Sinusoidal Corrugation Research Articles

Effects of total internal reflection on the reflectivities of dielectric gratings

We point out that the phenomenon of total internal reflection appearing on interaction of an electromagnetic wave, incident from a dielectric at the corrugated interface separating this medium from vacuum, can give rise to very large reflectivities (close to 100%), even at angles of incidence with the mean plane of the interface that are well below the critical angle. Computer simulations for sinusoidal corrugations show >90% efficiency in the zeroth reflected order for an appropriate choice of the grating period and amplitude and of the wavelength of the incident wave at normal incidence. Blaze effects, analogous to those taking place in metallic gratings, also appear. An analysis of this phenomenon in terms of resonances created under this interaction is presented.

Bragg reflectors

A Bragg reflector composed of periodic cylindrically symmetric corrugations can provide a reflection of nearly unity through the principles of constructive interference, allowing the formation of a frequency selective resonator. Mode conversion will occur, but can be reduced by tapering the amplitude of the corrugations. Reflection measurements are compared with theoretical predictions for untapered sinusoidal and rectangular corrugation as well as a reflector tapered according to the Hamming-window prescription. Measurements of Bragg resonators are also presented. >

Linear theory of electromagnetic wave generation in a plasma-loaded corrugated-wall resonator

A linear theory of the excitation of electromagnetic waves in a plasma-filled corrugated-wall waveguide with an arbitrarily large sinusoidal corrugation has been derived and analyzed numerically. The theory predicts that, when driven by an electron beam, the presence of a plasma in the slow wave structure will cause an increase in the oscillation frequency, and that the temporal growth rates of a high-frequency mode approach those of the fundamental mode for high plasma densities. The latter result may account for the high-frequency modes observed in the authors' plasma-filled backward-wave oscillator. >

On mountain wave drag over complex terrain

Mountain wave drag is calculated for rotating, stratified, nonhydrostatic Boussinesq flow over a mountain ridge using linear theory for a variety of mountain profiles representing complex/irregular terrain. The inclusion of a sinusoidal corrugation to the familiar witch-of-Agnesi profile creates a “stegosaurus” profile. The associated drag is greatly enhanced for mesoscale mountains when the corrugation wave-number matches that for the dominant inertia-gravity wave contribution to the cross-mountain surface pressure gradient. Similarly, increasing the jaggedness (by decreasing the exponentb) increases the drag for mesoscale mountains whose topographic spectral intensity,M(k), has the form of a power law:M(k)=mk−b wherek is the zonal wavenumber.

Study of Cutoff Frequencies of Open or Closed Periodic Waveguides by Conformal Mapping

Using the studies realized by Meinke [1], Tisher and Yee [2] and Laura [3] to determine by conformal mapping the cutoff frequencies for TM or TE waves in waveguides of very general cross-section, we show that it is possible to generalize it to periodic waveguides with EH waves [4]. For rectangular overdimensioned waveguides with sinusoidal or rectangular corrugations, the comparison of the theoretical and experimental results is satisfactory when corrugations are relatively large compared with wavelength.

Radiation characteristics of elastodynamic line sources buried in layered media with periodic interfaces. I.SH- wave analysis

AbstractUsing the T matrix method, or the extended boundary condition, the solution for a class of problems involving an SH line source in an elastic wave guide is determined. The boundaries of the wave guide may be periodically corrugated and the wave guide may be embedded between elastic media. Numerical results are given for a seismically interesting case of wave propagation in a one-layer crustal model over a mantle half-space with a corrugated free surface representing the Basin and Range topography in the Western United States. Analysis of the scattered fields at the surface, and of the fields radiated into the half-space, shows complicated field behavior, even with sinusoidal free surface corrugation. These results are directly applicable to regional wave propagation and scattering.

A rigorous analysis of a thin‐film dielectric waveguide with a sinusoidal surface corrugation

The problem of wave guidance in thin‐film dielectric waveguides is formulated using the modematching method in the sense of least squares. The result is applied to analysis of the first‐order Bragg interactions in a three‐layered dielectric waveguide having a sinusoidal surface corrugation. The precise numerical results of the dispersion relation near the first‐order stopband are presented for both of the lowest TE and TM modes and compared with those obtained by a conventional perturbation approximation.

