Triangular Aperture Research Articles

Unveiling square and triangular optical lattices: a comparative study

We study square and triangular optical lattice formation using a diffraction technique with light-possessing orbital angular momentum (OAM). We demonstrate that it is possible to use Fraunhofer diffraction of light by a square aperture to unveil OAM about two times bigger than would be possible with a triangular aperture. We notice that the pattern remains truncated until a topological charge (TC) equal to 20 with good precision. Even though a square pattern cannot be used to determine the TC sign, it is possible to measure high order of the modulus and sign of the TC up to 20, combining patterns of the triangular and square apertures.

Triaxial testing and discrete-element modelling of geogrid-stabilised rail ballast

Geogrids have been found to improve the performance of unbound aggregate layers in transportation applications by providing confinement and arresting movement through interlock between individual aggregate particles and their apertures. Geogrid reinforcement offers an effective remedial measure when railway structures are susceptible to track geometry defects resulting from excessive movement and particle reorientation within the ballast layer. This paper presents an ongoing research study at the University of Illinois aimed at quantifying the effects of geogrid reinforcement on the shear strength and permanent deformation behaviour of geogrid-stabilised railroad ballast. Geogrids with triangular, rectangular and square apertures were tested in the laboratory experiments. Cylindrical ballast specimens were prepared and tested with geogrids placed at different heights within the specimen using a large-scale triaxial apparatus. An imaging-based discrete-element-method approach was developed to model triaxial test results and investigate geogrid-reinforcement mechanisms. With the capability to create actual ballast aggregate particles as three-dimensional polyhedron elements having the same particle-size distributions and imaging quantified average shapes and angularities, the modelling was able to capture the ballast behaviour with and without geogrid reinforcement reasonably accurately.

Two philometrids (Nematoda: Philometridae) infecting the tigertooth croaker Otolithes ruber (Bloch & Schneider) (Teleostei: Sciaenidae) off Iran, including erection of a new genus

Two philometrid nematodes (Philometridae) are described from the marine perciform fish (tigertooth croaker) Otolithes ruber (Bloch & Schneider) (Sciaenidae) from off Iran: Clavinemoides annulatus n. g., n. sp. based on female specimens from the caudal fin of fish from the Persian Gulf and Philometra otolithi Moravec & Manoharan, 2013 from subgravid and nongravid females collected from the ovary of fishes in the Sea of Oman and the Persian Gulf. The monotypic genus Clavinemoides n. g. is mainly characterised by a triangular oral aperture, a markedly large anterior oesophageal bulb, a distinctly annulated body and numerous fine elevated transverse cuticular bands. The finding of P. otolithi in Iranian waters represents a new geographical record of this parasite species. An updated key to the genera of the Philometrinae Baylis & Daubney, 1926 is provided.

Diffraction-assisted extreme ultraviolet proximity lithography for fabrication of nanophotonic arrays

In this article, the possibilities and limitations of proximity lithography with extreme ultraviolet (EUV) radiation are explored theoretically and experimentally. Utilizing partially coherent EUV radiation with a wavelength of 10.88 nm from a Xe/Ar discharge plasma EUV source, proximity patterning of various nanoantenna arrays has been performed. The experimental results are compared with the results of numerical scalar diffraction simulations, and it is shown that proximity printing in the Fresnel diffraction mode can enable production of high-resolution features even with lower resolution masks, successfully demonstrating sub-30 nm edge resolution in the resist. The potential of the method is explored by simulation of the patterning through circular and triangular apertures as well as through bowtie antenna patterns, with the results suggesting that precise control of the proximity gap and the exposure dose together with simulation-supported mask design optimizations may allow for a wide variety of high-resolution structures to be printed through relatively simple transmission masks. The method is especially suited for high-performance manufacturing of submicrometer sized nanophotonic arrays.

PRESERVATIONAL AND MORPHOLOGICAL VARIABILITY OF ASSEMBLAGES OF AGGLUTINATED EUKARYOTES IN CRYOGENIAN CAP CARBONATES OF NORTHERN NAMIBIA

