Superficial waves are called guided flat inhomogeneous slow electromagnetic waves class E or class H, with dispersion. Guiding systems, along which they spread surface waves, are slowing (impedance) surfaces.
Surface waves have two main features , distinguishing them from all other guided waves.
1.) The amplitudes of the E and H vectors of surface waves decrease exponentially in the direction of the normal to the slowing surfaces along which they propagate.
2.) Surface waves are slow (Vph
The decrease in the amplitudes of the vectors E and H of a surface wave in the direction normal to the surface along which it propagates is not associated with active losses in the medium, but is caused by special phase relationships between the components of the vectors E and H of this wave, due to which the flow of the Poynting vector in in this direction on average for the period =0.
The energy flux density transferred by a surface wave along a guide surface is maximum immediately at this surface and decreases sharply with distance from it. Figuratively speaking, propagating along a guide surface, the wave seems to “stick” to it, which determines the name “surface” for waves of this type.
48.Approximate Leontovich boundary conditions.
Let us assume that a plane electromagnetic wave is incident from air at an angle onto a plane interface with a fairly conducting medium described by the complex refractive index:
From the establishment of the concept of a well-conducting medium, it follows that. The extreme inequality according to Siell's law represents that the angle of refraction must be very small. It can be approximately assumed that a refracted wave enters Medium 2 in the direction of the normal in different meaning angle of incidence. This is the main thing physical definition Leontovich's conditions. According to the above, the equivalent circuit of a metal-like medium takes the form of a homogeneous long line with a characteristic resistance calculated by general formula
At the beginning of the line (that is, at the interface), the tangential components of the magnetic and electrical vectors must satisfy the undoubted relationship that directly follows from the definition of characteristic resistance:
As is known, on the surface of an ideal conductor. A nonzero tangential component appears at the interface in the case of large but finite conductivity. Despite the smallness of this value (since at ), it determines the flow of power into the metal used to heat it.
If the axis z is directed inside Environment 2, and the interface coincides with the plane , then at the interface, accordingly, must be fulfilled following conditions:
With this arrangement of signs, as can be easily verified, the flow of the Poynting vector corresponding to heat losses will always be directed along the positive direction of the z axis. Using Leontovich boundary conditions in the form 
or in the form, you need to see the tangent component magnetic vector.
49. Interference. Interference in thin plates 
50. 49. Interference. Interference in Newton's rings 
Retarding surfaces
A retarding (impedance) surface is the interface between media on which the tangent components of the vectors E and H of the alternating EM field (existing on both sides of this boundary) are shifted in phase relative to each other by 90°. Due to this, the flow of the Poynting vector in the direction of the normal to the slowing surface on average over period = 0, and the transfer of energy by EM waves is possible only in the direction parallel to such a surface.
When solving boundary problems of electrodynamics, a parameter called surface impedance (surface resistance) is often used to characterize interfaces. equal to the ratio complex amplitudes of the tangent components of the vectors E and H on this surface.
Complex surface resistance module
Argument (phase) of complex surface resistance
Due to the phase shift between the tangent components of the E and H vectors on the slowing surface, its surface impedance is a purely imaginary quantity .
If Z is positive, then surface waves of class E propagate along the slowing surface.
If Z is negative, then surface waves of class H propagate along the slowing surface.
Flat slowing surfaces can be the interface between two dielectrics having different dielectric constants (air - dielectric), and the interface between a dielectric - a comb metal structure (air - a comb metal structure).
Until now we have been talking about volumetric acoustic waves propagating in the volume of an isotropic solid. In 1885, the English physicist Rayleigh theoretically predicted the possibility of propagation of surface acoustic waves, which are commonly called Rayleigh waves, in a thin surface layer of a solid body bordering air. In the Rayleigh problem, we limit ourselves to the formulation of the problem and its end results. There is a flat boundary between vacuum and isotropic solid medium. The interface coincides with the plane, the axis is directed deep into the solid medium.
The starting points for solving the problem are the Lamé equation of motion (4) and the boundary condition, where nj are the components of the unit normal to the surface. On the border with vacuum external forces Fi are absent, and the normal (Fig. 3) has one component along z.
For harmonic waves the initial wave equations and boundary conditions will take the form
The solution is sought in the form of plane harmonic waves traveling along the x axis in a solid half-space.
For the surface effect, the amplitudes should decrease along the normal to the boundary
The first type of solution to the problem posed has the form
where B is the amplitude constant determined by the wave excitation conditions. This solution corresponds to a homogeneous volumetric (no decrease in amplitude along the normal to the surface) shear wave polarized in the direction perpendicular to the direction propagation along x and normal to the surface. This wave is unstable in the sense that small deviations in the formulation of the problem (for example, a load on the surface layer or the presence of a piezoelectric effect in the medium) can make this wave a surface wave. The second type of solution to the problem determines the Rayleigh surface wave.
Wave vectors, and are interconnected due to boundary conditions and the Rayleigh wave is a complex acoustic wave.