Piezoelectric saw device with a corrugated surface

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Characteristics of a high Q filter composed of a magnetic thin-film layered structure with periodic corrugation

The X-band microwave filter characteristics of magnetostatic surface waves (MSSW) in a magnetic layered structure with sinusoidal corrugation on top layer are described. Bragg reflection type filters having a high Q value are numerically evaluated by solving the dispersion relation derived from a singular perturbation method using multiple space scales (MSS). We can conclude that the high Q filter, Q=10000 on our model can be easily obtained by adjusting the saturation magnetization of a noncorrugated layer and the length of corrugation period. The results of our model can smoothly apply for another model, one, two or metal backed layered structures.

A rigorous analysis of a magnetic thin-film layered structure with a sinusoidal surface corrugation

The microwave filter characteristics of a magnetostatic surface wave in a magnetic layered structure with sinusoidal corrugation on one layer and noncorrugated on the other are described. A rejection filter properties having a high Q value are numerically evaluated by solving the dispersion relation derived from Floquet theory. Also, high Q characteristics obtained in our model are satisfactorily confirmed in comparison with results which were analyzed based on perturbation theory with a multiple space scale method. It is found that the high Q property of the filter in our model can be easily obtained by adjusting the saturation magnetization of the noncorrugated layer.

Microwave saw monochromator

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Shear buckling of corrugated composite panels

Corrugated composite panels are used in aerospace vehicles primarily because of their ability to withstand higher loads before buckling compared to plain sheets. Shear buckling is one of the important modes of failure. In this paper are presented details of prediction of the shear buckling loads of composite panels having sinusoidal or hat type corrugation. The given panel is idealised as an homogeneous orthotropic plate whose equivalent properties are determined based on the given parameters of the panel. In the analysis Kirchhoff-Love assumptions are used. Two opposite edges of the panel in one direction are assumed to be simply supported and the panel is assumed to be very long in the other direction. Critical buckling loads are obtained using conventional orthotropic plate theory. A large class of 0°/90°/45°-45° lamination schemes leading to quadridirectional, tridirectional and bidirectional T300/N5208 corrugated panels is examined and ranked based on buckling loads. Results indicate that by proper choice of lamination scheme, very significant increases in buckling load compared to the quasi-isotropic case can be obtained. Having the corrugation plane normal to the shorter side is significantly better than having the corrugation plane normal to the longer side. Optimum layup schemes are found for 8, 6, 4 and 2 ply cases.

Stopbands in a corrugated parallel plate waveguide

The stopband structure of a two-dimensional periodically corrugated waveguide is investigated by means of the null-field method. In the numerical examples, the walls are assumed to be hardwalled with symmetric, antisymmetric, or one-sided sinusoidal corrugations. The interaction pattern and the stopband widths are determined for the lowest modes. The resonances are found to be of the stopband type, and it appears that geometrical symmetries of the boundaries suppress well-defined sets of resonances.

Asymmetrically corrugated plate heat exchanger plates

Design flexibility for plate heat exchangers is a measure of the ability to adjust the characteristics of individual channels (semi-)independently to suit a particular application. Conventional plate heat exchangers with approximately sinusoidal corrugations have limited design flexibility since the channels for the two heat- exchanging streams are generally geometrically identical. Corrugations that are assymetrical in profile make it possible to construct physically different configurations from a set of identical plates: channels of different cross-sectional free flow area are feasible. Such plates used in various orientations with respect to each other were found to be less efficient than plates with sinusoidal corrugations because a lower heat transfer rate is obtained per unit of pumping power. However, when the flow rates or allowable pressure drops of the two streams exchanging heat differ greatly, such plates may be advantageous.

