Ray-tracing Calculations Research Articles

Optical microscopy of 3D carpet cloaks:ray-tracing calculations

In a recent publication (T. Ergin et al., Science 328, 337 (2010)), three-dimensional broadband dielectric carpet cloaks have been fabricated and experimentally characterized by optical bright-field and dark-field microscopy using unpolarized light from an incandescent lamp. A direct comparison with theory has not been provided so far. In the present work, we treat the carpet cloak as well as the entire optical microscope within the ray-optics approximation and the cloak within the effective-medium approximation. We find good qualitative agreement between experimental results and our calculations.

LOCALIZATION OF A TYPE III RADIO BURST OBSERVED BY THESTEREOSPACECRAFT

Ray tracing calculations show that (1) emissions from a localized source escape as direct and reflected waves along different paths, (2) the reflected waves experience higher attenuation and group delay because they travel longer path lengths in regions of reduced refractive index, and (3) widely separated spacecraft "A" and "B" can detect the direct as well as reflected emissions escaping along different directions. It is proposed that the source of a radio burst observed by twin spacecraft "A" and "B" can be localized if at a given frequency the emission at one of them is identified as the direct emission and is identified at the other as the reflected emission by comparing the observed time delays ΔT, as well as intensity ratios IB/IA with the corresponding values of the direct and reflected emissions obtained for a given coronal model. A type III event observed by the STEREO spacecraft "A" and "B" shows that its characteristics are consistent with direct and reflected emissions by being less intense and delayed at "A" in comparison to that at "B." By applying the proposed technique to this event, the location of its source is found to lie between the turning point of the ray and the harmonic layer corresponding to fpe = f/2, where f and fpe are the frequency of the emission and the electron plasma frequency, respectively. The comparisons of the widths of the fundamental and harmonic emission cones with the angular separation of spacecraft "A" and "B" indicate that the mode of the observed emission is probably the harmonic.

Design of an aberration corrected low-voltage SEM

The low-voltage foil corrector is a novel type of foil aberration corrector that can correct for both the spherical and chromatic aberration simultaneously. In order to give a realistic example of the capabilities of this corrector, a design for a low-voltage scanning electron microscope with the low-voltage foil corrector is presented. A fully electrostatic column has been designed and characterised by using aberration integrals and ray tracing calculations. The amount of aberration correction can be adjusted relatively easy. The third order spherical and the first order chromatic aberration can be completely cancelled. In the zero current limit, a FW50 probe size of 1.0 nm at 1 kV can be obtained. This probe size is mainly limited by diffraction and by the fifth order spherical aberration.

Research of Electron Cyclotron Resonance Heating Methods and Relevant Experiments

For expanding applicable parameter ranges of electron cyclotron resonance heating (ECRH), various methods of ECRH have been studied with use of millimeter-wave sources of 77-, 82.7-, 84-, and 168-GHz gyrotrons in the Large Helical Device (LHD). The fundamental ordinary (O-) mode and the second-harmonic extraordinary (X-) mode are mainly used for starting up, sustaining, and controlling the plasma. Heating efficiencies of ECRH by launching of these modes have been investigated experimentally for wide range of the central electron density and compared with power absorption rates obtained by ray-tracing calculation. ECRH by the third-harmonic X-mode has been performed in each magnetic configuration Bax = 1 and 2 T with launching of 84-GHz range and 168-GHz millimeter waves. Increases of the electron temperature and the stored energy were observed in both cases. ECRH by the electrostatic electron Bernstein wave (EBW) has been expected to be a promising substitute in parameter ranges where the conventional methods of ECRH by the electromagnetic modes are not available. To perform ECRH by the EBW in LHD, extraordinary-EBW (X-B) and ordinary-extraordinary-EBW (O-X-B) mode conversion processes, the propagation of the wave, and the absorption have been investigated experimentally and theoretically.

