Mirror Geometry Research Articles

Damage thresholds for blaze diffraction gratings and grazing incidence optics at an X-ray free-electron laser.

The Linac Coherent Light Source is upgrading its machine to high repetition rate and to extended ranges. Novel coatings, with limited surface oxidation, which are able to work at the carbon edge, are required. In addition, high-resolution soft X-ray monochromators become necessary. One of the big challenges is to design the mirror geometry and the grating profile to have high reflectivity (or efficiency) and at the same time survive the high peak energy of the free-electron laser pulses. For these reasons the experimental damage threshold, at 900 eV, of two platinum-coated gratings with different blazed angles has been investigated. The gratings were tested at 1° grazing incidence. To validate a model for which the damage threshold on the blaze grating can be estimated by calculating the damage threshold of a mirror with an angle of incidence identical to the angle of incidence on the grating plus the blaze angle, tests on Pt-coated substrates have also been performed. The results confirmed the prediction. Uncoated silicon, platinum and SiB3 (both deposited on a silicon substrate) were also investigated. In general, the measured damage threshold at grazing incidence is higher than that calculated under the assumption that there is no energy transport from the volume where the photons are absorbed. However, it was found that, for the case of the SiB3 coating, the grazing incidence condition did not increase the damage threshold, indicating that the energy transport away from the extinction volume is negligible.

Structurally embedded reflectors and mirrors for elastic wave focusing and energy harvesting

The harvesting of elastic waves propagating in structures can be enhanced dramatically via spatial focusing using mirror and lens concepts. Recent efforts on the mirror design have employed cylindrical stubs that form elliptical and parabolic geometries to focus structure-borne waves originating from a point source and incident plane waves, respectively. In those first-generation heuristic efforts, bulky cylindrical attachments served as effective reflectors while drastically altering thin host structures. Enabling structurally embedded mirror (SEM) configurations that avoid substantial modification of the host system requires a thorough understanding of the elastic mirror dynamics. This work presents a detailed investigation of SEM design, analysis, and experimental validation for enhanced elastic wave energy harvesting, among other applications that can benefit from spatially focused wave intensity. The SEM concept proposed in this effort uses metallic spheres (e.g., tungsten, lead, and steel) inserted into blind holes in a flat aluminum plate domain. The results show that, while SEM performance improves with property mismatch between the inclusion and the host materials, transmission resonances of the inclusions are detrimental to reflection performance and have to be avoided. A relationship between elastic mirror geometry and wavelength is unveiled to minimize the energy concentration in the side lobes around the intended focus, enabling small-sized and simple harvester design. These basic concepts and principles, demonstrated through finite-element simulations, are validated experimentally over a range of frequencies. Dramatic enhancement of the harvested power (by an order of magnitude) is also demonstrated using an elliptical SEM made from spherical tungsten inclusions in an aluminum plate. The case of a perforated mirror is also addressed briefly.

Brane brick models in the mirror

Brane brick models are Type IIA brane configurations that encode the 2d mathcal{N}=left(0,2right) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how 2d (0, 2) triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is n − 1 for a Calabi-Yau n-fold. This makes us conjecture the existence of a quadrality symmetry in 0d. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of 2d (0, 2) theories in terms of 4-manifolds.

Optimization and Rapid Prototyping of Catadioptric Omnidirectional Stereo Sensors

Omnidirectional stereo imaging provides useful depth information for autonomous navigation. In principle, omnidirectional stereo images can be achieved at a low cost, using a single camera and two curved mirrors, but such systems are not widely deployed. Here we describe the optimization and rapid prototyping of a low-cost omnidirectional stereo sensor for a telepresence robot. We consider single-viewpoint and non-single-viewpoint designs. We present a new way of relaxing single-viewpoint constraints, while retaining the ability to vertically rectify images. We also present a method of optimizing the resulting design to minimize depth errors. However, we show that despite these steps, nonsingle-viewpoint designs produce stereo disparities over a more practical range of distances. The lack of a single viewpoint could potentially introduce distortions that affect stereo matching, but these distortions are removed by projecting rays through the mirror geometry. We also describe a new method for rapid prototyping of curved mirrors using 3D printing and vacuum forming.

