Beam Propagation Research Articles

Fully angularly resolved 3D microrheology with optical tweezers

Microrheology with optical tweezers (MOT) is an all-optical technique that allows the user to investigate a materials’ viscoelastic properties at microscopic scales, and is particularly useful for those materials that feature complex microstructures, such as biological samples. MOT is increasingly being employed alongside 3D imaging systems and particle tracking methods to generate maps showing not only how properties may vary between different points in a sample but also how at a single point the viscoelastic properties may vary with direction. However, due to the diffraction limited shape of focussed beams, optical traps are inherently anisotropic in 3D. This can result in a significant overestimation of the fluids’ viscosity in certain directions. As such, the rheological properties can only be accurately probed along directions parallel or perpendicular to the axis of trap beam propagation. In this work, a new analytical method is demonstrated to overcome this potential artefact. This is achieved by performing principal component analysis on 3D MOT data to characterise the trap, and then identify the frequency range over which trap anisotropy influences the data. This approach is initially applied to simulated data for a Newtonian fluid where the trap anisotropy induced maximum error in viscosity is reduced from ~ 150% to less than 6%. The effectiveness of the method is corroborated by experimental MOT measurements performed with water and gelatine solutions, thus confirming that the microrheology of a fluid can be extracted reliably across a wide frequency range and in any arbitrary direction. This work opens the door to fully spatially and angularly resolved 3D mapping of the rheological properties of soft materials over a broad frequency range.

The SMILE Effect in the Beam Propagation Direction Affects the Beam Shaping of a Semiconductor Laser Bar Array

Near-field bending of a laser diode bar (i.e., the SMILE effect) degrades the laser beam brightness, adversely affecting optical coupling and beam shaping. Previous reports mainly focused on the two-dimensional near-field bending of a laser diode bar. However, the near-field bending of a laser diode bar not only occurs in the laser bar growth direction, but also in the beam propagation direction. The present article proposes the three-dimensional near-field bending of a laser diode array, which is commonly known as the three-dimensional spatial SMILE effect. Through theoretical and simulated investigations, it has been found that a laser bar array not only deforms in the fast axis direction to cause the traditional two-dimensional SMILE effect but also experiences an additional deformation of approximately 2 μm in the laser emission direction simultaneously. Due to the SMILE effect in the beam propagation direction, not all emitters are aligned in a straight line, and some emitters experience defocusing during collimation. Consequently, there is an increase in the residual divergence angle and beam width, resulting in a degradation of the laser bar array’s beam quality. According to the theoretical calculations, ZEMAX simulations, and experimental results, for a FAC (fast axis collimation) with a focal length of 300 μm, the divergence angle of single emitter after collimating in the fast axis increases from 4.95 mrad to 6.46 mrad when the offsetting of the working distance between the incident beam waist and FAC lens increases from 0 μm to 2 μm.

Generation and propagation of circular Airy derivative beams carrying rotationally-symmetric power-exponent-phase vortices.

In this paper, the circular Airy derivative beams carrying rotationally-symmetric power-exponent-phase vortices are proposed for the first time, whose evolutionary properties are explored by theoretical analysis as well as experimental verification. The intensity and phase distributions of this kind of beam can be flexibly modulated by controlling its parameters such as derivative order, topological charge, and power order. Intriguingly, the evolution of such beams with different fractional topological charges is also investigated in detail by means of phase singularities distribution. In addition, from the perspective of transverse gradient force, the proposed beam is capable of efficiently protecting the trapped Rayleigh particles located at the beam center from the impact by surrounding particles. Furthermore, the beam width, orbital angular momentum (OAM) density and spiral spectrum are also compared and analyzed under different beam parameters. The proposed beams are expected to be useful for extending applications of optical vortices and autofocusing beam, especially for multi-regional particle gathering and central particle protecting.

