Rayleigh Range Research Articles

Inhomogeneous thermal analysis of microlayer mold for glass molding of fast-axis collimation lens array

Fast-axis collimation (FAC) lens arrays play a crucial role in laser systems, offering precise beam shaping and focusing for applications such as laser marking, and optical communication. Achieving high precision in these applications requires a FAC lens array with a long Rayleigh range. While precision glass molding with nickel-phosphorus (Ni-P) microlayer molds has revolutionized the mass production of FAC lens arrays, the extreme conditions during the molding process can lead to poor profile accuracy. To address this issue, we developed an optical collimation system to derive the final characteristic parameters and obtain the beam waist radius and Rayleigh range of the collimated laser. Additionally, we conducted a thorough analysis of the inhomogeneous thermal expansion process of the microlayer mold and established a mathematical solution for thermal compensation to modify the mold's shape. We validated the proposed method by fabricating an FAC lens array mold and measuring the profile error and waist radius of a molded FAC lens array. We also calculated the profile error of this method using a finite element (FE) model in ABAQUS. The results indicate that incorporating the inhomogeneous thermal expansion reduces the shape error of the FAC lens array from 0.577 μm to 0.135 μm. Moreover, using inhomogeneous thermal compensation significantly improves the Rayleigh range of the FAC lens array from 1.285 μm to 9.8 × 104 μm.

Confocal corrected attenuation coefficient imaging in phantoms and in vivo using chromatic focal shift calibration.

Optical coherence tomography (OCT) is conventionally used for structural imaging of tissue. Calibrating the intensity values of OCT images can give information on the tissue's inherent optical properties, such as the attenuation coefficient, which can provide an additional parameter to quantify possible pathological changes. To obtain calibrated intensity values, the focus position and Rayleigh length of the incident beam need to be known. We explore the feasibility of extracting the focus position from an OCT scan acquired with a single focus setting using the chromatic aberration of the system. The chromatic focal shift of an OCT system is exploited to achieve different focus positions for sub-spectrum reconstructed OCT images. The ratios of these images are used to estimate the focus position. Reconstruction of a high-resolution B-scan from coherent addition of sub-spectrum confocal function corrected B-scans and subsequent high-resolution OCT attenuation coefficient imaging is demonstrated. Furthermore, we introduce a method to experimentally determine the chromatic focal shifts of an OCT system in phantoms and an in vivo human retina. These shifts are compared to the theoretically expected shifts calculated with ray tracing.

Photon centroids and their subluminal propagation

We examine properties of the energy-density and photon-probability centroids of electromagnetic wavepackets in free space. In the second-order paraxial approximation, both of these centroids propagate with the same subluminal velocity because of the transverse confinement of the wavepacket and its diffraction. The tiny difference between the energy and probability centroid velocities appears only in the fourth order. We consider three types of wavepackets: Gaussian, Bessel, and non-diffracting Bessel. In all these cases, the subluminal propagation is clearly visible in the intensity distributions and can be measured experimentally in both classical-light and single-photon regimes. For Gaussian wavepackets, the half-wavelength delay is accumulated after propagation over about 12 Rayleigh lengths.

Identifying the influence of bubble size and position on crater formation during underwater nanosecond laser ablation of stainless steel

Underwater laser ablation can be employed both as a means to produce nanoparticles and to texturize surfaces of various materials. In this approach, a stationary or flowing water layer above the target surface confines laser induced plasma which cools to form short lived cavitation bubbles, positively influencing the amount of removed material per laser pulse. Plasma and cavitation bubble evolution additionally give rise to bubbles which may persist in the water throughout the ablation process. These bubbles are known to have a detrimental effect on material removal rates particularly in stationary water, but the quantitative influence of bubble dimensions and position on removed material volume is currently unknown. Here we show the laser intensity profile changes induced by bubbles located at 0–0.4 Rayleigh lengths above a stainless steel surface and couple these changes to removed crater volume. Our results show that water flowing at Reynolds numbers in the range of 1–100 positively contribute to crater volumes for pulse frequencies up to 1 kHz. At 1 kHz, it was found bubbles have insufficient time to flow from the vicinity of the laser spot, regardless of the Reynolds number within the range investigated. These conclusions assist in selecting an appropriate combination of laser and flow conditions to optimize laser ablation material removal rate.

Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror

In this paper we study the propagation of structured optical scalar beams in a Lorentz-violating (LV) vacuum parametrized by a constant 4-vector u μ and in the presence of a semi-transparent mirror. The two bosonic degrees of freedom of the electromagnetic field can be described by a LV extension of the massless scalar field theory, whose LV part is characterized by the term (u · ∂ϕ)2. The mirror at a surface Σ is modelled by a delta-type potential in the Lagrange density for the LV scalar field, i.e. λ δ(Σ)ϕ 2, where the parameter λ controls the degree of transparency of the mirror. Using Green’s function techniques, we investigate the propagation of a Gaussian beam in the presence of a mirror which is perpendicular to the propagation direction and for two particular choices of the background 4-vector: parallel and perpendicular to the propagation direction. To quantify the Lorentz-violating effects we introduce the fidelity as a measurement of the closeness of the propagated field distribution with respect to that in the conventional vacuum. In the absence of the mirror (λ = 0) the fidelity is found to be close to one, and hence LV effects are quite small. However in the presence of the mirror, there are regions where the fidelity drops to zero, thus implying that LV effects could be clearly differentiated from the propagation in vacuum. Within the paraxial approximation we determine analytically the LV effects upon the Rayleigh range, the radius of the beam, the Gouy phase and the radius of curvature of the wavefronts. We discuss possible scenarios where our results could apply, by using optically transparent multiferroic materials, which offer unprecedented opportunities to tailor structured beam propagation, as well as to simulate an LV vacuum.

A Pulsed Lidar System With Ultimate Quantum Range Accuracy

A light detection and ranging (lidar) system using a multi-output quantum pulse gate (mQPG) for quantum uncertainty limited range resolution is presented. Due to the inherent phase-sensitivity of the process, the proposed mQPG enhanced lidar system is able to beat the theoretical Rayleigh range resolution limit and the single detection Craméer-Rao bound (CRB) of classic pulsed lidar. To achieve this behavior, gating pulses interact with the backscattered lidar pulse while propagating through the optically non linear waveguide within the mQPG. The intensity of the discrete spectral channels of the mQPG contains finally the target distance informations. The mQPG was fabricated in a periodically poled (PP) titanium-indiffused lithium niobate waveguide and the entire system was built up in a lab environment. Measurement up to 1500 μm were performed around an arbitrary set reference point, and show excellent agreement with the theory up to 600 μm for a pulse length of 1.56ps, and up to 1100 μm for a pulse length of 2.12ps.

Flying focus laser Wakefield scheme for efficient acceleration

The acceleration of charged particles with a short laser pulse is a revolutionary acceleration technology, but many restrictions limit their advantages. Wave breaking and dephasing are most important of these restrictions which weaken acceleration efficiency in the laser Wakefield acceleration scheme. The purpose of this paper is to demonstrate that flying focus laser Wakefield acceleration (FF-LWFA) can confirm this effectiveness. Flying focus creates in the focal region of a hyper-chromatic lens when the chirped laser pulse passing through them. Therefore, by controlling the lens chromaticity and initial chirp characteristics, the focal point velocity can be controlled and adjusted near the speed of light. For a realistic working parameter, two-dimensional simulation results show the flying focus pulse can retain its shape and energy within a few centimeters (one order of magnitude greater than Rayleigh's length). We introduce a velocity interval around velocity of light in which dephasing and wave breaking are restricted and high acceleration gradients (about a hundred of GeV/m) are achieved in the flying focus region. Moreover, in the optimized condition for negative chirp, wakefield amplitude is increased 50 %. Under this ideal situation, 0.5 % of background electrons accelerate to 2GeV in the 5 cm, where the acceleration gradient reaches to, 40GeV/m, and about 0.2 % of them accelerate up to 10GeV.

