Three-dimensional Intensity Distribution Research Articles

Soft X-ray wavefront sensing at an ellipsoidal mirror shell

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon K α, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21–25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {\cal W}. In units of the test wavelength (C K α), an r.m.s. value \sigma_{\cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

Intensity patterns of a focused electromagnetic spherical wave with aberration

The laser pulse focused by a relativistic flying parabolic mirror can exceed the laser intensity focused by conventional physical focusing optics. Depending on the Lorentz γ-factor, the focal length of the relativistic flying mirror in the boosted frame of reference becomes much shorter than the incident beam size. The 4π-spherical focusing scheme is applied to describe such a focused field configuration. In this paper, a theoretical formalism has been developed to describe the field configuration focused by the 4π-spherical focusing scheme with an arbitrary phase error of an incident electromagnetic wave. The focused field configuration is described by the linear combination of the product of the spherical Bessel function and the spherical harmonics, resulting in the same expression as the multipole radiation. The mathematical expression showing the focused field for the femtosecond laser pulse, as well as the continuous wave, has been derived for the application to the femtosecond high-power laser. We show the three-dimensional intensity distribution near focus for the 4π-spherically focused electromagnetic field with phase error.

Investigation of collagen reconstruction mechanism in skin wound through dual-beam laser welding: Insights from multi-spectroscopy, molecular dynamics simulation, and finite element multiphysics simulation

Since the mechanism underlying real-time acquisition of mechanical strength during laser-induced skin wound fusion remains unclear, and collagen is the primary constituent of skin tissue, this study investigates the structural and mechanical alterations in collagen at temperatures ranging from 40 °C to 60 °C using various spectroscopic techniques and molecular dynamics calculations. The COMSOL Multiphysics coupling is employed to simulate the three-dimensional temperature field, stress-strain relationship, and light intensity distribution in the laser thermal affected zone of skin wounds during dual-beam laser welding process. Raman spectroscopy, synchronous fluorescence spectroscopy and circular dichroism measurement results confirm that laser energy activates biological activity in residues, leading to a transformation in the originally fractured structure of collagen protein for enhanced mechanical strength. Molecular dynamics simulations reveal that stable hydrogen bonds form at amino acid residues within the central region of collagen protein when the overall temperature peak around the wound reaches 60 °C, thereby providing stability to previously fractured skin incisions and imparting instantaneous strength. However, under a 55 °C system, Type I collagen ensures macrostructural stability while activating biological properties at amino acid bases to promote wound healing function; this finding aligns with experimental analysis results. The COMSOL simulation outcomes also correspond well with macroscopic morphology after laser welding samples, confirming that by maintaining temperatures between 55 °C–60 °C during laser welding of skin incisions not only can certain instantaneous mechanical strength be achieved but irreversible thermal damage can also be effectively controlled. It is anticipated that these findings will provide valuable insights into understanding the healing mechanism for laser-welded skin wounds.

Three-dimensional intensity distribution in the far zone of focused fields in systems with different Fresnel numbers

Three-dimensional intensity distribution near the focus in systems with different Fresnel numbers has been investigated by Li and Wolf on the basis of the Huygens–Fresnel principle and Lommel analysis [J. Opt. Soc. Am. A 1, 801 (1984)JOAOD61084-752910.1364/JOSAA.1.000801]. Their computed results have been summarized into a group of isophotes of intensity distribution near the focus. In order to show the behavior of focused fields beyond the focal region, this study enlarges the research scope from intensity distribution near the focus to that in the half-space from the focal plane to infinity. To this end, a mapping transformation function is proposed that allows the plotting of isophotes within a finite area. Using this technique, both analytical and numerical expressions of far-zone behavior predicted by the Huygens–Fresnel principle for systems with different Fresnel numbers and the predictions of the Rayleigh diffraction integrals for systems with high relative aperture are obtained and compared with the predictions of Debye’s theory of focusing, which is found to be unable to describe the far-zone behavior correctly in most cases but is able to give an approximation to systems with high Fresnel numbers.

Collimation by a polycapillary half lens at 277 eV.