Distribution of intensity and M2 factor for a partially coherent flat-topped beam in bidirectional turbulent atmosphere and plasma connection

This study investigates the bidirectional transmission of a partially coherent flat-topped beam in a turbulent atmosphere and plasma. Analytical formulas for the intensity distribution and M2 factor are derived based on the optical transmission matrix, Collins formula, and second moment theory with Wigner distribution function. Numerical results show that the beam order and transverse spatial coherence width can be selected appropriately to mitigate turbulence and plasma induced evolution properties. The partially coherent flat-topped beam propagation through a turbulent atmosphere and plasma of the forward transmission effect on the intensity distribution and M2 factor are smaller than that of the reverse transmission. Under the same conditions, the M2 factor of a partially coherent flat-topped beam is smaller than the Gaussian beam in bidirectional transmission. Our results can be used in long-distance free-space optical communications.

Abrupt autofocusing beam from a phase-only mask.

Airy beams have become an important beam shape for structured light beams because of their interesting self-accelerating and parabolic propagation properties. Many variants of Airy beams have been proposed, among which the Airy beam with cylindrical symmetry [also known as the circular Airy beam or abrupt autofocusing (AAF) beam] is particularly peculiar and has attracted special attention due to its shape transformation during propagation. Much effort has been devoted to understanding the properties of the AAF beam. In this work, we present simulation results for generating the AAF beam using a phase-only mask. A cubic chirp-modulated axicon phase is used to create the mask. We found an optimal value for the axiconic phase, and the cubic phase is essential for controlling the AAF beam's shape. We demonstrate that a phase-only mask is an effective and simple method for generating high contrast between the initial and AAF plane. We present the results for beam formation and propagation dynamics of the AAF beam using the control parameters of the phase mask. We also discuss the design parameters and their influence on the AAF beam shapes. Our results pave the way for a deeper understanding of the beam formation and propagation dynamics of the AAF beam.

Impact of flow-induced beam deflection on beam propagation in ignition scale hohlraums

Experiments examining the amount of specular reflection (or “glint”) within hohlraums containing different gas fill densities have recently been performed. Simulations of these experiments are presented that show using a single flux limiter cannot explain the decrease in glinted power with increasing gas fill density. The hypothesis that flow-induced beam deflection alters laser absorption is presented. A model is proposed that can be implemented into a ray tracing description of the laser commonly used in radiation hydrodynamic codes. It is shown that simulations using this model capture the trend with gas fill density improving agreement with measurements. This formulation is then applied to an ensemble of laser-driven inertial confinement fusion experiments performed at the National Ignition Facility. The proposed model shows little impact on the total x-ray drive on the capsule but a large impact on the resulting implosion symmetry.

Improvement of misalignment tolerance in free-space optical interconnects

In this paper, the use of micro lenses with non-uniform transmittance apertures as an alternative to those with uniform transmittance apertures in optical communication systems is proposed. In particular, we consider the use of micro lenses with tapered Gaussian transmittance profiles to improve the misalignment tolerance in optical interconnects. We study the effects of utilizing Gaussian transmittance profiles on the propagation of light beams and the signal to crosstalk ratio of misaligned optical systems. Moreover, we consider the use of uniform transmittance profiles in optical systems for the sake of comparison. To this end, the crosstalk optical noise is modeled at the plane of the detectors array considering the two scenarios of uniform and Gaussian apertures. This was possible after finding the optical field for both scenarios at the of the detectors array. Numerical results clearly demonstrate the significant improvement in decreasing the crosstalk and increasing the signal to crosstalk ratio in the considered optical systems upon utilizing the Gaussian profiles.

On the spin-quantization-axis selection for the spin polarization modeling during laser–electron collision

Spin polarized electron beams have wide applications in high energy physics. The generation of such electron beams has recently attracted considerable attention where the collision of intense laser pulses with high energy electron beams is proposed as one of the potential methods. In previous numerical studies, different spin-quantization axes (SQA) are used, which lead to different calculation results in some configurations of laser interaction with an electron beam. To be consistent with the well-known Thomas–Bargmann–Michel–Telegdi (TBMT) equation, we have proposed a new SQA which is along the TBMT precession direction. We clearly show the difference among the three kinds of SQA selections by comparing the temporal evolution of the electron beam's polarization during the perpendicular collision of an electron beam with s-polarized two-color laser pulses, where the magnetic fields have a parallel component along the electron motion direction. Calculation shows that such differences could be experimentally measured by nowadays facilities. To get the maximum electron polarization degree in the two-color laser pulses based schemes, we also find the optimized condition for the two-color laser parameters. Our studies give a better understanding of spin-polarization calculation and will be beneficial for future experimental designs for electron polarization manipulation.