Minimization of the Ohmic Loss of Grooved Polarizer Mirrors in High-Power ECRH Systems

A set of two corrugated polarizer mirrors is typically used in high-power electron cyclotron resonance heating (ECRH) systems to provide the required polarization of the ECRH output beam. The ohmic losses of these mirrors can significantly exceed the losses of plane mirrors depending on the polarization of the incident beam with respect to the orientation of the grooves. Since polarizer mirrors incorporated into miter bends of a corrugated waveguide line are limited in size, active water cooling can become critical in high-power cw systems like the one for ITER. The ohmic loss of polarizer mirrors has been investigated experimentally at high power. A strategy to minimize the losses for given mirror geometries has been found.

Europium-Doped NaYF4 Nanocrystals as Probes for the Electric and Magnetic Local Density of Optical States throughout the Visible Spectral Range.

Absorption and emission in the ultraviolet, visible, and infrared spectral range are usually mediated by the electric-field component of light. Only some electronic transitions have significant “magnetic-dipole” character, meaning that they couple to the magnetic field of light. Nanophotonic control over magnetic-dipole emission has recently been demonstrated, and magnetic-dipole transitions have been used to probe the magnetic-field profiles of photonic structures. However, the library of available magnetic-dipole emitters is currently limited to red or infrared emitters and mostly doped solids. Here, we show that NaYF4 nanocrystals doped with Eu3+ have various electric- and magnetic-dipole emission lines throughout the visible spectral range from multiple excited states. At the same time, the colloidal nature of the nanocrystals allows easy handling. We demonstrate the use of these nanocrystals as probes for the radiative electric and magnetic local density of optical states in a planar mirror geometry. A single emission spectrum can reveal enhancement or suppression of the density of optical states at multiple frequencies simultaneously. Such nanocrystals may find application in the characterization of nanophotonic structures or as model emitters for studies into magnetic light–matter interaction at optical frequencies.

Technique for measuring the three-dimensional shapes of telescope mirrors

Telescope mirrors determine the imaging quality and the observation ability of the telescopes. Unfortunately, manufacturing highly accurate mirrors remains a bottleneck problem in space optics. One primary cause is the lack of a technique to robustly measure the three-dimensional (3-D) shapes of mirrors for inverse engineering. After centuries of study, researchers developed different techniques for testing the quality of telescope mirrors and proposed different methods for measuring the 3-D shapes of mirrors. Among them, interferometers become popular in evaluating the surface errors of the manufactured mirrors. However, interferometers could not measure some important mirror parameters, e.g., paraxial radius, geometry dimension, and eccentric errors, directly and accurately although these parameters are essential for mirror manufacturing. For those methods that could measure these parameters, their measurement accuracies are far beyond satisfactory. We present a technique for robust measurement of the 3-D shapes of mirrors with single-shot projection. Experimental results show that this technique is significantly more robust than state-of-the-art techniques, which makes it feasible for commercial devices to measure the shapes of mirrors quantitatively and robustly.

80 nm tunable DBR-free semiconductor disk laser

We report a widely tunable optically pumped distributed Bragg reflector (DBR)-free semiconductor disk laser with 6 W continuous wave output power near 1055 nm when using a 2% output coupler. Using only high reflecting mirrors, the lasing wavelength is centered at 1034 nm and can be tuned up to a record 80 nm by using a birefringent filter. We attribute such wide tunability to the unique broad effective gain bandwidth of DBR-free semiconductor disk lasers achieved by eliminating the active mirror geometry.

