Wave propagation and resonance in four-layer systems for organic light-emitting diodes

Wave propagation and surface plasmon resonance are examined in four-layer optical systems in slab geometry for an OLED (organic light-emitting diode) with an embedded thin metal film. For this purpose, both leaky and bound modes are examined in all ranges of the propagation constant, which determines how surface and volume waves are allowed. Intensive parametric studies are performed on the thicknesses of the two embedded layers, along with the cathode condition and the metal's material dispersion. As a way of interpreting the results, the direction of the depthwise wave propagation is examined in connection with possible excitations arising from light sources within the organic electroluminescence layer. Consequently, several new features are observed on the multiple-wave branches, including exchange of the phase speeds and depthwise standing waves for dissipationless systems. By the insertion of a thin metal film, the light extraction is found to be enhanced through leaky waves from the source layer out toward the viewer's side.     

Periodic Green's functions analysis of SAW and leaky SAWpropagation in a periodic system of electrodes on a piezoelectriccrystal

A method of periodic Green's functions with a propagation factor exp(iβx), unknown in advance, is used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface. To describe the charge distribution on the electrodes both a step approximation and Chebyshev polynomials are used, the last being more adequate in most cases. Numerically determined values of the Green's function are used and interpolated either linearly or using a modified variant of Ingebrigtsen's formula. Such basic parameters as stopband width, stopband center frequency, wave velocity and attenuation in the stopband are found. These parameters can be used in the coupling-of-modes (COM) analysis and design of SAW devices. The analysis includes bulk wave radiation and scattering. The dependence of the corresponding attenuation coefficient on frequency is determined. Results obtained allow the determination directly and properly of the COM parameters and the design of SAW devices having large number of electrodes most precisely and rapidly. Numerical results for Rayleigh waves on YZ-LiNbO₃ and leaky waves on 36°YX-LiTaO₃ substrates are presented     

Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.     

Dispersion relation of guided-mode resonances in multimode grating waveguide structures

It is well known that the location of guided-mode resonance (GMR) in grating waveguide structures closely tracks the leaky mode dispersion curves. In this paper, taking Bragg reflection due to periodicity and interaction between different modes into account, we first present a schematic diagram of the dispersion relations of leaky modes in multimode grating waveguide structures, both for s-polarized (TE mode) and p-polarized (TM mode) incident waves. Due to the perturbation of the grating layer, the interaction between different resonance modes (transverse standing waves) is inevitable. This transverse interference will result in the non-Bragg nature resonance band gaps in the dispersion curves. Exploiting the characteristics of leaky mode dispersions over the full range of the first Brillouin zone, we hoped we could gain some insight into the relationship among the mode interactions, band gaps, and their benefits to optical elements utilizing the GMR effect in grating waveguide structures. Finally, a specific structure is analyzed.     

Gap acousto-electric waves in structures of arbitrary anisotropy

A theoretical study has been performed of the acousto-electric waves guided by an air gap between two identical piezoelectric crystals of arbitrary anisotropy. The permissible number of such gap waves traveling slower than all bulk modes in the structure has been established. The interdependence between the existence of these "subsonic" gap waves and surface acoustic waves on the mechanically free surface of crystals constituting the structure has been investigated. The occurrence of leaky gap waves also has been discussed. In addition, the specific features of the resonance reflection in gap structures caused by the excitation of leaky waves have been analyzed.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Experimental study of construction mechanism of V(z) curves obtained by line-focus-beam acoustic microscopy

The propagation characteristics, viz., phase velocity and attenuation, of leaky surface acoustic waves (LSAWs), excited on the water/sample boundary are obtained through analyzing the V(z) curves measured by line-focus-beam acoustic microscopy. However, different values of these characteristics are obtained, depending upon different ultrasonic devices and operating frequencies employed. The construction mechanism of V(z) curves was investigated experimentally by measuring the amplitude and phase for Teflon to provide an understanding of the device performance for velocity measurements. A V(z) curve measured for Teflon, on which no leaky waves are excited when water is the coupling medium, can be used for the characteristic device response, depending only upon the device parameters and the operating frequencies. From the investigation of the ultrasonic device and the frequency dependences of the characteristic device responses, the phase gradient was found to be directly related to values of measured LSAW velocities. From this result, apparent frequency dependences in LSAW velocity measurements are explained quantitatively for a specimen of gadolinium gallium garnet.     