Optical signatures of radiation belt electron precipitation induced by ground‐based VLF transmitters

Numerical simulations are presented of optical emissions in the ionosphere due to electron precipitation caused by ground‐based VLF transmitters. Ray tracing and precipitation calculations are made to estimate the flux precipitated from the inner magnetosphere for existing ground‐based VLF transmitters as well as hypothetical transmitters with controlled parameters. The resulting precipitated fluxes are used to estimate ionization profiles through Monte Carlo simulations, and the ionization profiles are converted to photon volume emission rates. The results are extended over a range of L shells and longitudes. Results show that the NWC transmitter at North West Cape, Australia, creates the strongest optical signature because of its high power, latitude of ∼35°, and low frequency. The resulting optical signal has a peak of <0.1 R; however, we calculate that this should be detectable using sensitive photometric instruments and controlled modulation experiments.

ECCD Experiments Using the Upgraded Launching System in Heliotron J

AbstractElectron cyclotron current drive (ECCD) experiments have been made in Heliotron J by using an upgraded EC launching system. A focused Gaussian beam is injected with the parallel refractive index, N||, ranging from ‐0.05 to 0.6. Ray tracing calculation shows that the EC power is more localized than that in the previous launching system. In the initial ECCD experiment, the EC injection angle has been successfully scanned as designed. Comparison between perpendicular and oblique launching experiments shows that for standard configuration, the EC current of 1 kA is driven at N|| ∼ 0.3 in the Fisch‐Boozer direction, and the bootstrap current flows up to 1 kA. A large increase in electron cyclotron emission (ECE) signals has been observed when the EC current was driven (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Reciprocal Sound Propagation Experiment in Very Shallow Water Area of Hashirimizu Port

A fundamental experiment for environmental monitoring using reciprocal sound propagation was conducted in a very shallow water area in Hashirimizu Port near the entrance to Tokyo Bay. Sound propagation systems with a 12.5 kHz transducer were placed at opposite piers with a distance of about 120 m. Sound travel time was monitored using M-sequence phase-modulated signals so that an accurate arrival time could be detected even in a noisy environment. Arrival time changed throughout the experiment period about 3 weeks almost in accordance with the changes in seawater temperature. However, under certain conditions, such as a low tide and a high negative gradient of the temperature profile in the depth direction, the arrival time was longer than expected. Ray tracing calculation using Bellhop revealed that all rays radiated by the transducer were refracted downward because of the sound speed profile changes. It turns out that the ray path changes depending on ocean environmental changes, especially changes in temperature and the tides. Current speed estimation from reciprocal travel time showed a trend similar to the measurement result of the acoustic doppler current profiler (ADCP). The low reliability of current can be improved by changing the peak tracking method. It also has a potential to get wide area of ocean environment using reflected waves.

Vergence analysis reveals the influence of axial distances on accommodation with age and axial ametropia

Despite numerous investigations, the aetiology and mechanism of accommodation and presbyopia remains equivocal. Using Gaussian first-order ray tracing calculations, we examine the contribution that ocular axial distances make to the accommodation response. Further, the influence of age and ametropia are also considered. The data show that all changes in axial distances during accommodation reduce the accommodation response, with the reduction in anterior chamber depth contributing most to this overall attenuation. Although the total power loss due to the changes in axial distances remained constant with increasing age, hyperopes exhibited less accommodation than myopes. The study, therefore, enhances our understanding of biometric accommodative changes and demonstrates the utility of vergence analysis in the assessment of accommodation.