We report on the efficient collimation of soft X-rays with an energy of 277 eV by a halved polycapillary lens (PCL), made of borosilicate glass. Using electron-excited, micro fluorescence emission in the focus of the PCL, experiments reveal an angular divergence of (6.9 ± 0.2) mrad in the far field of the emitted beam. For a source of ≈5μm in size, that result is confirmed by simulations, obtained with a newly developed ray tracing code. An analytical fit model is proposed and applied to characterize the evolution of the measured as well as calculated, three-dimensional (3-D) intensity distribution. The photon flux density in a free-space propagation distance of (0.4 - 0.9) m from the PCL is enhanced by a factor of ≈(30 - 90) in comparison to the direct, not collimated radiation, as it is detected through a mm-sized transmission slit. Our findings could help to establish the halved PCL as a versatile tool in the table-top metrology of optical elements, such as mirrors and gratings for soft X-rays.

Three-dimensional sculpting of laser beams

We demonstrate three-dimensional sculpting of laser beams using two-dimensional holograms. Without relying on initial guesses of the analytic properties or the Fourier transform of the desired light field, we show that an improved numerical phase retrieval algorithm can produce continuous three-dimensional intensity distributions of arbitrary shapes. We benchmark our algorithm against optical bottle beams and double-helix beams and then show the extension to complex optical structures.

Three-dimensional iterative reconstruction of pulsed radiation sources using spherical harmonic decomposition.

Neutron and x-ray imaging are essential ways to diagnose a pulsed radiation source. The three-dimensional (3D) intensity distribution reconstructed from two-dimensional (2D) radiation images can significantly promote research regarding the generation and variation mechanisms of pulsed radiation sources. Only a few (≤5) projected images at one moment are available due to the difficulty in building imaging systems for high-radiation-intensity and short-pulsed sources. The reconstruction of a 3D source with a minimal number of 2D images is an ill-posed problem that leads to severe structural distortions and artifacts of the image reconstructed by conventional algorithms. In this paper, we present an iterative method to reconstruct a 3D source using spherical harmonic decomposition. Our algorithm improves the representation ability of spherical harmonic decomposition for 3D sources by enlarging the order of the expansion, which is limited in current analytical reconstruction algorithms. Prior knowledge of the source can be included to obtain a reasonable solution. Numerical simulations demonstrate that the reconstructed image quality of the iterative algorithm is better than that of the analytical algorithm. The iterative method can suppress the effect of noise in the integral projection image and has better robustness and adaptability than the analytical method.

Development of LED-based opto-mechanical instrumentation for phototherapeutic applications

This work reports an optomechanical, electronic system consisting of LEDs emitting light in the near-infrared region. The 147 light-emitting diodes were distributed in a semi-spherical dome so that each focused light upon the center of the radius. The LEDs received electrical polarization so that the optical power of each provided 16 ± 0.36 mW for a total of 2.4 W. The developed system allows multifunctional applications in phototherapy, making it possible to perform this clinical technique for the treatment of skin lesions and contusions at the musculoskeletal level. The geometry of the developed system also allows the use of phototherapy in the treatment of neurological pathologies. In terms of instrumentation, the three-dimensional light intensity distribution and the thermographic images were obtained using three working distances from the system to the target. Three-dimensional light intensity distributions were obtained considering each working distance. These were inserted in the thermographic images as indications of the emitted temperature distributions. This work verified that the optomechanical and electronic system developed with LEDs may be used for multiple applications in phototherapy.

Sensitivity enhancement in inductively coupled plasma mass spectrometry using nebulization methods via nitrogen mixed gas effect.

We demonstrate the sensitivity enhancement in inductively coupled plasma mass spectrometry (ICP-MS) by combining ultrasonic nebulization via the nitrogen mixed gas effect. We showed the effect of nitrogen gas concentration (0-5%) in the nebulizer gas on the signal sensitivity for 63 elements using commercially available (concentric and ultrasonic) nebulizers. In addition, the limit of detection (ng L-1) was calculated in each case. Finally, we compared the sensitivity (i.e., the slope of the calibration curve), background noise intensity, and three-dimensional intensity distribution in the plasma to elucidate the effects of the concurrent use of mixed gas plasmas and nebulization methods.