Laminated carbonates of the Rasthof Formation, deposited in the aftermath of the early Cryogenian low-latitude glaciation (Sturtian, 717–662 Ma), preserve abundant round tests of agglutinated microscopic eukaryotes. Previously, fossil tests were reported in two localities (Ongongo and Okaaru) from microbially laminated carbonates in the Rasthof Formation, which revealed a previous unexplored Cryogenian taphonomic window. In order to better understand the lateral variability in these microfossil assemblages, this work systematically examines fossil tests from two additional localities, South Ombepera and Ombepera, and compares their preservation in thinly and thickly laminated microbial laminites. Cap carbonates in South Ombepera and Ombepera contain abundant, hollow, spheroidal agglutinated tests (50 to 225 µm in diameter). Some of these tests exhibit slitlike or triangular apertures. In contrast, much larger, oval tests with a tapering end dominate the assemblages at Okaaru, whereas oval, laterally compressed and round structures with slits, visors, or central apertures are found at Ongongo. The thinly laminated microbial laminites from Ombepera, South Ombepera, and Okaaru also preserve rare agglutinated tubes attributed to fossils of early Foraminifera. At all four localities, the thinly laminated microbial laminites preserve more microfossils than thickly laminated microbial laminites although these two facies commonly interfinger and are interbedded. This difference shows that conditions present during formation of the thinly laminated microbial laminites favored the preservation of round agglutinators, perhaps during early burial, lithification, and fossilization of the test walls.

An assessment of the geometry effect of geosynthetics for base course reinforcements

ABSTRACT Geosynthetic-reinforced base course is potentially a cost-effective solution for flexible pavement construction. With the recent advance in the mechanistic-empirical pavement design in the United States, there is a need to develop the next generation design method for geosynthetic-reinforced bases in flexible pavements. To develop such a design method requires an improved understanding about the mechanistic behavior, especially the in-plane elastic behavior, of geosynthetics. In this paper, the geometry effect of geosynthetics was discussed. The author first reviewed recent experimental and numerical studies. Analytical equations based on cellular material mechanics were presented for determining the in-plane elastic properties of geosynthetics. The analytical equations were used to evaluate a few geosynthetics with typical geometries. The results showed that, with the same polymeric material and typical product geometries, the geocell has a better confinement effect than geogrids, and the triaxial geogrid with a triangular aperture has a better confinement effect than the biaxial geogrid with a rectangular aperture. It was also demonstrated that the traditional uniaxial tensile modulus may be a poor indicator of the effectiveness of geosynthetics for base course reinforcements.

Performance of Triangular Aperture Geogrid-Reinforced Base Courses over Weak Subgrade under Cyclic Loading

Geogrid (uniaxial or biaxial) is one type of geosynthetics that has been successfully used in slopes, walls, roads, and other applications. The main application of biaxial geogrid is to stabilize soft subgrade and reinforce weak base courses by providing lateral confinement. The confinement due to the interaction between aggregates and the ribs of biaxial geogrid depends on the geometry properties of the geogrid, such as rib shape and apertures size, the stiffness of the ribs, and the properties of aggregates. Research has shown that biaxial geogrid cannot provide uniform tensile resistance in all directions. To overcome this problem, a geogrid product with triangular apertures was developed and introduced into the market. Recent studies showed that the triangular aperture geogrid can provide nearly uniform tensile resistance in all directions and is more efficient in improving the performance of reinforced bases as compared with biaxial geogrid. However, the performance of triangular aperture geogrid-reinforced bases under dynamic loading and the influence of base course thickness on the confinement effect of triangular aperture geogrids have not been well evaluated. In this study, unreinforced and triangular aperture geogrid-reinforced bases at different thicknesses over a weak subgrade were constructed in a large geotechnical testing box (2×2.2×2 m) at the University of Kansas and tested under cyclic loading. During the tests, surface deformations and vertical stresses at the interface between the base and the subgrade were monitored. The test results indicated that triangular aperture geogrids reduced permanent deformation and maximum vertical stress at the interface as compared with the unreinforced bases. The geogrids improved the performance of the aggregate bases at different thicknesses. The benefit became more pronounced when a heavier-duty geogrid was used. The back-calculations from the test data showed that the stress distribution angle and the modulus ratio of base course to subgrade decreased with an increase of the load cycles. The stress distribution angle increased with the increase of the base thickness. The vertical stress distributions were compared with the computed distribution by the layered linear elastic theory. These test data provide the basis for the development of a design method for triangular aperture geogrid-reinforced bases over weak subgrade in the future.

Measurement of the orbital angular momentum at photon level via the spatial probability distribution

We demonstrate that by diffracting light at single photon level with orbital angular momentum (OAM) by an equilateral triangular aperture, it is possible to determine their OAM amount by simply counting the number of maxima in the side of a generated triangular shaped hexagonal lattice in the spatial photon probability distribution. The sign of the OAM is obtained by the orientation of the latticed triangle. We also show that by changing the aperture size it is possible to discriminate OAM state superpositions.