Plasma wave simulation based on a versatile finite element method solver

The possibility of plasma wave simulation based on the finite element method (FEM) was explored, and a new full wave simulation code of the lower hybrid (LH) wave, Lower Hybrid wavE Analysis based on FEM (LHEAF), was developed. The efficient iterative solver for the LH wave [O. Meneghini, S. Shiraiwa, and R. Parker, Phys. Plasmas 16, 090701 (2009)] was coupled to one-dimensional Fokker–Planck calculation to obtain the self-consistent distribution function. In LHEAF, seamless handling of the core, scrape off layer, and antenna regions were realized and the wave launching structure were naturally included into the simulation. Simulation results of a Maxwellian tokamak plasma showed good agreement with ray tracing calculations and the TORIC-LH spectral solver [J. C. Wright, P. T. Bonoli, A. E. Schmidt et al., Phys. Plasmas 16, 072502 (2009)]. Compared to spectral domain solvers, the computational requirements are reduced significantly, allowing an Alcator C [M. Porkolab, J. J. Schuss, B. Lloyd et al., Phys. Rev. Lett. 53, 450 (1984)] scale plasma simulation on a desktop computer. Also, the LH full wave simulation of an ITER scale plasma was demonstrated for the first time with moderate increase in the problem size. In addition, the flexibility of the FEM approach has been exploited to address issues of antenna-plasma coupling in the LH and ion cyclotron range of frequencies (ICRF). Techniques using the FEM package for this purpose were validated on the traditional grill antenna and have been applied to the interdigital-line antenna of LH wave. Application to the near field analysis of the new Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] ICRF antenna is in progress.

Development of terahertz gyrotrons and their application to CTS on LHD

Development of a high-power, sub terahertz pulse gyrotron has started in FIR FU for application to CTS on LHD. A new electron gun was designed to produce a laminar electron beam with a good quality. Second harmonic TE6,5 and TE8,5 modes were selected as oscillation modes well isolated from other competing modes. Single mode oscillation has been confirmed for both TE6,5 and TE8,5 modes. The maximum power is larger than 50 kW for TE6,5 mode (0.349 THz) and about 40 kW for TE8,5 mode (0.390 THz). These powers are new records of second harmonic gyrotron in this frequency range. Feasibility study of CTS with a 0.4 THz pulse gyrotron from a high density plasma in LHD was carried out. The CTS condition is satisfied for a wide operation regime and scattering angles large enough for good spatial resolution. Ray tracing calculation shows that the launched scattered beams are propagated almost straight. CTS spectra calculated with a newly developed code indicates that a large signal to noise ratio can be obtained against ECE for use of a 100 kW gyrotron.

Towards gravitational-wave astronomy of core-collapse supernova explosion

We study properties of gravitational waves based on the three-dimensional (3D) simulations, which demonstrate the neutrino-driven explosions aided by the standing accretion shock instability (SASI). Pushed by evidence supporting slow rotation prior to core-collapse, we focus on the asphericities in neutrino emissions and matter motions outside the protoneutron star. By performing a ray-tracing calculation in 3D, we estimate accurately the gravitational waveforms from anisotropic neutrino emissions. In contrast to the previous work assuming axisymmetry, we find that the gravitational waveforms vary much more stochastically because the explosion anisotropies depend sensitively on the growth of the SASI which develops chaotically in all directions. Our results show that the gravitational-wave spectrum has its peak near ~ 100 Hz, reflecting the SASI-induced matter overturns of ~ O(10) ms. We point out that the detection of such signals, possibly visible to the LIGO-class detectors for a Galactic supernova, could be an important probe into the long-veiled explosion mechanism.

Measurements of high energy density electrons via observation of Cherenkov radiation

Direct measurement of extremely high energy density electrons created in ultraintense laser-plasma interactions is crucial issue for fast ignition. Recently Cherenkov radiation has been studied to obtain the energy distribution of electrons because the emission angle depends on the electron energy. However in the previous studies [F. Brandl et al., Europhys. Lett. 61, 632 (2003); M. Manclossi et al., Phys. Rev. Lett. 96, 125002 (2006)], the experimental configurations using a planar target raised issues of spatial overlapping among the light from the different energy electrons as well as from the other emissions, such as transition radiation. A novel prism shaped target is developed in which Cherenkov lights emitted from different energy electrons are spatially separated, realizing an absolute measurement of the energy spectrum by counting the light intensities in each observed position. The observed image clearly shows the horseshoe pattern as expected in fully three-dimensional ray-trace calculations, and the image is successfully converted into the electron spectrum inside the target. In addition, it is found from the blur of the outer edge of the Cherenkov pattern that the electrons have a small beam divergence. The calibrated energy spectrum well agrees with particle simulations.

