Longitudinal Intensity Profile Research Articles

Iterative suppression of Kerr-induced instabilities in Bessel beams using on-axis intensity shaping

Kerr-induced instabilities in zeroth-order Bessel beams with low focusing angle prevent the formation of longitudinally uniform plasma rods in the filamentation regime. These instabilities lead to the oscillation of the beam on-axis intensity via the generation of new spatial frequencies by a first stage of spectral broadening followed by a second stage of four-wave mixing. Here, we numerically demonstrate an efficient approach to drastically reduce the instabilities due to the second stage. It is based on shaping the longitudinal intensity profile with spatio-spectral components in opposition of phase to the Kerr-generated ones via an iterative approach. Zeroth-order Bessel beams with a longitudinal flat intensity plateau can be generated in a few iterations in the nonlinear regime. This is performed in both monochromatic and pulsed femtosecond regimes.

Transmission characteristics of vortex frozen waves in different obstacle channels.

The obstacle in a channel is a typical scenario for free-space optical (FSO) communications, however, it will destroy the information in channels, especially for the orbital angular momentum (OAM) multiplexing systems and cause performance degradation. Motivated by the feature of predefining intensity profile, here we propose to use frozen wave (FW) carrying OAM for the FSO communications to mitigate the influence of obstacles on the beam propagation. The key idea is to design the longitudinal intensity profile of FW to distribute the beam energy of the location where the obstacle exists over a large region and focus again on the central region after the obstacle for propagation. By analyzing the cases under different sizes, positions, and shapes of the obstacles with on-axis and off-axis scenarios, it has been demonstrated that the detection probability of OAM mode carried by FW can be improved by 0.35 and 0.15 in short-distance and long-distance transmission scenarios, respectively, when compared to that carried by Bessel-Gaussian beam. It demonstrates the FWs have great potential in the OAM-based FSO communications, especially for the obstacle channels.

Simulation of approaching boundary layer flow and wind loads on high-rise buildings by wall-modeled LES

This study presents a simulation framework of approaching boundary layer flow with appropriate characteristics by large-eddy simulation (LES), which is critically important for predictions of wind pressures and loads on buildings and other structures. The framework is consisted of spectral representation (synthesis) approach for inflow turbulence field generation and adjusting strategies to achieve appropriate approaching flow characteristics. The adjusting strategies include implementation of wall-stress model based on the equilibrium law of wall and adjusting of inflow turbulence parameters. The wall-stress model facilitates modeling of the effects of ground roughness without explicitly resolving the geometric roughness elements, also bypassing the prohibitive near-wall grid resolution requirement. The adjusting of inflow turbulence parameters, including correlation coefficient of inflow longitudinal and vertical fluctuating velocity components and amplification factor of inflow vertical fluctuation level, is proposed based on Reynolds stress budget to shorten the buffer region and to mitigate the decay of longitudinal turbulence intensity profile. To verify the proposed framework, the approaching flow corresponding to a wind tunnel test is firstly simulated and a comprehensive parametric study is conducted. With the adequately simulated turbulence field, the wind pressures and integrated loads on a high-rise building model are then simulated and compared with the wind tunnel test results. The results demonstrate effectiveness of the proposed wall-modeled LES framework for approaching flow simulation and wind loads assessment.

A hybrid image processing method for measuring 3D bubble distribution using digital inline holography

The paper presents a hybrid bubble hologram processing approach for measuring the size and 3D distribution of bubbles over a wide range of size and shape. The proposed method consists of five major steps, including image enhancement, digital reconstruction, small bubble segmentation, large bubble/cluster segmentation, and post-processing. Two different segmentation approaches are proposed to extract the size and the location of bubbles in different size ranges from the 3D reconstructed optical field. Specifically, a small bubble is segmented based on the presence of the prominent intensity minimum in its longitudinal intensity profile, and its depth is determined by the location of the minimum. In contrast, a large bubble/cluster is segmented using a modified watershed segmentation algorithm and its depth is measured through a wavelet-based focus metric. Our processing approach also determines the inclination angle of a large bubble with respect to the hologram recording plane based on the depth variation along its edge on the plane. The accuracy of our processing approach on the measurements of object size and 3D distributions are assessed through synthetic bubble holograms and oil droplet holograms from an experiment separately. In addition, we evaluate the ability of this algorithm to estimate the bubble inclination with respect to the hologram recording plane through measuring a 3D-printed physical target of pillars with different inclination angles. The holographic measurement technique is further implemented to capture the fluctuation of instantaneous gas leakage rate from a ventilated supercavity generated in a water tunnel experiment. Overall, our paper introduces an inexpensive and compact solution for high resolution characterization of bubbles and other particles in multiphase flows from a broad range of applications.

