Theoretical Ray Research Articles

Analysis of wave converging phenomena inside the shocked two-dimensional cylindrical water column

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$ , $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

Optical Fiber Hydrogen Sensor Based on the EVA/Pd Coated Hollow Fiber

A novel optical fiber hydrogen sensor based on the dielectric/metal coated hollow fiber structure is proposed. The palladium (Pd) and ethylene-vinyl acetate (EVA) layers are sequentially coated on the inner surface of the hollow core of the silica capillary to fabricate the EVA/Pd coated hollow fiber sensor. Theoretical ray transmission model is carried out to analyze the influence of the thicknesses of the Pd and EVA films. The experimental transmission spectra of the proposed sensor filled with hydrogen gas of different concentrations are measured. The experimental results show that the interference peak in the spectrum has a red shift with the increase of hydrogen concentration. Then the hydrogen concentration can be obtained by measuring the wavelength of the interference peak. In the range of 0–4% hydrogen concentration, the total shift is 10.64nm and the average sensitivity is 2.66 nm/%. Compared to other optical fiber hydrogen sensors, the proposed sensor has the advantages of simple structure, easy fabrication, low cost, high sensitivity and good safety performance.

Blue-shifted deep ocean currents in the equatorial Indian Ocean

Spectra from two decades of zonal current data at $$\sim $$ 4000 m in the central and western equatorial Indian Ocean show a shift in the dominant frequencies from the west to the east. The 120–180-day period is stronger at 77 $$^\circ $$ E, the 60–120-day period at 83 $$^\circ $$ E, and the 30–90-day period at 93 $$^\circ $$ E. The weakening of lower frequencies near the eastern boundary can be explained using theoretical ray paths of Kelvin waves and reflected Rossby waves. The equatorial Kelvin wave forced by winds reflects from the eastern boundary as Rossby waves with different meridional modes. After reflection, the low (high) frequency Rossby beams travel a larger (shorter) distance before reaching the bottom, thereby creating a shadow zone, a region with low wave energy, between the ray path and the eastern boundary. The shift in frequency with longitude is not evident in the top 1000 m, where the current is dominated by the semi-annual cycle.

Mechanically-tuned optofluidic lenses for in-plane focusing of light

In-plane lenses are desired for light manipulation within on-chip platforms. Such an in-plane lens can be achieved through optofluidic lens technologies that provide tunability of optical parameters through alterations to the shape or size of the lens. However, passive optofluidic lenses are often more desirable than active optofluidic lenses. In this work, we design a passive mechanically-tuned optofluidic lens. Tunability is brought about by placing a microdroplet between two substrate plates and varying the plate separation. We carry out analyses with an experimental optical setup and theoretical ray tracing. The experimental optical setup makes use of a fluorescent dye filler fluid to assist in the visualization and measurement of the back focal length. Ultimately, the sensitivity of the back focal length to a change in plate separation is shown, with strong agreement between experimental and theoretical analyses. It is envisioned that such a mechanically-tuned optofluidic lens will be used in a myriad of in-plane optical applications.

Investigation into the wave system of a generic submarine moving along a straight path beneath the free surface

Abstract The present study aims to investigate the wave system of a generic submarine traveling along a straight path beneath the free surface by using the unsteady Reynolds-averaged Navier–Stokes equations with a Reynolds stress turbulence model implemented in commercial code STARCCM+ over submergence depths and body length Froude numbers ranging from h = 1 . 1 × D to h = 3 . 3 × D ( D : submarine diameter) and from F n = 0 . 205 to F n = 0 . 512 , respectively. The wave characteristics that are analyzed include the maximum wave height, wake angle and the centerline wave profiles at hump and hollow Froude numbers. The analysis of the centerline wave profiles at hump and hollow Froude numbers indicates that the interaction between the positive bow and the negative aft shoulder waves has a dominant effect on the submarine-generated wave system. Additionally, it is observed that an increase in Froude number or a decrease in submergence depth generally leads to an approximately consistent reduction in the wake angle. In this regard, to explain this reduction in the wake angle, an attempt is made to use an existing theoretical model, which estimates the ray angles along which the largest waves are located because of constructive interference between the positive bow and negative aft shoulder waves. Generally, a poor agreement is observed between the numerical wake angles and the theoretical ray angles. In spite of this poor agreement, the constructive interference effects between the positive bow wave and the negative aft shoulder wave is assumed to be the primary reason for the decrease in the wake angle with an increase in Froude number or a decrease in submergence depth. Moreover, the large discrepancies between the numerical wake angles and the theoretical ray angles suggest that to use the theoretical model for submarines, this model should be modified to account for the submergence depth effect on both the aft shoulder wave and the normalized distance between the origins of the main contributors to the submarine wave system.

