Paraxial Plane Research Articles

Optical chirality induced by spin-orbit interaction of light in a tightly focused Laguerre-Gaussian beam

Optical chirality is one of the important and fundamental dynamic properties of light besides energy, momentum, and angular momentum. The quantification of electromagnetic chirality has been conceptualized only recently. Now, it is well known that for paraxial plane waves of light, the optical chirality is proportional to the ellipticity of the polarization ellipse, i.e., completely independent of the phase distribution. Here it is shown that optical vortex and state of polarization of the source paraxial field both have contributions to the optical chirality of the nonparaxial field generated by tightly focused Laguerre–Gaussian (LG) beam, which is in Stark contrast to the paraxial plane wave of light known from classical optics. The physical reason is the redistribution of local electromagnetic polarization in three dimensions associated with spin–orbit interaction.

Wavefront measurement of a multilens optical system based on phase measuring deflectometry

Usually, a multilens optical system is composed of multiple undetectable sublenses. Wavefront of a multilens optical system cannot be measured when classical transmitted phase measuring deflectometry (PMD) is used. In this study, a wavefront measuring method for an optical system with multiple optics is presented based on PMD. A paraxial plane is used to represent the test multilens optical system. We introduce the calibration strategy and mathematical deduction of gradient equations. Systematic errors are suppressed with an N-rotation test. Simulations have been performed to demonstrate our method. The results showing the use of our method in multilens optical systems, such as the collimator and single-lens reflex camera lenses show that the measurement accuracy is comparable with those of interferometric tests.

Modeling infrared behavior of multilayer diffractive optical elements using Fourier optics.

In this paper, we propose to explore the infrared (IR) behavior of multilayer diffractive optical elements (MLDOEs). IR MLDOEs are designed for the development of space instruments dedicated to Earth observation. The phase effect of the MLDOE on a paraxial plane wave is studied using exact kinoform shapes for each layer. The modeling of the optical path difference uses thin element approximation. Until now, MLDOEs have been designed and simulated on ray-tracing software with binary diffractive layers. In this study, after passing through the MLDOE, the field is propagated using a method that utilizes the angular spectrum of plane waves. The Strehl ratio is used to determine the "best focus" plane, where it is shown that the focalization efficiency is above 95% for the working order in the mid- and long-wave IR bands. This result, along with the very low energy content of the other orders, proves the strong imaging potential of MLDOEs for dual-band applications. It is also demonstrated that the MLDOE has the same chromatic behavior as standard DOEs, making it a very useful component for IR achromatization.

Long-range optical pulling force device based on vortex beams and transformation optics

In this work, a method for generating a long-range optical pulling force is presented which is realized by utilizing a vortex beam and a device designed based on transformation optics through conformal mapping. The device works by transforming an input perfect vortex beam into an almost paraxial plane wave, and generates a pulling force by maximizing the forward momentum of the beam. A three-dimensional full-wave analysis of the device is performed and the optical force is computed by the Maxwell stress tensor method. The simulation results show a very good agreement with the theoretical calculations.

Assessment of stability of orthodontic mini-implants under orthodontic loading: A computed tomography study.