Interplanetary spread of solar energetic protons near a high-speed solar wind stream

Aims. We study how a fast solar wind stream embedded in a slow solar wind influences the spread of solar energetic protons in interplanetary space. In particular, we aim at understanding how the particle intensity and anisotropy vary along interplanetary magnetic field (IMF) lines that encounter changing solar wind conditions such as the shock waves bounding a corotating interaction region (CIR). Moreover, we study how the intensities and anisotropies vary as a function of the longitudinal and latitudinal coordinate, and how the width of the particle intensities evolves with the heliographic radial distance. Furthermore, we study how cross-field diffusion may alter these spatial profiles. Methods. To model the energetic protons, we used a recently developed particle transport code that computes particle distributions in the heliosphere by solving the focused transport equation (FTE) in a stochastic manner. The particles are propagated in a solar wind containing a CIR, which was generated by the heliospheric model, EUHFORIA. We study four cases in which we assume a delta injection of 4 MeV protons spread uniformly over different regions at the inner boundary of the model. These source regions have the same size and shape, yet are shifted in longitude from each other, and are therefore magnetically connected to different solar wind conditions. Results. The intensity and anisotropy profiles along selected IMF lines vary strongly according to the different solar wind conditions encountered along the field line. The IMF lines crossing the shocks bounding the CIR show the formation of accelerated particle populations, with the reverse shock wave being a more efficient accelerator than the forward shock wave. The longitudinal intensity profiles near the CIR are highly asymmetric in contrast to the profiles obtained in a nominal solar wind. For the injection regions that do not cross the transition zone between the fast and slow solar wind, we observe a steep intensity drop of several orders of magnitude near the stream interface (SI) inside the CIR. Moreover, we demonstrate that the longitudinal width of the particle intensity distribution can increase, decrease, or remain constant with heliographic radial distance, reflecting the underlying IMF structure. Finally, we show how the deflection of the IMF at the shock waves and the compression of the IMF in the CIR deforms the three-dimensional shape of the particle distribution in such a way that the original shape of the injection profile is lost.

Polarization oscillating beams constructed by copropagating optical frozen waves

Polarization oscillating beams, namely, polarization standing waves, commonly formed by a pair of coherent counterpropagating light waves with orthogonal polarizations, oscillate their states of polarization periodically within a wavelength interval, offering conceptual and practical interests in light-matter interactions such as the nonreciprocal magnetoelectric effect, and impressive applications in optical imaging, sensing, and chirality detection. Here, we propose a new class of polarization oscillating beams that longitudinally vary states of polarization with spatial intervals within centimeters via the superposition of two copropagating optical frozen waves with preshaped longitudinal intensity profiles and transverse phase structures. The flexibility and manipulability are demonstrated by creating several polarization oscillating beams with different polarization structures. This work paves a new way to manipulate other waves and may be useful for applications of optical standing waves in optical manipulation, light guiding of atoms, polarization-sensitive sensing, etc.

Prime number decomposition using the Talbot effect.

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.

Arbitrary Control of Polarization and Intensity Profiles of Diffraction-Attenuation-Resistant Beams along the Propagation Direction

We report on the theory and experimental generation of a class of diffraction-attenuation-resistant beams with state of polarization (SoP) and intensity that can be controlled on demand along the propagation direction. This is achieved by a suitable superposition of Bessel beams, whose parameters are systematically chosen based on closed-form analytic expressions provided by the Frozen Waves (FWs) method. Using an amplitude-only spatial light modulator, we experimentally demonstrate three scenarios. In the first, the SoP of a horizontally polarized beam evolves to radial polarization and is then changed to vertical polarization, with the beam intensity held constant. In the second, we simultaneously control the SoP and the longitudinal intensity profile, which was chosen such that the beam's central ring can be switched-off over predefined space regions, thus generating multiple foci with different SoP and at different intensity levels along the propagation. Finally, the ability to control the SoP while overcoming attenuation inside lossy fluids is shown experimentally for the first time in the literature (to the best of our knowledge). Therefore, we envision our proposed method to be of great interest for many applications, such as optical tweezers, atom guiding, material processing, microscopy, and optical communications.

Spatial effect of conical angle on optical-thermal distribution for circumferential photocoagulation.