New diffraction-limited laser systems with variable output parameters operating in visible spectral range on copper atomic transitions for advanced material micromachining

New considerably improved laser systems (LS) featuring beam propagation factor equal to unit, two different laser pulse durations and an average output power from several tens of Watts up to 50 W are reported. Micron-sized machining is also demonstrated.

Focused Shear Wave Beam Propagation in Tissue-Mimicking Phantoms.

Ultrasound transient elastography (TE) technologies for liver stiffness measurement (LSM) utilize vibration of small, flat pistons, which generate shear waves that lack directivity. The most common cause for LSM failure in practice is insufficient shear wave signal at the needed depths. We propose to increase shear wave amplitude by focusing the waves into a directional beam. Here, we demonstrate the generation and propagation of focused shear wave beams (fSWBs) in gelatin. Directional fSWBs are generated by vibration at 200-400 Hz of a concave piston embedded near the surface of gelatin phantoms and measured with high-frame-rate ultrasound imaging. Five phantoms with a range of stiffnesses are employed. Shear wave speeds assessed by fSWBs are compared with those by radiation-force-based methods (2D SWE). fSWB amplitudes are compared to predictions using an analytical model. fSWB-derived shear wave speeds are in good agreement with 2D SWE. The amplitudes of fSWBs are localized to the LSM region and are significantly greater than unfocused shear waves. Overall agreement with theory is observed, with some discrepancies in the theoretical source condition. Focusing shear waves can increase the signal in the LSM region for TE. Challenges for translation include coupling piston vibration with the patient skin and increased attenuation in vivo compared to the phantoms employed here. Fibrosis is the most predictive measure of patient outcome in non-alcoholic fatty liver disease. Increased shear wave amplitude in the LSM region can reduce fibrosis assessment failure rates by TE, thus reducing the need for invasive methods like biopsy.

Analysis of misaligned optics effects on beam pointing stability in dual-pass optical system

The high-power laser device utilizes a multi-pass amplification system to achieve elevated power laser output. Laser beam is transmitted several times through the amplifier, and the pointing stability is a critical factor affecting the efficiency of the system. Any perturbation of the optics during laser transmission can cause misalignment and further lead to beam pointing errors. Laser beam propagation simulation was conducted using the ray tracing method. Equivalent experiment was performed using a laser with a wavelength of 532 nm, and the centroid position data of the laser beam were collected to characterize the effect of the optics misalignment on laser pointing. A model evaluating the sensitivity of the optics was constructed, and the analysis of how various optics impact pointing accuracy was conducted. Results indicate that, a linear relationship exists between the misalignment of the optic and the pointing shift and angular deviation of the beam when a single optic is misaligned. If multiple optics are misaligned, the shift in centroid position of the laser beam can be calculated by adding up the shifts caused by each misaligned optic. Furthermore, the shift in the centroid position of the laser beam is the linear superposition of the misalignment of each optic.

Resonant second-harmonic generation of self-focused oblique incident laser beam in plasma

The present manuscript aims to realize the effect of self-focusing on second-harmonic generation (SHG) by oblique incident laser beams in plasma. When an intense laser beam is obliquely incident on the plasma, it is resolved into reflected and refracted components, and resonant SHG is produced in the reflected component on account of the self-focusing of the incident laser. With the help of paraxial approximation, we have obtained a mathematical expression for the beam width parameter and for the normalized amplitude of the second harmonic. It has been observed that the amplitude of the second-harmonic pulse is significantly influenced by the intensity of the incident laser beam, the wiggler magnetic field, and the normalized plasma frequency. The analysis was performed for different values of the angle of incidence and laser parameters. The results show stronger self-focusing and, hence, efficient SHG when the angle of incidence is the critical angle.