Generation of Bessel-like beams with reduced sidelobes for enhanced light-sheet microscopy

Bessel beams have found important applications due to their propagation invariant nature. However, the presence of sidelobes has proven a hindrance in key imaging and biophotonics applications. We describe the design and generation of sidelobe-suppressed Bessel-like beams (SSBB) that provide enhanced contrast for light-sheet imaging. The sidelobe suppression is achieved by the interference of two Bessel beams with slightly different wavevectors. Axicon phase functions for each Bessel beam are combined into a single phase function using the random multiplexing technique. This phase function is realised using a spatial light modulator to generate a SSBB. The generated beam at 633 nm has a 1/e 2 radius of 44 µm and a propagation invariant distance of 39 mm which is more than four times that of the Rayleigh range of a Gaussian beam with the same 1/e 2 radius. Within this distance, the overall peak intensity of the sidelobes of the SSBB is less than 10% that of the main lobe peak intensity. In addition, through numerical simulation for the recovery of spatial frequencies, we show that the SSBB improves image contrast compared to a Bessel beam for light-sheet imaging. We also show that the designed phase function can be realised using a meta-optical element.

Use of the Airy beam to extend the micro-hole measurement range of an OCT system

Optical coherence tomography (OCT) has the advantage of high precision in measuring micrometre-scale precision structures, but its measurement range is limited by the correlation with Rayleigh length of Gaussian beam. Therefore, this study used the Airy beam to extend the focal depth of the OCT system. The system’s coupled power was increased by 7.34 times when the sample position was at an optical defocus of 3 mm. Measurements of the resolution plate and silicon wafer sample showed that Airy beam OCT had a lateral resolution of 7.4 μm and the focal depth was >6 mm. While the focal depth of the Gaussian beam OCT with the equivalent lateral resolution was less than 1 mm. This improved OCT system demonstrates significant potential for sample measurements at large aspect ratios in the industrial surface detection field.

Huge spikes and dips of the orbital angular momentum in structured Laguerre-Gaussian beams resistant to simple astigmatism

The article investigated conditions for shaping astigmatic-invariant structured Laguerre-Gaussian (LG) beams in the case of simple astigmatism. We have theoretically and experimentally confirmed that the conditions of astigmatic invariance are that the q-phase parameter of the structured LG (sLG) beam is equal to the arctangent of the ratio of the Rayleigh length z0 to the focal length fcyl of a cylindrical lens for a single amplitude parameter of epsilon;=1. For the rest amplitude parameter values, epsilon;NotEqual;1, the astigmatic invariance condition is set by the equality of the orbital angular momenta (OAM) of structured sLG and astigmatic-invariant sLG (asLG) beams. We have also found sharp spikes and dips of the OAM in astigmatic asLG beams in the region where OAM turns into zero. The height and depth of these spikes and dips significantly exceed the maximum and minimum OAM values in the conventional structured sLG beams. It has been shown that the occurrence of spikes and dips of the OAM is caused by a radical restructuring of the LG mode spectra in the form of their strong ordering. Theoretical calculations, accompanied by a computer simulation, and an experiment agree well with each other.

Propagation and focusing dependency of a laser beam with its aberration distribution: understanding of the halo induced disturbance

In various applications, it is necessary to understand laser field dynamics during its propagation, especially at the focal position including the dispersed energy surrounding the main pulse, called the halo effect. For instance, the properties of electron beams produced by laser wakefield acceleration (LWFA) strongly depend on the laser energy distribution and its halo in the vicinity of the focus. Indeed, under certain conditions, this halo, or even its internal structures, can propagate and be self-focused independently of the main pulse in the plasma. This paper aims to provide sufficient tools to properly describe the behavior of a focused laser beam, including the halo. Subsequently, an optical description regarding the source of this halo is provided. A more accurate estimation of the input laser beam that should be used in simulations of high-power laser applications may now be obtained. Finally, one may also find ways to positively manipulate the laser beam. Using Fresnel diffraction theory, the propagation and focusing of an experimental high-power (sub-petawatt) aberrated beam is numerically calculated. The shape of the focused beam pattern within a few Rayleigh lengths is analysed as a function of main aberrations (up to the 14 th term of Zernike polynomials). Furthermore, at the focus position, the spreading of the energy is compared to both the case of a perfect diffraction-limited Gaussian and a super-Gaussian beam.