Response of acoustic imaging systems using convergent leaky waves to cylindrical flaws

A theoretical study of imaging systems utilizing focused leaky surface acoustic waves (SAWs), and their response to certain kind of defects is presented. In particular, circular cylindrical inhomogeneities with axes perpendicular to the surface are considered. The scattering of the SAW from this cylinder is formulated with some approximations. The surface wave incident on the inhomogeneity is initially found as an angular spectrum of plane waves. However, to apply the boundary conditions at the cylindrical surface, the incident field has to be transformed into a superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAWs, is converted back to a plane wave spectrum. A formula is obtained for the transducer output voltage in terms of the position and the radius of the cylinder, and it is suitable for computer evaluation. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. By comparing the output voltages for cylinders of different radii, the sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are in agreement with the experimental observations.     

Propagation of longitudinal leaky surface waves under periodic metal grating structure on lithium tetraborate

The dispersion properties of longitudinal leaky surface waves propagating under the periodic Al strip grating on lithium tetraborate (Li(2)B(4)O(7); LBO) are described theoretically and experimentally for applications of the mode to high frequency SAW devices. A theoretical method developed here is based on Floquet's theorem using space harmonics as an orthogonal function set and real boundary integral equations derived from the method of weighted residuals for a period of each region, i.e., substrate, metal, and free space. The boundary integral equations are solved by using the Galerkin procedure. The periodic strip gratings with both single-electrodes and double-electrodes are investigated, considering the convergency of the numerical computation for the number of the space harmonics. As a result, the propagation loss for shorted gratings was found to be relatively low in the thickness range of the Al strip below about 1% for the single-electrodes and 2% for the double-electrodes, although it greatly increases for a thickness over 2% for the single-electrodes and 3% for the double-electrodes.     

Characteristic parameters of surface acoustic waves in a periodic metal grating on a piezoelectric substrate

The coupling problem between electrodes due to the propagation of acoustic waves in a periodic metal grating on a piezoelectric substrate is theoretically studied. A method for the determination of the mutual admittance between the grating electrodes is presented, and an analytical expression for the contribution of surface acoustic waves (SAWs) is proposed. The SAW characteristic parameters are determined with a numerical technique that is able to deal with a leaky SAW as well as a true SAW (conventional Rayleigh type or Bleustein-Gulyaev type). Using this technique, the SAWs' contribution to the mutual admittance can be removed, and the analysis of other contributions becomes possible. In particular, the amplitude decay rate of the residual mutual admittance with electrode separation gives information about the propagation of the surface skimming bulk waves (SSBWs). The method presented is applied to several currently used material-cut configurations.     

Phase and Dispersion of Cylindrical Surface Waves

Most theoretical and experimental work on surface waves does not take into account dispersion. When propagating along a flat planar half space, surface waves are known as Rayleigh waves and are not dispersive. When the radii of curvature are large, surface waves behave like Rayleigh waves. However, when the radii are small, dispersion becomes a contributing factor. Experimental measurements indicate that along with dispersion, there appears to be a strong phase shift effect as the wave propagates along the circumferential path of cylindrical specimens. The phase shift effect is observed even under conditions where dispersion is not detected. Classical theories provide the velocity-frequency equations, which represent the dispersion relationships, for surface waves. An alternate theoretical approach is discussed in this article that demonstrates the phase-dispersion relationship for cylindrical surface waves. Experimental data support the theoretical conclusions and indicate phase shift is directly related to the radius of curvature to an extent much more sensitive than dispersion.     

Acoustic loss mechanisms in leaky SAW resonators on lithiumtantalate

Discusses acoustic losses in synchronous leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalate (LiTaO₃ ) substrates. Laser probe measurements and theoretical models are employed to identify and characterize the radiation of leaky waves into the busbars of the resonator and the excitation of bulk acoustic waves. Escaping LSAWs lead to a significant increase in the conductance, typically occurring in the vicinity of the resonance and in the stopband, but they do not explain the experimentally observed deterioration of the electrical response at the antiresonance. At frequencies above the stopband, the generation of fast shear bulk acoustic waves is the dominant loss mechanism     

Ultrasonic leaky interface waves for composite-metal adhesive bond characterization