A uniformly diffusing applicator can be advantageous for laser treatment of tubular tissue. The current study investigated various conical angles for diffuser tips as a critical factor for achieving radially uniform light emission. A customized goniometer was employed to characterize the spatial uniformity of the light propagation. An ex vivo model was developed to quantitatively compare the temperature development and irreversible tissue coagulation. The 10-mm diffuser tip with angle at 25° achieved a uniform longitudinal intensity profile (i.e., 0.90 ± 0.07) as well as a consistent thermal denaturation on the tissue. The proposed conical angle can be instrumental in determining the uniformity of light distribution for the photothermal treatment of tubular tissue.

Controlling nonlinear instabilities in Bessel beams through longitudinal intensity shaping.

During ultrafast laser pulse propagation in dielectrics, the nonlinear generation of new spatial frequencies can be deleterious to reach high intensities and to generate uniform plasma channels. In this context, diffraction-free Bessel beams have attracted major recent interest because of their enhanced stability when compared to conventional Gaussian beams. However, Bessel beams can still suffer from significant modulation instability arising from noise-induced nonlinear four-wave mixing (FWM). In this Letter we report control of the nonlinear instability growth by shaping the longitudinal intensity profile of the incident field. Our results show that tailored longitudinal intensity shaping of a nondiffracting Bessel beam can strongly reduce FWM-induced oscillations and stabilize nonlinear propagation at ablation-level intensities.

Relating multi-sequence longitudinal intensity profiles and clinical covariates in incident multiple sclerosis lesions.

The formation of multiple sclerosis (MS) lesions is a complex process involving inflammation, tissue damage, and tissue repair — all of which are visible on structural magnetic resonance imaging (MRI) and potentially modifiable by pharmacological therapy. In this paper, we introduce two statistical models for relating voxel-level, longitudinal, multi-sequence structural MRI intensities within MS lesions to clinical information and therapeutic interventions: (1) a principal component analysis (PCA) and regression model and (2) function-on-scalar regression models. To do so, we first characterize the post-lesion incidence repair process on longitudinal, multi-sequence structural MRI from 34 MS patients as voxel-level intensity profiles. For the PCA regression model, we perform PCA on the intensity profiles to develop a voxel-level biomarker for identifying slow and persistent, long-term intensity changes within lesion tissue voxels. The proposed biomarker's ability to identify such effects is validated by two experienced clinicians (a neuroradiologist and a neurologist). On a scale of 1 to 4, with 4 being the highest quality, the neuroradiologist gave the score on the first PC a median quality rating of 4 (95% CI: [4,4]), and the neurologist gave the score a median rating of 3 (95% CI: [3,3]). We then relate the biomarker to the clinical information in a mixed model framework. Treatment with disease-modifying therapies (p < 0.01), steroids (p < 0.01), and being closer to the boundary of abnormal signal intensity (p < 0.01) are all associated with return of a voxel to an intensity value closer to that of normal-appearing tissue. The function-on-scalar regression model allows for assessment of the post-incidence time points at which the covariates are associated with the profiles. In the function-on-scalar regression, both age and distance to the boundary were found to have a statistically significant association with the lesion intensities at some time point. The two models presented in this article show promise for understanding the mechanisms of tissue damage in MS and for evaluating the impact of treatments for the disease in clinical trials.

Analytical approach of ordinary frozen waves for optical trapping and micromanipulation.

The optical properties of frozen waves (FWs) are theoretically and numerically investigated using the generalized Lorenz-Mie theory (GLMT) together with integral localized approximation. These waves are constructed from a suitable superposition of equal-frequency ordinary Bessel beams and are capable of providing almost any desired longitudinal intensity profile along their optical axis, thus being of potential interest in applications in which intensity localization may be used advantageously, such as in optical trapping and micromanipulation systems. In addition, because FWs are composed of nondiffracting beams, they are also capable of overcoming the diffraction effects for longer distances when compared to conventional (ordinary) beams, e.g., Gaussian beams. Expressions for the beam-shape coefficients of FWs are provided, and the GLMT is used to reconstruct their intensity profiles and to predict their optical properties for possible biomedical optics purposes.