High-precision laser focus positioning of rough surfaces by deep learning

This work presents a precise positioning detection based on a convolutional neural network (CNN) to control the laser focus in laser material processing systems. The images of the diffraction patterns measured at different positions of the laser focus concerning the workpiece are classified in the range of the Rayleigh length of the focusing lens with an increment of about 7% of it. The experiment was carried out on different materials with different levels of surface roughness, such as copper, silicon, and steel, and over 99% accuracy in the positioning detection was achieved. Considering surface roughness and camera noise, a theoretical model is established, and the effects of these parameters on the accuracy of focus detection are also presented. The proposed method exhibits a noise-robust focus detection system and the potential for many precise positioning detection systems in industry and biology.

Optical design of vertical edge Thomson scattering on HL-2M tokamak

A vertical edge Thomson scattering (ETS) diagnostic system on HL-2M tokamak has been designed. The ETS system collects the scattered light from Nd:YAG laser (1064 nm, 2 J, 30 Hz, 15 ns). The laser beam propagates vertically through the plasma region and the polarization is parallel to the toroidal magnetic field. A special designed Galileo-type telescope with long Rayleigh length is applied to focus the laser size and ensure collimation. A group of double-Gaussian collection lenses image the 600 mm vertical scattered region onto rectangular fiber arrays with a spatial resolution of 10 mm. The 2.20 mm × 2.86 mm fiber optic bundle consists of 130 low hydroxyl (OH) 200/220 μm (core/cladding) diameter fibers with numerical aperture NA = 0.22, carrying the light to remotely located multi-channel polychromators. Effect of oblique incidence on narrow band filter has been analyzed. The designed electron temperatures range from 5 to 1000 eV and electron densities from 5 × 1018 to 1 × 1020 m−3.

3D Printed Lenses for Vertical Beam Collimation of Optical Phased Arrays.

This article presents the design, fabrication, and characterization of edge-coupled 1D optical phased arrays (OPAs) combined with collimating lenses. Our concept was tested with two OPAs having different collimation ranges. Both OPA designs have 3-μm waveguide spacing and the maximum beam steering range is about 30° based on wavelength tuning around 1550 nm. The first generation had 37 channels with 108 μm of waveguide array width and the second generation had 512 channels with 1.5 mm array width. As the array outputs are edge coupled, suitable lenses are required to collimate the beam vertically. We report the comparison between a commercially available straight cylindrical lens and custom 3D printed curved cylindrical lenses. In the experiments, we demonstrate 1D beam steering of the light outcoupled from the waveguide facets and collimated by these lenses and analyzed parameters such as Rayleigh range and beam divergence. These parameters are estimated to be 9.9 mm and 7.0 mrad (0.4°), respectively, for the commercial lens, whereas 40.1 mm and 3.5 mrad (0.2°) for the dedicated 3D printed lens, showing a clear improvement.

Self-focusing of a q-gaussian laser beam under the influence of an exponential plasma density ramp in plasma

The goal of the current manuscript is to investigate how a plasma density ramp affects the ability of a q-Gaussian laser beam (q-GLB) to self-focus in plasma. The laser beam exhibits oscillatory self-focusing and defocusing behaviour with increasing distance of propagation. We used an exponential plasma density ramp to combat this defocusing tendency, allowing the particular laser beam to achieve a minimal spot size and nearly retain it up to several Rayleigh lengths. In addition to that, it has been observed that self-focusing increases with increasing q-values and the laser intensity. However, the lower values of q suggest strong self-focusing. By warily selecting the plasma and laser parameters, the density ramp could play a key role in the self-focusing of q-Gaussian laser. Self-focusing is seen to become stronger as propagation distance increases and the q-parameter affects the behaviour of the beam-width parameter in the plasma as shown.

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes.

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes are originally and systematically investigated. The quantum theory of the coherent state is exploited to derive an analytical wave representation for the transformed output beams. The derived wave function is further employed to numerically analyze the propagation dependent orbital angular momentum densities. The parts of the negative and positive regions in the orbital angular momentum density are found to rapidly change in the Rayleigh range behind the transformation.