Miniscrews have been used in recent years for anchorage in orthodontic treatment. However, it is not clear whether the miniscrews are absolutely stationary or move when force is applied. This prospective clinical study was undertaken to evaluate the mobility of orthodontic miniscrews under orthodontic loading using computed tomography. Ten adult patients (7 females and 3 males with mean age of 19 years, 7 mm overjet) who required en masse retraction of upper and lower anterior teeth infirst premolar extraction spaces were included in this study. After initial alignment of anterior teeth, the 0.019" ×0.025" stainless steel archwire were placed in preadjusted edgewise appliance. The miniscrews (diameter - 1.3 mm, length - 7 mm) were inserted in between second premolar and thefirst molar in the maxilla (zygomatic buttress) and in mandible on the buccal side as direct anchorage. Immediately after placement of miniscrews without waiting period, NiTi coil springs (force of 150 g in the maxilla and 100 g in the mandible) were placed for the retraction. Denta Scans were taken immediately before force application (T1) and 6 months later (T2). The mean changes obtained at T1 and T2 in Denta Scans (axial plane, coronal plane, paraxial plane) were evaluated to determine any movement of different parts of miniscrews using one-way ANOVA test and Student's unpaired t-test. On average, miniscrews were extruded and tipped forward significantly, by 1 mm at the screw head in the axial plane (Group III) and 0.728 mm in the coronal plane (Group IV). Tail of miniscrews showed average tipping of 0.567 mm in the axial plane (Group I) and 0.486 mm in the paraxial plane (Group V). Least average mobility was shown by screw body of 0.349 mm in the axial plane (Group II). Clinically, no significant mobility was observed. Miniscrews are a stable anchorage for orthodontic tooth movement but do not remain absolutely stationary like an endosseous implant throughout orthodontic loading although miniscrews might move according to placement site, orthodontic loading, and inflammation of peri-implant tissue. Waiting period between miniscrews placement and orthodontic loading does not significantly affect the miniscrew mobility so immediate loading can be recommended. To prevent hitting any vital organs because of miniscrew mobility, it is recommended that they can be placed in a nontooth-bearing area that has no foramen, major nerves, or blood vessel pathway, or in a tooth-bearing area allowing a 1.5 mm safety clearance between the miniscrew and dental root.

MRI evaluation of tibial tunnel wall cortical bone formation after platelet-rich plasma applied during anterior cruciate ligament reconstruction

BackgroundAfter anterior cruciate ligament (ACL) reconstruction, formation of cortical sclerotic bone encircling the femoral and tibial tunnel is a part of intratunnel graft healing. During the physiological cascades of soft tissue healing and bone growth, cellular and hormonal factors play an important role. The purpose of this study was to non-invasively but quantitatively assess the effect of intraoperatively applied platelet-rich plasma (PRP) on the formation of cortical bone encircling the tibial tunnel.Patients and methodsIn fifty patients, standard arthroscopic ACL reconstructions were performed. The PRP group (n = 25) received a local application of PRP while the control group (n = 25) did not receive PRP. The proximal tibial tunnel was examined by MRI in the paraxial plane where the portion of the tibial tunnel wall circumference consisting of sclerotic cortical bone was assessed with testing occurring at one, two and a half and six months after surgery.ResultsAt one month after surgery, differences between the groups in the amount of cortical sclerotic bone encircling the tunnel were not significant (p = 0.928). At two and a half months, the sclerotic portion of the tunnel wall in the PRP group (36.2%) was significantly larger than in the control (22.5%) group (p = 0.004). At six months, the portion of sclerotic bone in the PRP group (67.1%) was also significantly larger than in the control (53.5%) group (p = 0.003).ConclusionsEnhanced cortical bone formation encircling the tibial tunnel at 2.5 and 6 months after ACL graft reconstruction results from locally applied platelet-rich plasma.

Evidences of spatial (angular) filtering of sound beams by sonic crystals

We report experimental evidences of spatial (angular) filtering of sound beams propagating through sonic crystals. We show that at specific frequencies of the incident wave the paraxial plane wave components of the beam can be efficiently transmitted through the crystal, whereas the components propagating at large angles are strongly reflected or deflected (filtered out) by the crystal. The modification of the angular field distribution results in formation of sound beams of relatively high spatial quality.

Focusing characteristics of curvilinear half-open Fresnel zone plate lenses: plane wave illumination

A diffraction field-focusing equation based on a specific conical-segment linearization procedure is derived for the Fresnel zone plate (FZP) lens of arbitrary curved profile and is applied for contrasting plane, spherical, parabolic and conical zone plate lenses, convex-side illuminated by a paraxial plane wave front. Two sets of 100-GHz curvilinear and plane FZP lenses are studied numerically with regards to their dimensions, axial focusing intensity and footprint, and frequency bandwidth. For the first set , where the curvilinear and plane lenses share a common lens base aperture and have equal focal lengths, the following new finding has resulted: regardless of their different in shape profiles the FZP lenses have equal zone numbers and produce similar axial focusing. The second set also consists of plane, spherical, parabolic and conical lenses. They share a common apex, and have equal in diameter base apertures and focal lengths but different thicknesses. For such disposition and proportions, the FZP lenses possess different zone numbers and focusing parameters (gain, efficiency, footprint and bandwidth). The belief that the curvilinear FZP have superior (or inferior) electromagnetic characteristics, compared to those of the plane FZP lens with equal number of zones is not in general true. Their relative focusing qualities can vary significantly depending on the lens positioning and dimensions.