Investigation of the Central Adriatic lithosphere structure with the AlpArray-CASE seismic experiment

The tectonics of the Adriatic microplate is not well constrained and remains controversial, especially at its contact with the Dinarides, where it acts as the lower plate. While the northern part of the Adriatic microplate will be accurately imaged within the AlpArray project, its central and southern parts deserve detailed studies to obtain a complete picture of its structure and evolution. We set-up the Central Adriatic Seismic Experiment (CASE) as a AlpArray Complementary Experiment with a temporary seismic network to provide high- quality seismological data as a foundation for research with state-of-the-art methods and high-precision seismic images of the controversial area. The international AlpArray- CASE project involves four institutions: the Department of Earth Sciences and the Swiss Seismological Service of ETH Zurich (CH), the Department of Geophysics of the Faculty of Science at the University of Zagreb (HR), the Republic Hydrometeorological Service of the Republic of Srpska (BIH) and Istituto Nazionale di Geofisica e Vulcanologia (I). The established temporary seismic network will be operational for at least 18 months. It combines existing permanent and temporary seismic stations operated by the involved institutions together with newly deployed temporary seismic stations, installed in November and December 2016, managed by ETH Zurich and INGV: five in Croatia, four in Bosnia and Herzegovina and one in Italy. We present our scientific aims and network geometry as well as newly deployed stations sites and settings. In particular, the new stations show favourable noise level (power spectral density estimates). The new network improves considerably the theoretical ray coverage for ambient noise tomography and the magnitude threshold shown in the Bayesian magnitude of completeness threshold map.

Effects of the symmetry axis orientation of a TI overburden on seismic images

In active tectonic regions, the primary formations are often tilted and subjected to the processes of folding and/or faulting. Dipping formations may be categorised as tilted transverse isotropy (TTI). While carrying out hydrocarbon exploration in areas of orogenic structures, mispositioning and defocusing effects in apparent reflections are often caused by the tilted transverse isotropy of the overburden. In this study, scaled physical modelling was carried out to demonstrate the behaviours of seismic wave propagation and imaging problems incurred by transverse isotropic (TI) overburdens that possess different orientations of the symmetry axis. To facilitate our objectives, zero-offset reflections were acquired from four stratum-fault models to image the same structures that were overlain by a TI (phenolite) slab. The symmetry axis of the TI slab was vertical, tilted or horizontal. In response to the symmetry axis orientations, spatial shifts and asymmetrical diffraction patterns in apparent reflections were observed in the acquired profiles. Given the different orientations of the symmetry axis, numerical manipulations showed that the imaged events could be well described by theoretical ray paths computed by the trial-and-error ray method and Fermat’s principle (TERF) method. In addition, outputs of image restoration show that the imaging problems, i.e. spatial shift in the apparent reflections, can be properly handled by the ray-based anisotropic 2D Kirchhoff time migration (RAKTM) method.

Selective excitation of higher-order modes in etched gelatin-coated few-mode fiber and demonstration of high relative humidity measurement.

We report here our experimental studies on efficient excitation of higher-order modes in a few-mode fiber realized through selective chemical etching of single-mode fiber, depositing a dynamic refractive index profile coating (gelatin) and designing a well-performing high relative humidity (RH) (73%-99% RH) sensor with sensitivity as high as ∼1.2 dBm/% RH and fast response (∼125 ms). The design relies on fixing quasi-adiabatic transition of the single-mode-few-mode-single-mode configuration to launch light at angles corresponding to desired higher-order modes, pushing more power into the coating. Our systematic study using the devised hybrid theoretical ray- and wave-optic model uniquely interprets the variety of experimental results.