Measuring the topological charge of ultrabroadband, optical-vortex beams with a triangular aperture

A simple technique for determining the topological charge of supercontinuum optical vortices is presented. The spatial dispersion inherent to generating broadband vortices with a single forked grating is compensated with a double-pass arrangement from a single spatial light modulator. The vortex charge is determined by inspecting the diffraction pattern through a triangular aperture. It is shown that the topological charge is constant, and can be consistently measured, across a wide range of colors.

Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum

A wide array of diffractive structures such as arrays of pinholes, triangular apertures, slits, and holograms have all recently been used to measure the azimuthal index of individual Laguerre-Gaussian beams. Here, we demonstrate a powerful approach to simultaneously measure both the radial and azimuthal indices of pure Laguerre-Gaussian light fields using the method of principal component analysis. We find that the shape of the diffracting element used to measure the mode indices is in fact of little importance and the crucial step is training any diffracting optical system and transforming the observed pattern into uncorrelated variables. The method is generic and may be extended to other families of light fields such as Bessel or Hermite-Gaussian beams.

Diffraction of transmission light through triangular apertures in array of retro-reflective microprisms

An array of microprisms was described by a model of multiperiod blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction array theorem. The relation between zonal/line ghost fringes and imperfectly fabricated array structures was analyzed. Geometrical performance (e.g., the dihedral angle of the microprism) was tested by measuring the features of diffraction patterns of samples from three retroreflective sheeting manufacturers.

Effects of dielectric substrate properties for optical phenomena in a nanoscale ridge aperture

In this paper, we show that the increase in power throughput is dependent on the thickness and the relative permittivity of the dielectric substrate in the aperture-on-dielectric-substrate configuration. We also show that, similar to a metal nanoparticle, an increase in the medium dielectric constant results in a red-shift in the plasmon resonance of a nanoscale ridge aperture. These results, which are verified by a numerical analysis, provide a new understanding of the phenomenon of surface-plasmon-enhanced transmission. We demonstrate that the red-shifted wavelength and dielectric properties can compensate for the optical loss due to plasmon red-shift. In addition, the dielectric substrate layer behaves like a Fabry–Pérot optical resonator, resulting in coherent constructive interference. The simulation results show that the |E|2 intensity of the triangular aperture is ∼200% greater when this dielectric effect and red-shift resonance are considered.

Geometrical phase and surface plasmon focusing with azimuthal polarization

Owing to a geometric phase effect, an isosceles triangular aperture etched into thin metal film leads to constructive or destructive interference of surface plasmons excited at the two equal sides under linearly polarized illumination. Through appropriate spatial arrangement of an array of triangles, a highly confined focal spot beyond the diffraction limit can be achieved at the geometric center under azimuthally polarized excitation with field enhancement comparable to a bull's eye plasmonic lens under radially polarized illumination. Through simply rotating the orientation of each triangle aperture by 90°, the plasmonic structure defocuses the same azimuthal polarization illumination due to destructive interference caused by a geometric π-phase difference between the two sides of the triangle and between the adjacent triangles.

Propagation of helical beams through amplitude diffractive optical elements and the measurement of topological charge

A new method is proposed to generate amplitude diffractive optical elements such as Young's double-slits and triangular apertures from a spatial light modulator (SLM). With the help of plane wave angular spectrum diffraction formula and Collins formula, the propagation property of helical beams passing through those two amplitude optical elements is studied, and the measurement of topological charge of helical beams is also achieved with those two amplitude diffractive optical elements. Due to the fact that the SLM can flexibly and accurately change the configurations and locations of optical elements, the measurements can be conveniently achieved.

Visualization of the birth of an optical vortex using diffraction from a triangular aperture

The study and application of optical vortices have gained significant prominence over the last two decades. An interesting challenge remains the determination of the azimuthal index (topological charge) ℓ of an optical vortex beam for a range of applications. We explore the diffraction of such beams from a triangular aperture and observe that the form of the resultant diffraction pattern is dependent upon both the magnitude and sign of the azimuthal index and this is valid for both monochromatic and broadband light fields. For the first time we demonstrate that this behavior is related not only to the azimuthal index but crucially the Gouy phase component of the incident beam. In particular, we explore the far field diffraction pattern for incident fields incident upon a triangular aperture possessing non-integer values of the azimuthal index ℓ. Such fields have a complex vortex structure. We are able to infer the birth of a vortex which occurs at half-integer values of ℓ and explore its evolution by observations of the diffraction pattern. These results demonstrate the extended versatility of a triangular aperture for the study of optical vortices.