NEUTRINO PAIR ANNIHILATION IN COLLAPSARS: A RAY-TRACING METHOD IN SPECIAL RELATIVITY

We develop a numerical scheme and code for estimating the energy and momentum transfer via neutrino pair annihilation ($\nu + {\bar \nu} \to e^{-}+ e^{+}$), bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs). To calculate the neutrino flux illuminated from the accretion disk, we perform a ray-tracing calculation in the framework of special relativity. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytical solutions. Using hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. We show that the neutrino energy deposition and momentum transfers are strongest near the inner edge of the accretion disk. The beaming effects of special relativity are found to change the annihilation rates by several factors in the polar funnel region. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we find that the neutrino-heating timescale in the vicinity of the polar funnel ($\lesssim 80$ km) can become shorter than the hydrodynamical timescale, indicating that the neutrino-heated outflows can be launched there. We point out that the momentum transfer can play as important role as the energy deposition for the efficient acceleration of neutrino-driven outflows. Our results suggest that the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.

Clinical implications of adopting Monte Carlo treatment planning for CyberKnife

It is documented that well‐modeled Monte Carlo dose calculation algorithms are more accurate than traditional correction‐based algorithms or convolution algorithms at predicting dose distributions delivered to heterogeneous volumes. This increased accuracy has clinical implications for CyberKnife, particularly when comparing dose distributions between the ray‐tracing and Monte Carlo algorithms. Differences between ray‐tracing and Monte Carlo calculations are exacerbated for highly heterogeneous volumes and small field sizes. In this study, the anthropomorphic thorax phantom from the Radiological Physics Center was used to validate the accuracy of the CyberKnife Monte Carlo dose calculation algorithm. Retrospective comparisons of dose distributions calculated by ray‐tracing and Monte Carlo were made for a selection of CyberKnife treatment plans; comparisons were based on target coverage and conformality. For highly heterogeneous cases, such as those involving the lungs, the ray‐tracing algorithm consistently overestimated the target dose and coverage. In our sample of lung treatment plans, the average target coverage for ray‐tracing calculations was 97.7%, while for Monte Carlo, the average coverage dropped to 69.2%. In each plan comparison, the same beam orientations and monitor units were used for both calculations. Significant changes in conformality were also observed. Isodose prescription lines and subsequent target coverage selected for treatment plans calculated with the ray‐tracing algorithm may be different from comparable treatment plans calculated with Monte Carlo, and as such, may have clinical implications for dose prescriptions.PACS number: 87.53.Wz

Antireflective properties of pyramidally textured surfaces

Antireflective properties of pyramidally textured surfaces at normal light incidence are studied by the finite-difference time-domain (FDTD) method. Optimal parameters for the period of the texture and the pyramid height are found. The asymptotic behavior of the reflection coefficient with an increasing height-to-base size ratio for the pyramids is also estimated for two limiting approximations: the effective medium theory (EMT) and geometric optics. For calculations in the geometric optics limit the ray tracing method was applied. The FDTD results for these limits are in agreement with the EMT and with the ray tracing calculations. It was found that the key factor influencing the optimal scatterer size is the character of the substrate tiling by the pyramid bases.

Ray tracing and amplitude calculation in anisotropic layered media

In an anisotropic medium, the direction of the energy propagation is different from the plane-wave propagation. This difference will cause velocity variation in different angles. Therefore, velocity modelling in anisotropic media is different from that in an isotropic medium. In this paper, a conventional algorithm has been extended based on ray tracing through an anisotropic model. The velocity model for ray tracing is parametrized in terms of blocky trapezoid cells where the velocity values change inside the cells linearly. Thomsen's approximations in weakly anisotropic media were used to estimate anisotropic velocity vectors. Rays were traced along the group vector in vertical transversely isotropic (VTI) media so that the phase angle and phase velocities satisfy the anisotropic Snell's law across the interface. To compute seismic amplitudes in the anisotropic media, a new parameter was defined as a partitioning factor which controls the seismic energy propagation in each interface. The effect of geometrical spreading was calculated by using Ursin's procedure. Synthetic models are computed to demonstrate the new ray tracing algorithm and to verify correctness of the traveltimes and amplitude calculations. It is shown that the difference between isotropic and anisotropic traveltimes increases with offset, especially when the ratio offset/depth exceeds 1.5. To calculate amplitudes in VTI media, a new parameter q was introduced and applied as the energy partitioning factor, which helps us obtaining a more accurate amplitude calculation. Ray tracing was also performed for the velocity model extracted from a large offset 2-D seismic line located on the southwest of Iran. Anisotropic parameters were estimated from seismic data under the elliptical anisotropic assumption. Reflected traveltimes were computed by ray tracing from top of the reservoir horizon (fifth reflector) in the anisotropic model. The calculated traveltimes once we explicitly included anisotropic velocities showed a much improved correlation with the seismic real data.