Performance of Orbital Angular Momentum Communication for a Non-Uniformly Correlated High-Order Bessel–Gaussian Beam in a Turbulent Atmosphere

We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, strength of the turbulent atmosphere, and topological charge effect on detection probability, SNR, and average BER of the signal OAM state were demonstrated numerically. The results show that the signal OAM state with low topological charge, a small receiver aperture, a narrow beam width, and a long wavelength can improve the performance of optical communications systems under conditions of weak atmospheric turbulence. Our results will be useful in long-distance free space optical (FSO) communications.

A modification to the extended Rytov theory

This paper proposes a heuristic modification to the extended Rytov theory of strong scintillation [Andrews L, Phillips R. Laser beam propagation through random media. 2nd ed., Washington, USA: SPIE Press; 2005, Andrews LC, Al-Habash MA, Hopen CY, et al. Theory of optical scintillation: Gaussian-beam wave model. Waves Random Media. 2001;11(3):271–291]. This is done by dividing the large and small scales in the extended Rytov theory into further sub-scales. Expressions for the induced irradiance variance, and log-irradiance, due to each sub-scale are presented. The modified theory is used to derive and justify recent results in irradiance fluctuation modeling and hence answer a question initially proposed in [Shishter YM, Young RC, Ali FH. Irradiance probability density function for turbulence induced fading in free space optics. JOSA A. 2022;39(7):1267–1274, Shishter YM, Young RC, Ali FH. General statistical model of irradiance fluctuations in free space optics. JOSA A. 2023;40(1):53–63]. Plots of the irradiance pdf under the modified theory are in support of the theory. The validity of the theory presented would result in modifications to the classical scintillation analysis of waves in random media, with applications to the design of optical systems. Moreover, it is observed that the mathematical framework developed also follows from the assumption of variations in the turbulence along a horizontal path. The work presented in this paper suggests the need of further theoretical and experimental investigations into the effect of variations in atmospheric turbulence characteristics along horizontal paths in the received signal irradiance distribution.

Cylindrical vector beam generation from a hybrid multimode Q-switched mode-locked fiber laser

We demonstrate a hybrid multimode Q-switched mode-locked fiber laser capable of delivering cylindrical vector beams (CVBs). The wavelength-tunable Q-switching, conventional mode-locking, Q-switched mode-locking (QML), and CVB generation under QML operation are respectively achieved in this hybrid multimode cavity. The mode-locking mechanism is based on carbon nanotubes as saturable absorber and two interferometric filtering structures, i.e., multimode fiber-single-mode fiber-multimode fiber and multimode fiber-few-mode fiber-multimode fiber. The mode-selective coupler is used as a mode selector converting the fundamental mode to higher-order mode and as an output coupler to obtain CVB. The Q-switched pulses allow for tunable wavelengths in the range of 1028.2 nm to 1038.2 nm, with a frequency of about 50 KHz. The conventional mode-locking is achieved with a repetition frequency of 15.6 MHz and a pulse interval of 66.7 ns. Specifically, the introduction of dual interferometric filtering structures in the cavity results in noteworthy nonlinear effects, facilitating the generation of third-harmonic mode-locking under the single-wavelength QML operation. These experimental findings highlight the promising applications such as mode-division multiplexed optical communication and laser processing.