Resolution of the scanning tunnel microscope

At a corrugated metal or semiconductor surface, incident waves are split into beams reflected by the surface and exponentially damped waves penetrating the vacuum region. A probing tip approaching this surface from the vacuum side collects these damped waves, resulting in a tunneling current flow between the surface and the tip. By relying on arguments like those used to derive resolution criteria for optical instruments, a similar formula can be found for free-electron-like metals. For a surface with a weak sinusoidal corrugation with amplitude h s /2, the amplitude Δd/2> of the observed corrugation of the equicurrent surface decreases as δ/h s = exp[ - π 2(φ2m/ 2 - 1 2 (d + r t)/a 2 , where φ= U — E F is the averaged local potential barrier (work function), U the potential, E F the Fermi energy, a the corrugation period, d the distance between the surface and tip, and r t the tip radius. The validity of this formula is confirmed by numerical computations of tunneling through a corrugated barrier.

Resolution of the scanning tunnel microscope

At a corrugated metal or semiconductor surface, incident waves are split into beams reflected by the surface and exponentially damped waves penetrating the vacuum region. A probing tip approaching this surface from the vacuum side collects these damped waves, resulting in a tunneling current flow between the surface and the tip. By relying on arguments like those used to derive resolution criteria for optical instruments, a similar formula can be found for free-electron-like metals. For a surface with a weak sinusoidal corrugation with amplitude h s 2 , the amplitude Δd 2 of the observed corrugation of the equicurrent surface decreases as Δ d h s = exp[−π 2( φ2m h 2 ) − 1 2 (d+r t a 2 ] , where φ= U− E F is the averaged lo (work function), U the potential, E F the Fermi energy, a the corrugation period, d the distance between the surface and tip. and r t the tip radius. The validity of this formula is confirmed by numerical computations of tunneling through a corrugated barrier.

Performance of small primary feeds with trapezoidal and sinusoidal corrugations

Small primary feeds with a 90° trapezoidally corrugated flange are studied. It is found that their performance is satisfactory within a wide frequency band and can be optimised readily. The computed results are also verified experimentally.

Growth of spontaneous periodic surface structures on solids during laser illumination

Spontaneous periodic surface structures, or ripples, are frequently observed after illumination of metals, semiconductors, and dielectrics by intense laser pulses. We develop a theory which predicts the observed spacing, polarization, and growth properties of these ripples. In this model, one or several Fourier components of a random surface disturbance scatter light from the incident beam very nearly along the surface. The interference of this diffracted optical wave with the incident beam then gives rise to optical interference fringes which can reinforce the initial disturbance. Sinusoidal corrugations on either metallic or molten surfaces seem to provide strong positive feedback for ripple growth, whereas sinusoidal gratings in temperature, electron-hole density, or dielectric constant seem much less well correlated with observations.

Buckling of Corrugated Open Cylindrical Shells

The purpose of this study is to determine the critical buckling stress of open cylindrical shells with sinusoidal corrugations with free longitudinal edges subjected to uniform compression in the direction of the corrugations. Practical considerations lead to the decision of limiting the length (L) to radius (R) ratio to 1 to 10, radius (r) to thickness (t) ratio of 2,500 to 15,000, and thickness (t) to amplitude of corrugation (f) ratio of 0.04 to 0.36. The last ratio has a dominant effect on the buckling stress in the range of L²/Rt < 10\u5. The buckling stress is found to be less sensitive to the magnitude of the half subtended angle (30° to 90°) and insensitive to other shell parameters such as curved to chord length ratio, the reduction factor of shear rigidity and the Poisson’s ratio. The results are given in figures in log-log plotting with buckling coefficient as ordinate and geometry property parameter as abscissa. This may be of use to the designers.

Horizontal shear acoustic waves on layered surfaces with sinusoidal corrugations

The propagation characteristics of shear horizontal acoustic waves on sinusoidally corrugated layered surfaces of elastically isotropic materials are investigated. The mathematical methods developed make no approximation with regard to the thickness of the substrate or the surface layer, nor to the depth of the corrugation. The general expression derived here is amendable to analyses of propagation characteristics for any values of these parameters. The general theory is applied to obtain an approximate dispersion relationship for the lowest-frequency mode, i.e., the surface wave and the width of the first frequency stopband. The main qualitative characteristics of the high-frequency bands are also briefly discussed.