Theoretical modelling and experimental verification of gradient thickness function for thin film deposition of linear variable filter

This study proposes a theoretical model for a gradient thickness function for thin film deposition of a linear variable filter (LVF), which is used for order sorting for a diffraction grating. To achieve linear variable filtering, the thin film must be fabricated with a gradient of increasing thickness along the direction of wavelength dispersion. The thickness gradient is created using a local mask on top of the substrate during thin film deposition inside the evaporation chamber. A theoretical model and ray tracing simulation are developed to obtain the thin film thickness distribution and the parameters for the fabrication of LVFs. Within the 25%–75% thickness range, the profile distribution exhibits a high degree of linearity (coefficient of determinations are greater than 0.9939). This study shows that the proposed theoretical model and ray tracing predict a thin film profile for an LVF with high precision (root–mean–square deviations are less than 4.52%).

Escaping losses of diffuse light emitted by luminescent dyes doped in micro/nanostructured solar cell systems

One approach to improve the efficiency of electricity generation of solar cells is to use a luminescent/fluorescent dye that absorbs a part of the spectrum of incident light and then simultaneously emits down-shifted light that matches the spectral response of the solar cells. In this study, the authors numerically simulated the escaping energy losses of isotropic diffuse down-shifted light emitted by luminescent dyes doped in micro/nanostructured solar cell systems. The simulation was accomplished by using the two-dimensional total-field finite-difference time-domain (FDTD) method, which simulates not only reflection and refraction but also diffraction. Two simulation models—one based on a V-grooved luminescent down-shifting (LDS) layer and the other based on a planar luminescent solar concentrator (LSC)—were used, and the size effects of the LDS layer and LSC, effect of doping position on the escaping energy loss, and angle dependency of the escaping energy loss were clarified. For the V-grooved LDS layer, the escaping loss was found to be less than 10% in the wavelength range of 400–1170 nm when the height and width of the V-groove were 360 and 424 nm, respectively. This value of the escaping loss is less than half of that calculated from ray optics, which simulates only reflection and refraction. A planar LSC with a thickness of 300 nm and a length in the submicron range also exhibited smaller escaping loss than a conventional-sized one. Furthermore, the authors confirmed that the reflectance of the micro/nanostructured solar cell systems is lower than the theoretical ray optical reflectance of an air–PMMA–Flat Si layer. This indicates that doping luminescent dyes in such micro/nanostructured solar cell systems potentially improves the light trapping efficiency of down-shifted diffuse light emitted by the luminescent dyes.

Strong cosmic ray cutoff rigidity decreases during great magnetospheric disturbances

The theoretical and experimental cosmic ray cutoff rigidities during great magnetospheric disturbances in November 2004 and May 2005 have been determined. The theoretical geomagnetic cutoffs were calculated by the trajectory tracing method in the magnetic field of Tsyganenko’s magnetospheric model T03, which describes great magnetospheric disturbances (at Dst < 65 nT). The experimental geomagnetic cutoffs were determined by the spectrographic global survey method on the basis of the world network data. The cutoff rigidity decreases at Dst minima can reach 70–80% for theoretical cutoffs and ∼40% for experimental cutoffs at mid latitudes.

Observations of Tidal Internal Wave Beams at Kauai Channel, Hawaii

Abstract To observe the across-ridge structure of internal tides, density and velocity were measured using SeaSoar and a Doppler sonar over the upper 400–600 m of the ocean extending 152 km on each side of the Hawaiian Ridge at Kauai Channel. Eighteen sections were completed in about 18 days with sampling intentionally detuned from the lunar semidiurnal (M2) tide so that averaging over all sections was equivalent to phase averaging the M2 tide. Velocity and displacement variance and several covariances involving velocity and displacement showed one M2 internal wave beam on each side of the ridge and reflection of the beams off of the surface. Theoretical ray slopes aligned with the observed beams and originated from the sides of the ridge. Energy flux was in agreement with internal wave generation at the ridge. Inferred turbulent dissipation was elevated relative to open ocean values near tidal beams. Energy flux was larger than total dissipation almost everywhere across the ridge. Internal wave energy flux and dissipation at Kauai Channel were 1.5–2.5 times greater than at the average location along the Hawaiian Ridge. The upper 400–600 m was about 1/3 to 1/2 as energetic as the full-depth ocean. Tidal beams interact with each other over the entire length of the beams causing gradients along beams in almost all covariances, momentum flux divergences, and mean flows. At Kauai Channel, momentum flux divergences corresponded to mean flows of 1–4 cm s−1.