Three-dimensional beam shaping by means of a spatial phase modulator for two-photon-polymerization

Two-photon-polymerization is an additive manufacturing method to produce parts with high resolution. With reachable voxel sizes below the optical diffraction limit, it is of particular interest for biomedical or micro-optical applications. Despite its high resolution, the spreading of this method is hindered by its low productivity in the µm³/s range. Scaling up productivity is in principle possible with already available laser sources with high pulse energy and beam shaping such as multi-spot approaches. This beam shaping is limited in the processable volume and has to be expanded to arbitrary beam shapes in three dimensions to make use of the next generation laser sources with higher pulse energy and higher average laser power. In this work, a three-dimensional Iterative Fourier Transform Algorithm for optimizing arbitrary three-dimensional intensity distributions using a spatial phase modulator was investigated for suitability for 2PP.

Wavefront Modulation and Beam Shaping into Arbitrary Three-Dimensional Intensity Distributions

In this study the methods of three-dimensional (3D) wavefront intensity modulation by employing contrast-inverted holography, previously introduced as Gabor inverted holography, are further investigated. The present study provides the recipes for creating 3D wavefront intensity modulations using phase-only and amplitude-only modulators and compares the results. The 3D wavefront modulation using spherical waves is also demonstrated, and the miniaturization of 3D intensity beams is discussed; it is shown that both the resolution and the size of the created 3D structures are ultimately given by the wavelength of the employed radiation. The manuscript also addresses the quality of the formed 3D intensity curves and determines the parameters that provide the best smooth appearance of the 3D curves. The presented methods of 3D intensity wavefront modulation can be realized for all kinds of waves: light, X-ray, electron, etc, provided the modulator can be manufactured for the corresponding wavelength. The methods of 3D intensity wavefront modulation can be applied in various techniques: lithography, micro-robotics, particle trapping, etc.

Influence of Vertical and Radial Distances of Nano-Resistors in SSI-LEDs on Light Intensity Distributions

Two- and three-dimensional light intensity distributions from nano-resistor based solid-state incandescent light emitting devices, made of MOS capacitors with a high-k gate dielectric deposited on the p-type Si substrate, has been simulated using physics-based analytical calculations. The inter-nano-resistor distance affected the resolvability of individual nano-resistor light sources. Formation of clusters of nano-resistors and the presence of few large-sized nano-resistors resulted in bright radiation spots observed at higher magnifications. Light from individual nano-resistors could not be resolved at lower magnifications. The device’s center region was brightest, with light intensity diminishing uniformly in the radially outwards direction.

New method to measure domain-wall motion contribution to piezoelectricity: the case of PbZr0.65Ti0.35O3 ferroelectric

A new data analysis routine is introduced to reconstruct the change in lattice parameters in individual ferroelastic domains and the role of domain-wall motion in the piezoelectric effect. Using special electronics for the synchronization of a PILATUS X-ray area detector with a voltage signal generator, the X-ray diffraction intensity distribution was measured around seven split Bragg peaks as a function of external electric field. The new data analysis algorithm allows the calculation of `extrinsic' (related to domain-wall motion) and `intrinsic' (related to the change in lattice parameters) contributions to the electric-field-induced deformation. Compared with previously existing approaches, the new method benefits from the availability of a three-dimensional diffraction intensity distribution, which enables the separation of Bragg peaks diffracted from differently oriented domain sets. The new technique is applied to calculate the extrinsic and intrinsic contributions to the piezoelectricity in a single crystal of the ferroelectric PbZr1−x Ti x O3 (x = 0.35). The root-mean-square value of the piezoelectric coefficient was obtained as 112 pC N−1. The contribution of the domain-wall motion is estimated as 99 pC N−1. The contribution of electric-field-induced changes to the lattice parameters averaged over all the domains is 71 pC N−1. The equivalent value corresponding to the change in lattice parameters in individual domains may reach up to 189 pC N−1.

Noniterative multiplane holographic projection

In this paper, we introduce a mixed complex and phase-only constraint for noniterative computer generation of phase-only holograms from multiplane intensity distributions. We are able to reproduce three-dimensional intensity distributions with the same number of planes achieved with the Gerchberg-Saxton (GS) algorithm; at the same time, we maintain the fast computation time of a noniterative method. In this way, we enable the possibility of multiplane light field control in dynamic applications. We show numerical results for three- and eight-plane holograms, for different interplane distances-using either the same or different amplitude constraints in each plane. In all of these tests, our method results in a comparable or better reconstruction quality than the GS algorithm, while achieving a significant decrease in computing time. Finally, we experimentally demonstrate the capability of our proposal to achieve multiplane holographic projection.

