Meridional Rays Research Articles

Boundary enhanced helical ray coupling to high‐frequency modes of solid aluminum cylinders.

Surface guided leaky Rayleigh waves have been shown to provide a significant contribution to the backscattering by a solid metallic cylinder [K. Gipson and P. L. Marston, J. Acoust. Soc. Am. 106, 1673 (1999)]. Free field observations of the backscattering by solid aluminum cylinders confirm that both meridional and helical rays contribute to the backscattering for different angles of cylinder tilt [K. Baik, Ph.D. thesis, WSU (2008)]. Those studies show that a previously developed criteria, based on the length of the cylinder, limits the range of tilt angles for which helical rays can contribute [F. J. Blonigen and P. L. Marston, J. Acoust. Soc. Am. 112, 528 (2002)]. Experiments with solid aluminum cylinders placed near a flat reflecting boundary suggest that the presence of a boundary can increase the number of helical ray paths that contribute to the backscattering; this increase can lead to increased backscattering amplitudes and an increased range of angles for which coupling to helical rays can occur. To investigate this effect, solid aluminum cylinders were suspended below the free surface of a water tank. Targets were illuminated from below at grazing incidence, and the backscattering was measured as a function of target rotation. [Work supported by ONR.]

等光程非球面子午截线的参数方程

等光程非球面子午截线的参数方程

Parameters optimization and phase analysis of decentered grating stretchers

A decentered grating stretcher for chirped pulse amplification systems is analyzed with oblique meridional ray tracing. Several formulae and conclusions are developed to design and optimize the stretcher. On basis of an analytical phase expression with an explicit significance, the expressions of the second-, third- and approximate fourth-order phases at the central wavelength are presented with only independent variables. These simplify the parameter design for this kind of stretcher and the phase compensation design of the whole amplifier system, which has been demonstrated with a practical example.

Solar light transmission of polymer optical fibers

Light transfer (10 m) has been shown in recent experiments that used large-core optical fibers. Theoretical models are not extensive, however, and a further correlation between the theory and experiments has not been given. In this paper, straight and bent fiber subsystem models are introduced with skew and meridional rays to predict the light transmission of POFs (plastic optical fibers). Such fibers have been realized, for example, in HSL (hybrid solar lighting) systems. The purpose of this paper is to combine the straight and bent fiber subsystems to estimate the light transmission of HSL systems. It is shown that meridional rays, for which the optical-loss parameters were estimated, better represent the experimental results compared to skew rays ( ± 5.3 % vs ± 24.7 % of %-difference). Model predictions were compared with the results of a commercial software. Sensitivity analysis on the subsystems indicated the most-to-least significant parameters in light transmission.

Interpreting free‐field scattering by metallic truncated cylinders and spherical shells.

When investigating the complications to the scattering caused by proximity of a target to a boundary, a detailed ray‐based interpretation of free‐field scattering is often helpful. For tilted metallic cylinders having flat ends, when ka exceeds about 10, strong contributions to the backscattering have been identified with the radiation of sound by guided elastic waves associated with meridional rays, helical rays, and face‐crossing rays [K. Gipson and P. L. Marston, J. Acoust. Soc. Am. 107, 112–117 (2000)]. These features also affect the frequency response as a function of tilt and bistatic synthetic aperture sonar (SAS) and acoustic holographic images [K. Baik, Ph.D. thesis, WSU, 2008]. When considering the response of shells to transient insonification, it can also be helpful to construct the time‐frequency response and to interpret the response using ray‐based methods [D. H. Hughes, Ph.D. thesis, WSU, 1992; S. F. Morse and P. L. Marston, J. Acoust. Soc. Am. 111, 1289–1294 (2002)]. Correct interpretation of the time‐frequency response requires detailed consideration of the dispersion and attenuation of elastic waves guided by the shell and the shape of the radiated wavefronts. When considering low‐frequency scattering, the inertia of the target significantly influences the scattering. [Work supported by ONR.]

Interfacial and elastic contributions to the backscattering of a right circular cylinder: Experiments and interpretation.