Do Peripheral Refraction and Aberration Profiles Vary with the Type of Myopia? - An Illustration Using a Ray-Tracing Approach

Purpose Myopia is considered to be the most common refractive error occurring in children and young adults, around the world. Motivated to elucidate how the process of emmetropization is disrupted, potentially causing myopia and its progression, researchers have shown great interest in peripheral refraction. This study assessed the effect of the myopia type, either refractive or axial, on peripheral refraction and aberration profiles. Methods Using customized schematic eye models for myopia in a ray tracing algorithm, peripheral aberrations, including the refractive error, were calculated as a function of myopia type. Results In all the selected models, hyperopic shifts in the mean spherical equivalent (MSE) component were found whose magnitude seemed to be largely dependent on the field angle. The MSE profiles showed larger hyperopic shifts for the axial type of myopic models than the refractive ones and were evident in -4 and -6 D prescriptions. Additionally, greater levels of astigmatic component (J180) were also seen in axial-length-dependent models, while refractive models showed higher levels of spherical aberration and coma. Conclusion This study has indicated that myopic eyes with primarily an axial component may have a greater risk of progression than their refractive counterparts albeit with the same degree of refractive error. This prediction emerges from the presented theoretical ray tracing model and, therefore, requires clinical confirmation.

Measurement of axial stress using mode-converted ultrasound

A new ultrasonic technique for stress measurement using mode conversion is proposed and applied to the estimation of axial stresses in high-tension bolts. The effect of axial stresses on acoustic wave velocities in axisymmetric cylindrical solids is analyzed, and a linear acousto-elastic equation is formulated. Theoretical ray analysis is performed to compute time of flight (TOF) of mode-converted waves in cylindrical solids. To evaluate the validity of the proposed method, mode-converted longitudinal and shear waves in carbon-steel bolts are generated and captured to measure the TOF of the waves. Simultaneous velocity measurement of two differently polarized acoustic waves are made with enough resolution to estimate axial stresses with values less than 10% of the yield stress of the bolt material. It is observed from experimental results that the TOF ratio of longitudinal and shear waves is linearly proportional to the axial stress in bolts within 5% error, as expected from theory.

Trapped whispering-gallery optical modes in white light-emitting diode lamps with remote phosphor

Three-dimensional ray tracing simulations show that a significant fraction of the phosphorescence emitted in high-power white light-emitting diode lamps with a remote phosphor is trapped as whispering-gallery modes propagating along the circumference of the encapsulant. The whispering-gallery modes, which are a significant optical loss mechanism and occur for multiple shapes of the encapsulation dome, are shown to be sensitively dependent on the diffusivity of the reflector cup employed in the lamp. By employing a diffuse reflector cup, up to 86% of the trapped modes is extracted out from the encapsulant. In addition, it is experimentally demonstrated that the phosphorescence efficiency is improved by up to 12.2% as the diffusivity of the reflector increases. The experimental results are consistent with theoretical ray tracing simulations.

Design of a Superparaboloidal Solid Immersion Mirror for Optomechatronic Near-Field Recording

We designed a superparaboloidal solid immersion mirror (SP-SIM) using a tilted parabolic mirror that applied total internal reflection to an optical flying head for near-field recording. As an SP-SIM does not need an objective lens or folding mirror, the height and weight of the optical flying head can be reduced. Using theoretical ray tracing, we found the optimal parameters for rotational symmetric beam intensity on a high-numerical-aperture (NA) focus. The effective NA of the SP-SIM was 1.32 for both the sagittal and meridional focuses. A 408-nm laser source and high refractive index material, NbFD13, was used for the simulation. The minimum spot sizes at full width 1/e/sup 2/ intensity were 237 and 232 nm in the sagittal and meridional directions, respectively, at normal incidence. The size of the beam spot was kept nearly uniform within a maximum 5% deviation as the field angle changed within /spl plusmn/0.15/spl deg/. The SP-SIM measured 0.83 mm/spl times/0.95 mm/spl times/0.27 mm (W/spl times/L/spl times/H) and weighed ca. 0.6 mg.