Highly stressed or damaged regions in aircraft structures are increasingly being reinforced by adhesively bonding an overlay of a unidirectional boron fiber-epoxy composite to the aircraft metallic substrate. While conventional C-scan ultrasonics can be used to detect disbonding of the overlay, nondestructive methods are also required to detect weak adhesive bonding. This paper describes a preliminary experimental investigation of the existence of ultrasonic leaky interface waves between overlays and 2024-T351 aluminum alloy and D6ac steel substrates, and their possible use for detection of weak bonds. The approach used was to excite these leaky waves using Rayleigh waves generated by a laser line-source on the substrate. The existence of the leaky waves, traveling normal to the composite fibers, between boron-epoxy overlays and either an aluminum or steel substrate, was confirmed by observations of the quasishear pulses leaked to the top of the overlay, and of the Rayleigh wave transmitted to the free surface beyond the overlay. When quantitative measurements were possible, measured values of the complex interface wave speed agreed satisfactorily with predicted values. This paper also demonstrates one case for which leaky interface waves are sensitive to weak bonding caused by the presence of a contaminant on the substrate surface prior to bonding: application of a low-concentration aqueous solution of hydraulic oil to the aluminum substrate prior to bonding of the overlay caused a marked increase, over that for the well-bonded case, in the observed amplitude of the quasi-shear pulses leaked to the top of the overlay by decay of the interface wave. More experiments are needed to establish whether leaky interface waves are sensitive to bond condition for various other combinations of substrate, overlay and contaminant.     

Suppression of the leaky SAW attenuation with heavy mechanical loading

We discuss effects on the propagation of surface acoustic waves (SAW) due to heavy mass loading on Y-cut lithium niobate and lithium tantalate substrates. An abrupt reduction in the leaky-SAW (LSAW) attenuation is observed in the measured admittance of a long resonator test structure on 64 degrees -YX-cut lithium niobate for aluminum electrodes of thickness h/lambda(0) beyond 9-10%. This experimental fact is explained theoretically as the slowing down of the leaky wave below the velocity of the slow shear surface-skimming bulk wave (SSBW), such that energy dissipation into bulk-wave emission becomes inhibited. An infinite transducer structure is modeled using the periodic Green's function and the boundary-element method (BEM); the computed theoretical properties well explain for the experimental findings. The model is further employed to quantify the leaky surface-wave attenuation characteristics as functions of the crystal-cut angle and the thickness of the electrodes. The resonance and antiresonance frequencies and the corresponding Q values are investigated to facilitate the selection of crystal cuts and electrode thicknesses. The transformation of the leaky SAW into a SAW-type nonleaky wave is also predicted to occur for gold electrodes, with considerably thinner finger structures.     

SAW/LSAW COM parameter extraction from computer experiments with harmonic admittance of a periodic array of electrodes

A novel numerical method for determining the surface acoustic wave and the leaky surface acoustic wave characteristics is proposed. The Green's function method is used to simulate an infinite periodic transducer driven by a periodic voltage. We show that the coupling of modes parameters and the dispersion relation can be extracted from the change in the admittance as the periodicity of the driving voltage is slightly shifted. The method first introduced here leads to significant savings in computing time.     

Nonlinear surface waves at ferrite-metamaterial waveguide structure

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film–cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film–cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.     

Characterization of 36°YX-LiTaO3 wafers byline-focus-beam acoustic microscopy

Application of line-focus-beam (LFB) acoustic microscopy is extended to characterization of substrates for SH-type SAW devices. Theoretical and experimental studies on a wave mode for characterization are carried out on 36°Y-cut LiTaO₃ wafers. A Rayleigh-type mode of leaky surface acoustic waves (LSAWs) must be employed instead of an SH-type mode of leaky pseudo-surface waves (LPSAWs). Experimental results show that the LSAW propagation should be directed along the X-axis because the LSAW velocities are more sensitive to chemical composition and elastic inhomogeneities. The relations among the LSAW velocities, densities, and Curie temperatures are determined. The LSAW velocity increases linearly at the rate of 0.52 m/s/°C with the Curie temperature. A chemical composition change of 0.03 Li₂ O-mol%, corresponding to temperature resolution of better than 0.3°C, is easily detected by the velocity measurements. Elastic inhomogeneities due to residual multi-domains, produced during the poling process during wafer fabrication, are interpreted quantitatively by this ultrasonic technology