Synthetic aperture sonar (SAS) images of elastic targets near an interface contain features resulting from the interaction of incident and scattered sound with the interface in addition to those associated with the free-field dynamical response of the target. To improve the understanding of these features, a right circular aluminum cylinder was suspended in a water tank through an air interface and insonified at a grazing incidence. Monostatic SAS images were obtained by scanning the source (and receiver) along a horizontal line. Backscattering measurements were also made as the distance from the target to the interface was varied. Some of the features could be explained using a previously developed ray-based theory [K. Gipson and P. L. Marston, J. Acoust. Soc. Am. 106, 1673–1680 (1999);, 107, 112–117 (2000)]. Among these features were responses due to guided generalized Rayleigh waves such as meridional rays and helical rays. Also, ray path calculations for edge diffraction contributions (as a function of target-interface distance) were used to identify certain echoes in the SAS images. [Research supported by ONR.]

Effects of gold film thickness on spectrum profile and sensitivity of a multimode-optical-fiber SPR sensor

Abstract For a multimode-optical-fiber surface plasmon resonance (SPR) sensor with a gold film supporting surface plasmon waves (SPWs), we have investigated the effects of gold thickness on sensor performance experimentally to find the optimal thickness when a white-light source is used. It is found that the sensor with a thickness of around 65 nm enables most precise measurement of a resonance wavelength and gives relatively high sensitivity, which is 1557 nm/RIU in the refractive index range of 1.333–1.3469. Also, we have confirmed that a simulation model based on meridional rays cannot explain the minimum reflectance of SPR spectra for values below 0.5.

Influence of skew rays on the sensitivity and signal-to-noise ratio of a fiber-optic surface-plasmon-resonance sensor: a theoretical study

We have theoretically analyzed the influence of skew rays on the performance of a fiber-optic sensor based on surface plasmon resonance. The performance of the sensor has been evaluated in terms of its sensitivity and signal-to-noise ratio (SNR). The theoretical model for skewness dependence includes the material dispersion in fiber cores and metal layers, simultaneous excitation of skew rays, and meridional rays in the fiber core along with all guided rays launching from a collimated light source. The effect of skew rays on the SNR and the sensitivity of the sensor with two different metals has been compared. The same comparison is carried out for the different values of design parameters such as numerical aperture, fiber core diameter, and the length of the surface-plasmon-resonance (SPR) active sensing region. This detailed analysis for the effect of skewness on the SNR and the sensitivity of the sensor leads us to achieve the best possible performance from a fiber-optic SPR sensor against the skewness in the optical fiber.

Optics of oblique meridional and nonmeridional rays of a conicoid

Based on the exact expression for the angular eikonal of an axisymmetric conicoid (a surface formed by revolution of a second-order curve, or conic) the expressions for the Gaussian optics of oblique meridional rays are obtained, which differ from the well-known Gullstrand-Young invariants for a sphere by a set of independent arguments and contain explicitly the parameters of an optical system. The collinear properties of an optical surface with oblique meridional beams are studied. The theory of astigmatism is extended to the case of oblique nonmeridional rays, which makes it possible to construct and analyze in the first approximation the focal surfaces of an actual wide beam of rays. The theory is tested using the example of optimization of an aplanatic lens for the case of an off-axis point of an object. Based on the exact expression for the angular eikonal, definitions of integral aberrations are given. It is proposed to use the method developed in optimization of optical systems.

The influence of skew rays on angular losses in air-clad fibres

Detailed experimental transmission properties of high numerical aperture air-clad undoped fibres are presented. Measurements of the angular transmissivity indicate a 15% lower numerical aperture (NA = 0.75) compared to theoretical predictions for the bridge thickness and wavelength ratio of δ/ λ = 0.226. The discrepancy is attributed to skew rays that are deliberately launched and which are subject to larger loss rates through diffractive tunnelling in frustrated total internal reflection than meridional rays. Measurements of the angular propagation losses show that light launched at angles less than the critical angle for total internal reflection experiences low initial losses as well as low propagation losses. Light launched at steeper angles experiences a significant initial loss attributed to loss of skew rays within 1.5 m of propagation as well as larger general propagation losses.