Design and optical performance of CPC based compound plane concentrators

To simplify the fabrication of compound parabolic concentrators (CPC) with a one-sided flat absorber and make solar radiation on the absorber more uniform, an attempt is made here to use multiple plane mirrors in place of parabolic reflectors to construct a compound plane concentrator (CPC-A, in short). The design procedure of such concentrator as an alternative to CPCs is presented based on the edge-ray principle, and its optical performance and design optimization are theoretically investigated. Analysis shows that the effective acceptance half-angle (θea) of CPC-A, dependent on plane mirror's number (N) and geometry of CPC based on which CPC-A is designed, is always less than the acceptance half-angle (θa) of CPC but gradually close to θa with the increase of N, and the optical efficiency of both CPC-A and CPC is almost identical for solar radiation withinθea. Results revealed that the annual collectible radiation of CPC-A oriented in the east-west direction is almost identical to that of CPC only if the sun is kept withinθea for at least 7 h in all day of a year by periodically adjusting its tilt-angle. A further analysis indicates that CPC-A designed based on the edge-ray principle is not an optimal design but can be regarded as optimal geometry for maximizing its annual radiation collection.

Design of a holographic combiner for a virtual display

Ways and methods of modeling and calculating a holographic combiner for a virtual display are presented. On the one hand, they allow Denisyuk holograms with high diffraction efficiency independent of the field angle to be generated. On the other hand, they allow the advantages of the holographic combiner when compared with a multilayer dielectric mirror to be maximally realized. Optimization and search of the design parameters of elements of an optical setup for generating an aspherical wavefront for recording a Denisyuk hologram are based on ray tracing. These processes are greatly facilitated by the use of an intermediate model in the form of a thin transparency for phase delay. The phase delay of this transparency, the mirror geometry of the optical setup that forms the aspherical wavefront for recording the hologram, and the actual model of Denisyuk hologram in this article are described in the form adopted in the Zemax environment for surfaces such as Binary1, Extended polynomial and Optically Fabricated Hologram.

AN EMERGING CLASS OF GAMMA-RAY FLARES FROM BLAZARS: BEYOND ONE-ZONE MODELS

Blazars radiate from relativistic plasma jets with bulk Lorentz factors closely aligned along our line of sight. In a number of blazars of the flat-spectrum radio quasar type, such as 3C 454.3 and 3C 279, gamma-ray flares have recently been detected with very high luminosity and few or no counterparts in the optical and soft X-ray bands. They challenge the current one-zone leptonic models of emissions from within the broad-line region (BLR). The latter envisage the optical/X-ray emissions to be produced as synchrotron radiation by the same population of highly relativistic electrons in the jet that would also yield the gamma rays by inverse Compton upscattering of surrounding soft photons. To meet the challenge, we present here a model based on primary synchrotron photons emitted in the BLR by a plasmoid moving out with the jet and scattered back toward the incoming plasmoid by an outer plasma clump acting as a mirror. We consider both a scenario based on a static mirror located outside the BLR and an alternative provided by a moving mirror geometry. We show that mirroring phenomena can locally enhance the density and anisotropy with associated relativistic boosting of soft photons within the jet, so as to trigger bright inverse Compton gamma-ray transients from nearly steady optical/X-ray synchrotron emissions. In this picture we interpret the peculiarly asymmetric light curves of the recently detected gamma-ray flares from 3C 279. Our scenario provides a promising start to understanding the widening class of bright and transient gamma-ray activities in blazars.

Special points of inflation in flux compactifications

We study the realization of axion inflation models in the complex structure moduli spaces of Calabi–Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell–Weil group of rank N−1 or an N-section, which admit an axion if N>3.

CFD AND CONJUGATE HEAT TRANSFER ANALYSIS OF HEAT SINKS WITH DIFFERENT FIN GEOMETRIES SUBJECTED TO FOCED CONVECTION USED IN ELECTRONICS COOLING