Compositional characterization of GaAs/GaAsSb nanowires by quantitative HAADF-STEM

The Sb concentration in axial GaAs1−xSbx inserts of otherwise pure GaAs nanowires has been investigated with quantitative high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The Sb concentration was quantified by comparing the experimental image intensities normalized to the incident beam intensity with intensities simulated with a frozen lattice multislice approach. Including static atomic displacements in the simulations was found to be crucial for correct compositional analysis of GaAs1−xSbx. HAADF intensities of individual nanowires were analysed both across the nanowires, exploiting their hexagonal cross-sectional shape, and along the evenly thick central part of the nanowires. From the cross-sectional intensity profiles, a decrease in the Sb concentration towards the nanowire outer surfaces was found. The longitudinal intensity profiles revealed a gradual build-up of Sb in the insert. The decrease of the Sb concentration towards the upper interface was either gradual or abrupt, depending on the growth routine chosen. The compositional analysis with quantitative HAADF-STEM was verified by energy dispersive X-ray spectroscopy.

Intuitive analysis of space-time focusing with double-ABCD calculation.

We analyze the structure of space-time focusing of spatially-chirped pulses using a technique where each frequency component of the beam follows its own Gaussian beamlet that in turn travels as a ray through the system. The approach leads to analytic expressions for the axially-varying pulse duration, pulse-front tilt, and the longitudinal intensity profile. We find that an important contribution to the intensity localization obtained with spatial-chirp focusing arises from the evolution of the geometric phase of the beamlets.

Overcoming Diffraction in FSO Systems Using (GRIN) Axicons for Approximating the Longitudinal Intensity Profiles

From Huygens-Fresnel integral in cylindrical coordinates and by conveniently choosing the phase function from energy considerations, we demonstrate the possibility of approximately achieving and almost freely chosen longitudinal intensity profile along the optical axis for Free Space Optics (FSO) using a simple theory. These phase functions represent optical elements that could be coupled to the transmitter and, in the case of this work, it is shown that axicons and gradient-index (GRIN) axicons, which are commercially available and cost-effective, can be easily designed for applications in FSO systems to overcome diffraction and possible atmospheric attenuations, to increase the link distance or to diminish the power emitted.

Rotation of single bacterial cells relative to the optical axis using optical tweezers

Using a single-beam, oscillating optical tweezers, we demonstrate trapping and rotation of rod-shaped bacterial cells with respect to the optical axis. The angle of rotation, θ, is determined by the amplitude of the oscillation. It is shown that θ can be measured from the longitudinal cell intensity profiles in the corresponding phase-contrast images. The technique allows viewing the cell from different perspectives and can provide a useful tool in fluorescence microscopy for the analysis of three-dimensional subcellular structures.

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

AbstractNon‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress −ufwf have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from −2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m3/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley &amp; Sons, Ltd.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

Inversionless distributed feedback semiconductor lasers: Ultranarrow linewidth and immunity against spatial hole burning

We propose and parametrically study an inversionless intrinsically single-mode distributed feedback laser structure. This laser is optically excited by a control laser field that is responsible for transferring a fully transparent waveguide structure into a coherent state, wherein a periodic variation of gain without inversion in the absence of any refractive index perturbation is generated. We show that such a laser can perform under the conditions where its gain is equal or even less than its loss, i.e., zero and negative net gain regimes. The results suggest that, via coherent control of the longitudinal mode intensity profile and standing wave effects, in the negative net gain regime such a laser can be operated at the Bragg wavelength with ultranarrow linewidth and virtual elimination of any sidemode. The inherent resistance of such a laser against spatial hole burning, despite of having strong nonuniform longitudinal mode intensity, and the effects of facet reflectivities are discussed.

ANALYSING LONGITUDINAL TURBULENCE INTENSITY IN VEGETATED CHANNELS

Vegetation altering hydrodynamic conditions of an open channel flow controls the exchanges of sediment, nutrients and contaminants. In this paper the turbulence structure of open-channel flow over a flexible grass vegetation is investigated. Velocity measurements were carried out, in a rectangular flume, using a 2D-ADV (Acoustic Doppler Velocimeter) for different values of stem concentration, water discharge, and bed slope. The experimental results showed that: 1) the maximum value of the longitudinal turbulence intensity occurs at a water depth close to the bent vegetation height; 2) the turbulence intensity damps for increasing values of the stem concentration; 3) above the vegetation height, an exponential distribution, similar to Nezu’s law, can be fitted to the measured longitudinal turbulence intensity profile. Finally, a new relative turbulence intensity distribution is proposed and fitted to the measured profiles. This relative turbulence intensity distribution needs the estimate of two parameters coinciding with the vegetation height and the water depth at which the maximum flow velocity occurs.