An Approximate Theoretical Model of Surface Plasmon Resonance Optical Waveguide and Fibre-optic Sensors

Optical surface plasmon resonance (SPR) excitation can be theoretically depicted and discussed using Fresnel’s equations. However, Fresnel’s equations cannot explicitly give expressions to reflect the characteristics of SPR systems, especially in SPR optical waveguide and fibre-optic sensors. In this paper a mathematical model based on the approximation proposed by Kretschmann in bulk optics is presented to describe the characteristics of SPR optical waveguide and fibre-optic sensors. The results show that the model keeps high accuracy when used in the area close to the minimum reflection, at which the resonance condition is achieved. This model can be used to analytically estimate the performance of SPR optical waveguide sensors, and SPR fibre-optic sensors in meridional rays approximation.

A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors

In fibre-optic evanescent wave absorption in spectroscopy and sensors, both meridional and leaky skew rays contribute to absorption of the evanescent wave. This paper presents a whole view of the absorption of evanescent wave in fibre-optic evanescent wave absorption spectroscopy and sensors. Results of this study show that previous models of evanescent wave absorption based only on meridional rays overestimates the absorption of fibre-optic evanescent wave absorption spectroscopy and sensors.

Prediction of light-transmission losses in plastic optical fibers

A theoretical expression is derived, based on a geometrical optics approach, with which to predict light-transmission losses in multimode plastic optical fibers for office or home lighting. Two types of optical ray arrangement, meridional ray and skew ray, are evaluated, and five loss mechanisms are identified and considered. The meridional arrangement results in a lower overall loss of light than the skew ray arrangement. The theoretical results were compared with experimental measurements taken for a 0.5-cm-diameter polymer optical fiber. For optical rays entering the fiber at incident angles of less than 20 degrees, the theoretical results are in good agreement with the empirical results.

Ordinary and extraordinary rays in gradient-index lenses.

We assume that the polarization modes of a gradient-index medium with circular cylindrical symmetry are radial and tangential. Making use of a ray-optics method developed for anisotropic crystals,we relate the polarization modes with the permittivity and the dielectric tensor constant of the medium. The polarized imaging response of gradient-index lenses is used to associate ordinary rays with the tangential mode and extraordinary rays with the radial mode. The polarization-mode description is in agreement with the experimental results here. These experimental results allow extending the mode description developed for meridional rays to include skew rays.

Computational studies of light acceptance and propagation in straight and curved multimodal active fibres

A Monte Carlo simulation has been performed to track light rays in cylindrical multimode fibres by ray optics. The trapping efficiencies for skew and meridional rays in active fibres and distributions of characteristic quantities for all trapped light rays have been calculated. The simulation provides new results for curved fibres, where the analytical expressions are too complex to be solved. The light losses due to sharp bending of fibres are presented as a function of the ratio of curvature to fibre radius and bending angle. It is shown that a radius of curvature to fibre radius ratio of greater than 65 results in a light loss of less than 10% with the loss occurring in a transition region at bending angles of pi/8 rad.

Meridional ray backscattering enhancements for empty truncated tilted cylindrical shells: measurements, ray model, and effects of a mode threshold.

Narrow-band backscattering experiments are used to characterize a meridional ray enhancement on a tilted, finite empty cylindrical shell having a blunt truncation. The meridional ray of the lowest order flexural leaky Lamb wave is examined, which has previously been shown to lead to large backscattering enhancements for excitation frequencies near and above the shell's coincidence frequency. The measurements are used to validate a convolution formulation ray theory describing the far-field backscattered amplitudes. Comparisons are also made with an approximate partial wave series solution for the finite cylindrical shell. The amplitude of the meridional ray enhancement is dependent on the nature of the reflection of the leaky wave from the shell truncation. While the peak measured amplitude agrees with predictions at low frequencies, experiments indicate the enhancement is degraded at high frequencies and exhibits an abrupt drop near the frequency of the mode threshold (cutoff) for the next-highest flexural mode. The nature of the leaky wave end reflection is examined using an approximate calculation of the energy reflection coefficient for leaky waves on a semi-infinite free plate. Results suggest the observed degradation is the result of mode conversion effects.