Research on Multibeam Line Measurement Problem Based on Iterative Algorithms

With the continuous advancement of marine resource development, an efficient and reasonable multi beam acoustic survey line design scheme is crucial for accurate sea area measurement. Firstly, in order to make the model closer to the actual complex scene, a three-dimensional coverage model was derived that comprehensively considers the relative angle between the measurement line and the normal direction of the seabed terrain slope projected on the horizontal plane, referring to the three-dimensional sound beam propagation characteristics of multi beam sound waves. Then, based on the working principle and geometric relationship of multi beam recording, a formula for calculating the recording coverage width under multi-directional slope conditions considering measurement equipment parameters was derived, and an expression for the overlap rate of adjacent measurement lines was given. In addition, different measurement lines and slope normal direction angles . Finally, based on the actual sea area situation of the rectangular area within the specific given range, iteratively traverse and set different combinations of survey lines, calculate the total length of the combination and the corresponding coverage area, and calculate the coverage rate. Select the survey line combination with the shortest total length and the highest coverage rate as the optimal solution. This article focuses on the design of multi beam acoustic survey lines and establishes a universal mathematical model to achieve optimization solutions in different practical scenarios.

Reuleaux triangle core fiber with triple rotational symmetry.

A Reuleaux triangle core fiber (RTF) with triple rotational symmetry is proposed and fabricated. Then the RTF is twisted to form the chiral fiber grating, which converts the core mode into a vortex mode containing 3rd-order orbital angular momentum (OAM). Based on the Fourier expansion of the core boundary, the straight-sided and arc-sided triangular core profiles were analyzed, revealing the mechanism of high-efficiency OAM3 generation. The experimental results show a 3rd-order vortex mode with a high conversion efficiency and purity, and the polarization-independent characteristics endowed by the core shape are also confirmed. The proposed RTF provides a new, to the best of our knowledge, way for higher-order vortex beam generation, which can be used in optical fiber communication systems with OAM multiplexing.

Bragg scattering of stochastic beams in PT-symmetric photonic lattices.

The propagation of a Gaussian-Schell beam through a PT-symmetric optical lattice, whose index of refraction is represented by a sinusoidal type of function, is theoretically investigated. Within the framework of standard coherence theory, one is able to access and elucidate unexpected consequences of the interplay between the spatial coherence properties of the beam and the non-Hermitian nature of the photonic lattice. We describe how one may use a non-Hermitian periodic medium to enhance the spatial coherence properties of a partially coherent beam.

Wideband directional-fed holographic metasurface with integrated monopole and parabolic reflector for far-/near-field beams manipulations

Holographic metasurface has been widely investigated, but suffers from the trade-off between bandwidth, gain, and integration. In this article, a wideband high-gain holographic metasurface with miniaturized integrated monopole is proposed. It employs the geometrical characteristics of parabolic reflector to realize directional-fed metasurface, and the footprint is reduced to only one-third of the conventional center-fed designs. By varying modulation index and paraboloid height, the bandwidth and gain are improved simultaneously. To validate the proposed idea, two prototypes are analyzed and fabricated to demonstrate flexible beam manipulation in respective far-field radiation and near-field propagation. Pencil beam pays more attention to the far-field and directionality of the beam, while Bessel beam focuses more on the near-field and non-diffractive of the beam. In both cases, the measured results are well-matched with the simulation. The proposed holographic metasurface for far-field applications features wide bandwidth, high gain, and planar integration simultaneously. Moreover, to the best of the authors’ knowledge, this is the first Bessel beam generator using directional-fed holographic metasurface with parabolic reflector.

Fracture analysis of orthotropic functionally graded materials using element-based peridynamics

A fracture model of orthotropic functionally graded materials (FGMs) based on element-based peridynamics (EBPD) is proposed. Two-dimensional (2D) orthotropic FGMs use three-node triangular elements to describe the force density of EBPD. Due to the gradient difference of material properties inside the element, the Gauss integral formula is used to average the node performances to the integral point of the element. The equations of motion for EBPD is established, which is also applied to orthotropic FGMs by the Gauss integral formula. The micromodulus coefficient of the EBPD is derived for orthotropic FGMs. The critical strain energy density criterion is used as the failure criterion to simulate the quasi-static and dynamic fracture problems. A series of numerical examples, including displacement analysis, stress analysis, dynamic crack propagation of FGM beam, and crack growth of orthotropic FGMs under four-point bending load, are used to validate the accuracy of the fracture model of orthotropic FGMs. The proposed model can be helpful to the material gradient design for FGMs satisfying certain requirements.