, respectively. Scanning electron microscopy (SEM), optical microscopy and white light surface profiling were used to characterize and quantify the effects of surface modification.