Entry dynamics and acoustics/infrasonic/seismic analysis for the Neuschwanstein meteorite fall

Abstract— We have analyzed several types of data associated with the well‐documented fall of the Neuschwanstein meteorites on April 6, 2002 (a total of three meteorites have been recovered). This includes ground‐based photographic and radiometer data as well as infrasound and seismic data from this very significant bolide event (Spurný et al. 2002, 2003). We have also used these data to model the entry of Neuschwanstein, including the expected dynamics, energetics, panchromatic luminosity, and associated fragmentation effects. In addition, we have calculated the differential efficiency of acoustical waves for Neuschwanstein and used these values to compare against the efficiency calculated using available ground‐based infrasound data. This new numerical technique has allowed the source height to be determined independent of ray tracing solutions. We have also carried out theoretical ray tracing for a moving point source (not strictly a cylindrical line emission) and for an infinite speed line source. In addition, we have determined the ray turning heights as a function of the source height for both initially upward and downward propagating rays, independent of the explicit ray tracing (detailed propagation path) programs. These results all agree on the origins of the acoustic emission and explicit source heights for Neuschwanstein for the strongest infrasonic signals. Calculated source energies using more than four different independent approaches agree that Neuschwanstein was certainly &lt;500 kg in initial mass, given the initial velocity of 20.95 km/s, resulting in an initial source energy ≤0.0157‐0.0276 kt TNT equivalent (4.185 times 1012 J). Local source energies at the calculated infrasonic/seismic source altitudes are up to two orders of magnitude smaller than this initial source energy.

Numerical simulation of wave propagation in media with discrete distributions of fractures: effects of fracture sizes and spatial distributions

SUMMARY We model seismic wave propagation in media with discrete distributions of fractures using the pseudospectral method. The implementation of fractures with a vanishing width in the 2-D finite-difference grids is done using an effective medium theory (that is, the Coates and Schoenberg method). Fractures are treated as highly compliant interfaces inside a solid rock mass. For the physical representation of the fractures the concept of linear slip deformation or the displacement discontinuity method is used. According to this model, the effective compliance of a rock mass with one or several fracture sets can be found as the sum of the compliances of the host (background) rock and those of all the fractures. To first order, the background rock and fracture parameters can be related to the effective anisotropic coefficients, which govern the influence of anisotropy on various seismic signatures. We test the validity of the method and examine the accuracy of the synthetic seismograms by a comparison with theoretical ray traveltimes. We present three numerical examples to show the effects of different fracture distributions. The first example shows that different spatial distributions of the same fractures produce different wavefield characteristics. The second example examines the effects of variation of fracture scale length (size) compared with the wavelength. The final example examines the case of fractures with a power-law (fractal) distribution of sizes and shows how that affects the wavefield propagation in fractured rock. We conclude that characterization of fractured rock based on the concept of seismic anisotropy using effective medium theories must be used with caution. Scale length and the spatial distributions of fractures, which are not properly treated in such theories, have a strong influence on the characteristics of wave propagation.

Magnetospheric cusp observations using the image satellite radio plasma imager

On March 25, 2000, the Imager for Magnetopause-to-Auroral Global Exploration (IMAGE) satellite mission was launched with the Radio Plasma Imager (RPI) radio sounder instrument onboard. Once deployed, the RPI began remote detection of regions of differing plasma densities via the reflection of transmitted radio waves. One of these regions is the magnetospheric polar cusp, which contains solar wind particles injected onto magnetospheric field lines by the process of dayside reconnection. Using data from the first month of RPI active sounding operation, a candidate cusp plasma echo return was analyzed to confirm that these signatures are in fact due to cusp plasmas. Associated in situ measurements also taken by the RPI instrument, as well as theoretical ray traces within an idealized model magnetosphere, strongly indicate that the RPI can and does remotely observe particle densities within the cusp region.

Acoustic propagation and atmosphere characteristics derived from infrasonic waves generated by the Concorde.

Infrasonic signals generated by daily supersonic Concorde flights between North America and Europe have been consistently recorded by an array of microbarographs in France. These signals are used to investigate the effects of atmospheric variability on long-range sound propagation. Statistical analysis of wave parameters shows seasonal and daily variations associated with changes in the wind structure of the atmosphere. The measurements are compared to the predictions obtained by tracing rays through realistic atmospheric models. Theoretical ray paths allow a consistent interpretation of the observed wave parameters. Variations in the reflection level, travel time, azimuth deviation and propagation range are explained by the source and propagation models. The angular deviation of a ray's azimuth direction, due to the seasonal and diurnal fluctuations of the transverse wind component, is found to be approximately 5 degrees from the initial launch direction. One application of the seasonal and diurnal variations of the observed phase parameters is the use of ground measurements to estimate fluctuations in the wind velocity at the reflection heights. The simulations point out that care must be taken when ascribing a phase velocity to a turning height. Ray path simulations which allow the correct computation of reflection heights are essential for accurate phase identifications.