Generation of the Second and Fourth Harmonics with Retaining the Three-Dimensional Quasi-Ellipsoidal Distribution of the Laser Pulse Intensity for a Photoinjector

We consider the possibility of generating the second and fourth optical harmonics of laser pulses having a central wavelength of 1030 nm with retaining the three-dimensional quasi-ellipsoidal intensity distribution. The presented results of numerical simulation confirm that angular chirping allows one to retain the three-dimensional structure of the intensity distribution and enhance energy conversion. The proposed approach was tested experimentally using non-profiled laser beams. Energy conversion efficiency of 53% and 21% was achieved in the generation of the second and fourth harmonics, respectively.

Incorporating particle symmetry into orientation determination in single-particle imaging.

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

Structural Changes in a Single GaN Nanowire under Applied Voltage Bias.

GaN nanowires (NWs) are promising building blocks for future optoelectronic devices and nanoelectronics. They exhibit stronger piezoelectric properties than bulk GaN. This phenomena may be crucial for applications of NWs and makes their study highly important. We report on an investigation of the structure evolution of a single GaN NW under an applied voltage bias along polar [0001] crystallographic direction until its mechanical break. The structural changes were investigated using coherent X-ray Bragg diffraction. The three-dimensional (3D) intensity distributions of the NWs without metal contacts, with contacts, and under applied voltage bias in opposite polar directions were analyzed. Coherent X-ray Bragg diffraction revealed the presence of significant bending of the NWs already after metal contacts deposition, which was increased at applied voltage bias. Employing analytical simulations based on elasticity theory and a finite element method (FEM) approach, we developed a 3D model of the NW bending under applied voltage. From this model and our experimental data, we determined the piezoelectric constant of the GaN NW to be about 7.7 pm/V in [0001] crystallographic direction. The ultimate tensile strength of the GaN NW was obtained to be about 1.22 GPa. Our work demonstrates the power of in operando X-ray structural studies of single NWs for their effective design and implementation with desired functional properties.

Twisting phase and intensity of light with plasmonic metasurfaces

Twisting light in both phase and intensity has recently drawn great interests in various fields related to light-matter interactions such as optical manipulation of particles and quantum entanglement of photons. Conventionally, bulky optical components are required to produce such twisted optical beams, which significantly limits their applications in integrated photonics and optical chips. Here, we design and demonstrate aluminum plasmonic metasurfaces consisting of nanoslit antennas as ultracompact beam converters to generate the focused twisted beams in both phase and intensity across the visible wavelength range. The metasurface is encoded with the combined phase profile containing the helico-conical phase function together with a Fourier transform lens based on the Pancharatnam-Berry (PB) geometric phase. It is demonstrated that the created twisted beams simultaneously possess three-dimensional (3D) spiral intensity distribution around the propagation axis and complex phase structure containing both the central vortex and the peripheral vortex string. Moreover, the twisted beam exhibits an arithmetic intensity spiral at the focal plane with the maximum photon concentration located at the leading point of the spiral. Our results show the promising potential for advancing metasurface-based integrated devices in many applications of light-matter interactions.

Heart diffraction.

A theoretical study of the plane-wave diffraction by a heart-like sharp-edge aperture corresponding to the involute of a circle is proposed here. Through the recently developed paraxial boundary diffraction wave theory, expressed via the language of catastrophe optics, the presence of pseudo-nondiffracting regions within the three-dimensional spatial intensity distribution of the diffracted wavefield is intuitively explained and quantitatively characterized. The results of some old, beautiful, but nearly forgotten, diffraction experiments have also been reconsidered from such a peculiar and rather unorthodox perspective.

Effect of the electric-field distribution on the morphology of dot-array gratings fabricated by AFM-based nanolithography

Local electric-field-induced anodic oxidation is one of the earliest and most extensively studied techniques in bias-assisted AFM nanolithography. The electric field provides the oxidation kinetics of nanoscale electrochemical reaction and controls the spacial resolution of the fabricated structures. Once electric field is formed, its distribution and intensity can be modified by changing the tip-sample voltage and separation. In this paper, the influence of the bias voltage on the three-dimensional (3D) radial electric field intensity distribution in the space between the tip and the sample, the influence of the electric field strength on dot-array grating structures and the morphology distribution of the nanodot structure in the dot-array grating have been analysed deeply.