Resolution in Emission Microscopy

A commonly used estimate for the resolution limit imposed by spherical aberration in electron microscopes is the radius of the circle of least confusion rℓc. The radius of least confusion is calculated for a point object and a single energy, and is referred to object space. There are a number of reasons for questioning the usefulness of the radius of least confusion as a measure of resolution. If the intensity were uniformly distributed over the circle of confusion at different depths in the image it would be natural to assume that best resolution occurs in the plane in which the circle of confusion is smallest. However, the intensity is not uniform. Furthermore the effect of a distribution of electron energies and a non-zero object size (required for a non-zero current) should be included in calculating resolution, especially in emission microscopy, where the chromatic aberration can be very large, and low emission current density can limit the smallness of details which can be viewed or recorded. In an earlier work Storbeck, and recently my colleagues and I using a different approach, have taken these effects into account in resolution studies based on the intensity distribution in the image.In emission microscopy the aberrations introduced by the accelerating field as well as those due to the objective lens must be considered. In our calculations the spherical aberration coefficients due to the field and the lens are referred to virtual specimen space (the image space of the accelerated electrons) at unit magnification, where they are combined, as are the chromatic aberration coefficients. The object for the microscope is a small disc centered on the axis. The emission current density is uniform, with a cosine angular distribution, and an emission energy distribution chosen to fit the particular application. The intensity distribution in the image plane is calculated first for monoenergetic beams, as a function of the axial position of the plane. The distribution curves in Fig. 1 exhibit the effects of spherical aberration and object size as the defocus changes. The shapes of the curves are due to the behavior of the image disc as a function of the emission angle αe. Between the plane of least confusion and the paraxial plane, as αe increases from 0° the image disc at first moves away from the axis in the azimuth of emission (retrograde direction). After reaching a maximum displacement, which depends on the distance from the paraxial plane, the image disc moves back to the axis and into the opposite azimuth as αe continues to increase. The intensity on the axis is highest when the retrograde displacement is equal to the image disc radius, Fig. 1c. This intensity distribution turns out to be more favorable for resolution than does the distribution in the plane of least confusion, Fig. If, even though the beam spreads over a larger area. The smaller the object radius and spherical aberration coefficient are, the closer the high-intensity plane is to the paraxial plane. For a monoenergetic beam the high-intensity plane for the smallest object which can provide the required current in the image is the optimum image plane for geometrical resolution. For a beam with a range of energies the total intensity distribution is obtained from the weighted sum of single-energy distributions calculated for a series of values in the energy range and for a given position of the image plane, Fig. 2. A good approximation to the plane providing best resolution for the beam as a whole is the high-intensity plane for the average energy.

A closer look at the effect of lens aberrations and object size on the intensity distribution and resolution in electron optics

A geometrical optics approach is used to calculate the intensity distribution in the image of a small object centered on the axis. The calculations take into account the size of the object as well as the spherical and chromatic aberrations of the lens. The intensity distribution curves, calculated as a function of depth in the image, reveal the existence of a compact high intensity image peak in the caustic region between the paraxial image plane and the plane of least confusion. The intensity distribution curves show that the geometrical resolution is better in the plane with the high intensity peak than in the plane of least confusion. As the object radius approaches zero the plane in which the high intensity peaks occurs moves toward the paraxial plane, and the geometrical resolution approaches zero. For an object of finite brightness the intensity in the image peak also approaches zero. A geometrical error rg is introduced, which depends on the size of the smallest object providing the required intensity or current in the image peak. The geometrical error and the diffraction error are combined quadratically to obtain a resultant error. An adaptation of the geometrical approach, combined with wave optics, is explored in the case of a point source. Discussions of the intensity-distribution approach as it affects the resolution calculations in the transmission electron microscope and the emission electron microscope are included. In the case of a probe-type instrument a perhaps unexpected finding is that a larger source size along with a smaller angular aperture is preferable in some cases to a smaller source size and larger angular aperture.