Heat sinks are commonly used for cooling of electronic devices. Heat sinks, an array of heat fins, remove the heat from the surfaces of the chips by enhancing the heat Transfer rate through heat conduction process. Heat can also be removed from the chip surfaces through forced convection heat transfer. In this project work, CFD and conjugate heat transfer analysis is carried out for various fin geometries with Zigzag, Fluted, Slanted mirror, Custom pin fin and staggered array configurations for low thermal resistance and minimum pressure drop. Numerical simulations are carried out for each of the above mentioned fin geometries with common base plate thickness of 2 mm, fin height of 28 mm and fin thickness of 1 mm for three different heat loads namely 50 W, 75 W and 100 W with air flow of 3.933 m/s (15 ft3/min or 15 CFM) and air inlet temperature of 25 o C. The results are compared for thermal performance of a heat sink for each of above geometries and it is observe that the fin with Slanted Mirror geometry gives the best performance among all the other geometries for minimum Pressure drop. The average heat transfer coefficients for fins with slanted mirror geometry, zig zag configuration, fluted type, custom pin fin and staggered array are found to be 215 W/m2K, 164 W/m2K, 164 W/m2K, 157 W/m2K and 145 W/m2K respectively

Kirkpatrick-Baez mirrors to focus hard X-rays in two dimensions as fabricated, tested and installed at the Advanced Photon Source.

The micro-focusing performance for hard X-rays of a fixed-geometry elliptical Kirkpatrick-Baez (K-B) mirrors assembly fabricated, tested and finally implemented at the micro-probe beamline 8-BM of the Advanced Photon Source is reported. Testing of the K-B mirror system was performed at the optics and detector test beamline 1-BM. K-B mirrors of length 80 mm and 60 mm were fabricated by profile coating with Pt metal to produce focal lengths of 250 mm and 155 mm for 3 mrad incident angle. For the critical angle of Pt, a broad bandwidth of energies up to 20 keV applies. The classical K-B sequential mirror geometry was used, and mirrors were mounted on micro-translation stages. The beam intensity profiles were measured by differentiating the curves of intensity data measured using a wire-scanning method. A beam size of 1.3 µm (V) and 1.2 µm (H) was measured with monochromatic X-rays of 18 keV at 1-BM. After installation at 8-BM the measured focus met the design requirements. In this paper the fabrication and metrology of the K-B mirrors are reported, as well as the focusing performances of the full mirrors-plus-mount set-up at both beamlines.

Predicting the angular resolution of x-ray mirrors

The angular resolution of a grazing incidence focusing mirror is an important parameter in x-ray optics. It is often quantified by either the point spread function (PSF)—the distribution of the focused rays as a function of the distance from the center of the focal spot—or the half-energy width, which is double the PSF median value. The focusing of x-rays (with wavelengths 1000 shorter than visible light) is very sensitive to both a mirror’s surface profile and roughness (see Figure 1), i.e., surface relief on a variety of scales down to a few angstroms in height. PSF calculations for a focusing mirror must therefore account for both these factors. The surface roughness typically causes an x-ray scattering interference effect, which generally increases with x-ray energy. There are, however, several problems with computing the PSF by considering profile and roughness separately. It has long been known that x-ray focusing degradation caused by long-period deformations—e.g., Figure 1(a)—and surface roughness of mirrors—see Figure 1(c)—can be analyzed separately by treating the x-rays as rays or waves, respectively. When treating the x-rays as rays, geometric optics are applied. A well-established x-ray scattering (perturbation) theory1 is used when they are treated as waves, but it can be applied only to very smooth surfaces and to short-period features. However, the boundary between these two regimes2 is difficult to define and not clear-cut. Degradations in optical behavior caused by surface features in an intermediate spatial frequency range—see Figure 1(b)—cannot always be treated with either of the two methods mentioned.3 In addition, neither the geometric optics nor the scattering approach account for the effect of aperture diffraction. It can also be difficult to combine the separately derived geometry and scattering PSF values to obtain the total PSF of the mirror. We have created a new and self-consistent method that does not require boundaries between mirror geometries, profile frequencies, or surface roughnesses to be set.3 Our method is based Figure 1. Behavior of x-rays interacting with non-smooth grazing focusing mirrors. (a) Geometric optics can be applied to mirror defects with long spatial periods. (b) At mid-frequencies (i.e., centimeter to millimeter wavelength range) x-ray behavior is more uncertain. (c) Surface diffraction from micro-roughness is described by perturbation theory. (d) All three defects, as in (a), (b), and (c), are included and are difficult to treat consistently.