Measuring vortex charge with a triangular aperture

A triangular aperture illuminated with a vortex beam creates a truncated lattice diffraction pattern that identifies the charge of the vortex. In this Letter, we demonstrate the measurement of vortex charge via this approach for vortex beams up to charge ±7. We also demonstrate the use of this technique for measuring femtosecond vortices and noninteger vortices, comparing these results with numerical modeling. It is shown that this technique is simple and reliable, but care must be taken when interpreting the results for the noninteger case.

Stress Analysis on Triangular-Aperture Geogrid-Reinforced Bases over Weak Subgrade under Cyclic Loading

Geogrids have been successfully used to improve soft subgrade and reinforce weak base courses for low-volume roads by providing lateral confinement. However, uniaxial and biaxial geogrids with rectangular or square apertures cannot provide uniform resistance in all directions. A new geogrid product with triangular apertures was developed and introduced into the market to overcome this problem. The triangular-aperture geogrid has a more stable grid structure and can provide uniform resistance in all directions compared with uniaxial and biaxial geogrids. However, the performance of triangular-aperture geogrid-reinforced bases has not been well evaluated. In this study, unreinforced and triangular-aperture geogrid-reinforced bases over a weak subgrade were constructed in a large geotechnical testing box (2 × 2.2 × 2 m) at the University of Kansas and tested under cyclic loading. During the tests, surface deformations and vertical stresses at the interface between the base and the subgrade were monitored. The test results showed that triangular-aperture geogrids reduced permanent surface deformations and vertical stresses at the interface compared with an unreinforced base. The benefit became more pronounced when a heavier-duty geogrid was used. The backcalculations from the measured vertical stresses at the interface between base and subgrade showed that the stress distribution angle and the modulus ratio of base course to subgrade decreased with an increase in the number of cycles. The rates of reduction in the stress distribution angle and the modulus ratio for the unreinforced base were faster than those for the reinforced bases. This paper focuses on the stress analysis of the test sections under cyclic loading.

Numerical analysis of tensile behavior of geogrids with rectangular and triangular apertures

Geogrids, made of polymeric materials, have been used as a construction material for many applications, such as walls, slopes, roads, building foundations, etc. In the past, geogrids were manufactured with apertures in a rectangular or square shape. Recently, geogrids with a triangular aperture shape have been introduced into the market. The new geogrids are manufactured with ribs oriented in three equilateral directions and expected to have a more stable grid structure, which can provide more uniform resistance in all directions. In this study, the numerical software – FLAC was adopted to investigate the responses of geogrids with rectangular and triangular apertures when subjected to a uniaxial tensile load at different directions relative to the orientations of ribs in air. The geogrid ribs were modeled using beam elements jointed rigidly at nodes (i.e., the angle between two adjacent ribs did not change) and subjected to tension in one direction. The numerical results showed that the stress–strain responses of the geogrids were different at different loading directions relative to the orientations of ribs. The effects of aperture shape of geogrid, and elastic modulus and cross-section area of geogrid ribs on the tensile stiffness of the geogrid were also evaluated. The geogrid with triangular apertures had more uniform tensile stiffness and strength distributions than the geogrid with rectangular apertures. An increase of the elastic modulus and cross-section area of the geogrid ribs could increase the stiffness of the geogrid with triangular apertures. The numerical results were verified by experimental data for geogrids with rectangular and triangular apertures.

Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum

We show that the orbital angular momentum can be used to unveil lattice properties hidden in diffraction patterns of a simple triangular aperture. Depending on the orbital angular momentum of the incident beam, the far field diffraction pattern reveals a truncated optical lattice associated with the illuminated aperture. This effect can be used to measure the topological charge of light beams.

Influence of vertex angles on the extraordinary optical transmission characteristics of triangular and bow-tie-shaped apertures

The influence of vertex angles on the extraordinary optical transmission (EOT) characteristics of isosceles triangular apertures is numerically investigated with a three-dimensional finite-difference time-domain (FDTD) method. It has been found that the resonant peak characteristics are dependent on the vertex angles of triangular aperture (TA) and the polarized directions of incident light. The resonant peak amplitude is dramatically decreased, when the vertex angle is increased. A blue-shift/red-shift phenomenon is observed in both of the two cases. Detailed studies indicate that the transmission peak characteristics are due to the effects of localized surface plasmon modes excited along the sidewalls and Fabry–Pérot-like resonance. The EOT performance of TA arrays is compared with that of the rectangular aperture arrays. In addition, a bow-tie-shaped aperture (BTA) can be recognized as two overlapped TAs. The EOT properties of BTA with varying bow angles are also studied and analyzed.