Evolution of Wigner-distribution-function oblique Airy-Airy vortex wavepackets in a dispersive chiral medium

This paper introduces a distinctive perspective to describe and construct a new type of spatiotemporal optical field. Being different from the previous traditional wave packet obtained from the (3+1) D Schrödinger equation in the real space, the newly proposed nonclassical oblique Airy-Airy vortex (OAAV) wave packet located in the phase and momentum space is constructed based on the Wigner-distribution-function (Wdf) method. The spatiotemporal dynamics of the Wigner-distribution-function oblique Airy-Airy vortex (WdfOAAV) wave packet propagating in a dispersive chiral medium (DCM) are investigated from various aspects, including the targeted wave packet's nonclassicality, propagation properties, angular momentum density, and lateral optical force. It is found that the medium's chirality would remove the degeneracy of the propagation velocities in momentum space, which would result in the accelerated and decelerated wave packets propagating without diffusion within several Rayleigh lengths. The WdfOAAV wave packet associates the time-space optical field in the phase and momentum space with that in the real space, and offers the essential information about the joint spatial position and phase/momentum distribution in arbitrary real-space coordinates. Results obtained here might open a new perspective for the construction of a nonclassical spatiotemporal optical field and be applied in particle manipulation and versatile light bullets.

Self-focusing and defocusing phenomena of super-Gaussian laser beams in plasmas carrying density gradient

Considering nonlinearities due to relativistic mass variation and ponderomotive force driven depression in the electron density, a model is developed for the self-focusing of a super-Gaussian laser beam in inhomogeneous plasmas. Since paraxial ray approximation is not appropriate for the beams of super-Gaussian profile, the formulation is developed based on the moment theory. To have an in-depth understanding of self-focusing and defocusing phenomena and to develop generalized treatment, three different types of plasma density profiles namely linear, tangent and exponential density profiles, are considered and the results are compared. Due to the saturating nature of nonlinear permittivity with laser intensity, the beam is found to undergo periodic focusing because of competition between the diffraction divergence and nonlinear self-focusing effects. The ponderomotive nonlinearity enhances the self-focusing. As the super-Gaussian beam moves into higher density plasma region up to several Rayleigh lengths, stronger self-focusing is achieved and the value of minimum spot size decreases.

Efficient diffraction control using a tunable active-Raman gain medium

We present a scheme to create an all-optical tunable and lossless waveguide using a controllable coherent Raman process in an atomic rubidium vapor in an $\mathcal{N}$-type configuration. We employ a Gaussian Raman field and a Laguerre-Gaussian control field to imprint a high-contrast tunable waveguidelike feature inside the atomic medium. We numerically demonstrate that such a waveguide is able to guide arbitrary modes of a weak probe beam to several Rayleigh lengths without diffraction and absorption. Our results on an all-optical waveguide-based scheme may have potential applications in lossless image processing, high-contrast biomedical imaging, and image metrology.

Dithered single-objective light sheet for improved super-resolution imaging throughout mammalian cells.

Single-molecule super-resolution fluorescence microscopy is a powerful method for imaging detailed biological structures at the nanoscale. However, imaging single molecules precisely in thick samples such as mammalian cells is notoriously difficult due to increased fluorescence background. Light sheet fluorescence microscopy in which the sample is illuminated with a thin plane of light mitigates the problem of increased fluorescence background in thick samples and results in increased signal-to-background ratio and improved localization precision. However, light sheet illumination is sensitive to shadowing artifacts from imperfections in the optical path and scattering throughout the sample. Additionally, most light sheet systems employ two objectives, which may suffer from steric hindrance and drift between the sample and illumination objective. To overcome these disadvantages, we have developed a single-objective tilted light sheet illumination system which employs dithering to reduce stripe artifacts and achieve homogeneous illumination of the sample. Our light sheet has been designed with a width, thickness, and confocal parameter specifically suited for cellular imaging. We further improve the imaging capabilities of our system with a microfluidic device enabling Exchange-PAINT for multi-target imaging without chromatic offsets, using engineered point spread functions for 3D imaging, and employing deep learning algorithms for high-density localization of single molecules. Our approach achieves improved localization precision, imaging speeds, and multi-target accuracy, enabling fast and precise multi-target 3D single-molecule super-resolution cellular imaging. Here, we focus on the design and construction of our single-objective dithered light sheet and its range of applications from nuclear protein investigation to whole cell imaging. We think the improved cellular imaging resulting from this system will impact our understanding of the relationship between organization and function of subcellular structures and help us and others answer relevant biomedical questions involved in disease pathogenesis.