Computational Analysis of an effect of aerodynamic pressure on the side view mirror geometry

This paper describes the evaluation of aerodynamic flow effects on side mirror geometry for a passenger car using ANSYS Fluent CFD simulation software. Results from analysis of pressure coefficient on side view mirror designs is evaluated to analyse the unsteady forces that cause fluctuations to mirror surface and image blurring. The fluctuation also causes drag forces that increase the overall drag coefficient, with an assumption resulting in higher fuel consumption and emission. Three features of side view mirror design were investigated with two input velocity parameters of 17 m/s and 33 m/s. Results indicate that the half-sphere design shows the most effective design with less pressure coefficient fluctuation and drag coefficient.

Design considerations regarding ellipsoidal mirror based reflectometers

Hemi-ellipsoidal mirrors are used in reflection-based measurements due to their ability to collect light scattered from one focal point at the other. In this paper, a radiometric model of this energy transfer is derived for arbitrary mirror and detector geometries. This model is used to examine the imaging characteristics of the mirror away from focus for both diffuse and specular light. The radiometric model is applied to several detector geometries for measuring the Directional Hemispherical Reflectance for both diffuse and specular samples. The angular absorption characteristics of the detector are then applied to the measurement to address measurement accuracy for diffuse and specular samples. Examining different detector configurations shows the effectiveness of flat detectors at angles ranging from normal to 50°, and that multifaceted detectors can function from normal incidence to grazing angles.

Accurate optical model for design and analysis of solar fields based on heterogeneous multicore systems

This work deals with parallel algorithms for the optical design and analysis of solar fields for Central Receiver Systems. The proposed implementation based on desktop workstations equipped with multiple Graphics Processing Units (GPU) is motivated by the need to have an accurate and fast simulation environment for studying mirror imperfection and non-planar geometries. Since heliostat field layouts can be composed of thousands of mirrors, and for each one a complex 3D geometry problem must be solved, this can take a long time even with highly optimized CPU-based solvers. The GPU-accelerated solver outperforms an optimized OpenMP-based reference, running on 8 CPU cores, up to 52× depending on the complexity of the problem, at the cost of a very modest hardware upgrade of two GPU GTX 590 and one GTX 480 graphics cards. Several applications demonstrate that the parallel algorithm preserves flexibility to model complex mirror geometries and non-idealities.

A computational simulation of reflector and tube effects in ultraviolet phototherapy

While ultraviolet phototherapy is effective at treating a wide range of skin conditions, over exposure to ultraviolet radiation has a number of detrimental effects including but not limited to erythema, ocular damage and even oncogenesis. It is therefore important to quantify and control the dose received in order to maximize the effectiveness of treatment while minimizing the potentially damaging side effects. Recent dose models have been developed for this purpose, incorporating both the irradiance from the phototherapy lamps and the contributions from metallic reflectors. These models have good predictive power, but the situation is complicated by the huge variety of cabin and mirror geometries available. This work simulates a variety of possible treatment configurations to examine the implications these factors have on dose homogeneity and global irradiance, and shows that the relationship between global irradiance and number of tubes is complex and nonlinear. This has implications for both cabin design and treatment planning.

On gauge theory and topological string in Nekrasov-Shatashvili limit

We study the Nekrasov-Shatashvili limit of the \( \mathcal{N} \) = 2 supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau manifolds. In this limit one of the two deformation parameters ϵ1,2 of the Ω background is set to zero and we study the perturbative expansion of the topological amplitudes around the remaining parameter. We derive differential equations from Seiberg-Witten curves and mirror geometries, which determine the higher genus topological amplitudes up to a constant. We show that the higher genus formulae previously obtained from holomorphic anomaly equations and boundary conditions satisfy these differential equations. We also provide a derivation of the holomorphic anomaly equations in the Nekrasov-Shatashvili limit from these differential equations.