Leaky helical flexural wave backscattering contributions from tilted cylindrical shells in water: Observations and modeling

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)], flexural helical waves on cylindrical shells can significantly enhance the backscattering. These contributions are compared and modeled here for an empty cylinder. Experiments using tone bursts were performed on a tilted stainless steel shell to investigate the contributions caused by flexural leaky Lamb waves above the coincidence frequency of the shell. In some of the measurements the tone bursts were of sufficient duration to superpose helical wave contributions of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a quasi-steady-state backscattering amplitude for the cylinder. These measurements are compared with an approximate numerical partial-wave series solution and a ray theory as a function of the tilt angle. The data for ka = 20 follow the basic shape of the ray theory and the relevant features of the partial-wave model. They illustrate the importance of the interference of successive helical wave contributions. Measurements (also as a function of the tilt angle) using tone bursts that were sufficiently short to separate the earliest helical wave contribution from later contributions also support the ray theory.

Backscattering of transients by tilted truncated cylindrical shells: time-frequency identification of ray contributions from measurements.

Impulse backscattering measurements by a thick-walled finite cylindrical shell are examined in the time-frequency domain to identify and characterize individual ray contributions from generalized Lamb waves excited on the shell. Previous experiments and analysis in the frequency-aspect angle domain [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)] indicate that large backscattering enhancements occur in the midfrequency region for the shell tilted at large angles. Presently this experimental data is examined in the time-frequency domain for selected angles of incidence. Individual ray contributions are evident and their evolution over aspect angle is discussed. The most prominent contribution is due to the meridional ray of the a0 leaky Lamb wave. This feature distinctly highlights the truncation of the shell and is found over a range of aspect angles spanning 200 degrees for the frequencies examined. Also observed are periodic features corresponding to end-reflected helical waves of the a0-. These scattering features are significantly different from those reported for thin-walled finite cylinders at low frequencies. The present results may be useful for target identification and localization and as a comparison tool for high-frequency computational scattering models.

Scattering by tilted cylindrical shells in water above the coincidence frequency

Experimental, theoretical, and computational results indicate that flexural waves on bluntly truncated tilted cylindrical steel shells are a major contributor to the backscattering of sound at high frequencies over a wide range of tilt angles. Important contributions are associated with meridional rays and with helical rays [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998); S. F. Morse and P. L. Marston, J. Acoust. Soc. Am. 106, 2595–2600 (1999); S. F. Morse and P. L. Marston, IEEE J. Ocean. Eng. 26, 152–155 (2001)]. Successful development of a ray model for helical ray scattering contributions required the computation (at high frequencies) of the anisotropy of the flexural-wave velocity and radiation-damping parameters [F. J. Blonigen and P. L. Marston, J. Acoust. Soc. Am. (accepted for publication)]. In backscattering experiments with short and long tone bursts, the associated meridional and helical ray contributions are typically much larger than the scattering estimated for diffraction by a rigid tilted cylinder of the same size. The importance of the elastic response of shells was recognized in the early work of Junger [M. C. Junger, J. Acoust. Soc. Am. 24, 366–373 (1952)]. [Work supported by ONR.]

Backscattering from empty and water-filled tilted cylindrical shells due to leaky helical flexural waves: Comparison and ray theory

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998)], helical rays on empty and water-filled steel shells can significantly enhance the backscattering. These contributions are compared and modeled in the present work. Such contributions in the water-filled case are found to be weaker in amplitude, which is to be expected since additional energy is lost through radiation leaked to the inner fluid. A modified ray theory taking into account the increased radiation damping was compared with experimental results for the earliest helical wave arrival, yielding satisfactory agreement. However, the energy lost to the interior of the shell may be at least partially recovered, as internal rays can excite additional leaky waves on the shell. Contributions from rays with one internal chord inside the cylinder were superposed with those of the first helical wave, and the resulting backscattering amplitude was nearly that of the air-filled case for the first helical wave alone. This shows that we may regard the ray theory for the empty shell as an upper bound for corresponding amplitudes observed in the water-filled case. [Work supported by ONR.]