Heavy ion beam probe coordinate mapping and calibration at WEGA stellarator

The heavy ion beam probe (HIBP) is an established nonperturbing diagnostic for high spatially and temporary resolved measurements of magnetically confined plasma parameters such as potential, density, and temperature. These quantities can be determined from the change in the ion beam parameters (charge, intensity, and trajectory) passing through a plasma volume due to collisions with electrons and interaction with the confining magnetic field. One of the problems that should be solved during HIBP installation and tuning is the coordinate matching. Conventionally the coordinate mapping of the HIBP measurement point is provided by ray tracing calculations of the ion beam in the magnetic field. However, it is very difficult to include all physical effects and uncertainties in the model. Thus, the result of the calculations may differ from the real probing position. In order to improve the mapping precision of the HIBP installed at the WEGA stellarator an additional measurement of the beam position is provided using a primary beam detector array inside the vacuum vessel. This allows comparing the measured and calculated ion beam positions in order to prove the calculated coordinate precision and include adjustments in the calculation code if necessary. The principle and the results of this calibration, which is not specific to WEGA but could be adapted to other experiments as well, are presented in this work.

A COMPUTATIONAL MODEL FOR THERMAL RADIATION FROM THE ZONE OF MELT-WATER INTERACTION

This article is concerned with numerical modeling of thermal radiation from the zone of interaction of a melt jet with a water pool. This particular problem is a part of the analysis of complex interaction of the core melt with water in the case of a hypothetical severe accident in light-water nuclear reactors. The energetic contribution of thermal radiation has been studied in some detail in recent articles by the authors. In the present article, we focus on a solution related to possible optical diagnostics of the physical parameters of the process. These diagnostics can be based on comparison of the measured and calculated thermal radiation in the small-scale laboratory experiments. The sensitivity of the numerical data to some important parameters of the computational model is expected to be important to validate and improve the multiphase flow model. The radiation transfer model employed is based on the transport approximation. The numerical procedure includes ray-tracing calculations in the range of water semitransparency with a source function determined using the large-cell radiation model. It is shown that the visible radiation of the interaction zone contains important information on the process parameters, and these parameters might be identified on the basis of the developed computational procedure for the direct problem.

Development of a Bright Polychromator for Thomson Scattering Measurements

A bright polychromator for compact, efficient YAG Thomson scattering measurement was designed on the basis of ray-tracing calculations. The optical input of the polychromator is a 2-mm-diameter optical fiber with a numerical aperture of 0.37. High refractive index glass lenses with monolayer anti-reflection coatings were used to reduce aberration effects and achieve good efficiency. A fast, low-noise detection system consisting of an avalanche photodiode and operational amplifiers was designed and tested using YAG laser pulses; the measured full width at half maximum (FWHM) of the laser pulse was 10 ns. The measured noise was dominated by the thermal noise of the input resistance R (= 470 Ω) when the signal was low, and the shot noise became dominant when the number of detected photons was greater than about 500.

Enhanced Light Extraction of GaN-Based Light Emitting Diodes Fabricated with Deeply Etched Mesa Holes

We report on the enhanced light extraction of GaN-based light emitting diodes (LEDs) fabricated with deeply etched mesa holes. To maximize the extraction of trapped light, the geometry of mesa holes, which act as lateral exits in guided mode, could be optimized based on Snell's law. The LED fabricated with deeply etched mesa holes showed 27% enhancement in output power when compared to a reference LED. This result agreed with optical ray-tracing calculations.