The speed of the Rayleigh wave is given by
When Poisson's ratio changes approximately, the speed changes from to. The speed depends only on elastic properties solid body and does not depend on frequency and the Rayleigh wave does not have dispersion. The amplitude of the wave decreases rapidly with increasing distance from the surface. In a Rayleigh wave, particles of the medium move according to (14), (15) along elliptical trajectories, major axis The ellipse is perpendicular to the surface and the direction of movement of particles on the surface occurs counterclockwise relative to the direction of wave propagation. Rayleigh waves were discovered during seismic vibrations earth's crust, when three signals were recorded. The first of them is associated with the passage of a longitudinal wave, the second signal is associated with transverse waves, the speed of which is less than that of longitudinal waves. And the third signal is caused by the propagation of waves over the Earth's surface. In addition to waves, there are a number of other types of surface acoustic waves (SAWs). Surface transverse waves in a solid layer lying on a solid elastic half-space (Love waves), waves in plates (Lamb waves), waves on curved surfaces, wedge waves, etc. The energy of surfactants is concentrated in a narrow surface layer with a thickness of the order of the wavelength; they do not experience (unlike bulk waves) big losses to the geometric divergence into the volume of the half-space and therefore they can extend to long distances. Surfactants are easily accessible to technology, as if “they are easy to take.” These waves are widely used in acoustoelectronics.
Surface waves
A typical SAW device, used for example as a bandpass filter. The surface wave is generated on the left by applying an alternating voltage through printed conductors. Wherein Electric Energy transforms into mechanical. Moving along the surface, the mechanical high-frequency wave changes. On the right - the receiving tracks pick up the signal, while inverse conversion mechanical energy to variable electricity, through a load resistor.
Surface acoustic waves(surfactant) - elastic waves propagating along the surface of a solid body or along the boundary with other media. Surfactants are divided into two types: with vertical polarization and with horizontal polarization ( Love waves).
The most common special cases of surface waves include the following:
- Rayleigh waves(or Rayleigh), in the classical sense, propagating along the boundary of an elastic half-space with a vacuum or a fairly rarefied gaseous medium.
- at the solid-liquid interface.
- Stonley Wave
- Love waves- surface waves with horizontal polarization (SH type), which can propagate in the elastic layer structure on an elastic half-space.
Rayleigh waves
Rayleigh waves, theoretically discovered by Rayleigh in 1885, can exist in a solid body near it free surface bordering the vacuum. The phase velocity of such waves is directed parallel to the surface, and the particles of the medium oscillating near it have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. These particles describe elliptical trajectories in the plane during their oscillations, perpendicular to the surface and passing through the direction phase speed. This plane is called sagittal. The amplitudes of longitudinal and transverse vibrations decrease with distance from the surface deeper into the medium. exponential laws with different attenuation coefficients. This leads to the fact that the ellipse is deformed and the polarization far from the surface can become linear. The penetration of the Rayleigh wave into the depth of the sound pipe is on the order of the length of the surface wave. If a Rayleigh wave is excited in a piezoelectric, then a slow wave will exist both inside it and above its surface in vacuum electric field caused by the direct piezoelectric effect.
Used in touch displays with surface acoustic waves.
Damped Rayleigh waves
Damped Rayleigh-type waves at the solid-liquid interface.
Continuous wave with vertical polarization
Continuous wave with vertical polarization, running along the boundary of a liquid and a solid with a speed
Stonley Wave
Stonley Wave, propagating along the flat boundary of two solid media, the elastic moduli and density of which do not differ much.
Love waves
Links
- Physical encyclopedia, vol. 3 - M.: Bolshaya Russian Encyclopedia p.649 and p.650.
Wikimedia Foundation.
- 2010.
- Surface acoustic waves
Surface elastic waves
See what “Surface waves” are in other dictionaries: SURFACE WAVES - electromagnetic waves that propagate along a certain surface and have a distribution of fields E and H that decreases quite quickly as one moves away from it to one side (one-sided PV) or both (true PV) sides. Unilateral C. v. arises...
See what “Surface waves” are in other dictionaries: Physical encyclopedia - (see), arising on the free surface of a liquid or spreading along the interface of two immiscible liquids under the influence external cause (wind, thrown stone, etc.), bringing the surface out of balance... ...
Big Polytechnic Encyclopedia surface waves - - Topics Oil and gas industry
See what “Surface waves” are in other dictionaries:- waves propagating along the free surface of a liquid or at the interface of two immiscible liquids. arise under the influence of external influence (for example, wind) that removes the surface of the liquid from equilibrium state. IN… … Big Encyclopedic Polytechnic Dictionary
Surface waves- Elastic waves propagating along the free surface of a solid body or along the boundary of a solid body with other media and attenuating with distance from the boundary. The simplest and at the same time the most frequently encountered in practice P. in ... Great Soviet Encyclopedia
surface interference waves- - Topics: oil and gas industry EN ground rollssurface wave noise ... Technical Translator's Guide
SURFACE ACOUSTIC WAVES- (surfactant), elastic waves propagating along the free surface of a solid. body or along the border of the TV. bodies with other media and attenuating with distance from boundaries. There are two types of surfactants: with vertical polarization, those with vector oscillations. displacement h c… … - electromagnetic waves that propagate along a certain surface and have a distribution of fields E and H that decreases quite quickly as one moves away from it to one side (one-sided PV) or both (true PV) sides. Unilateral C. v. arises...
Rayleigh waves- surface acoustic waves. Named after Rayleigh, who theoretically predicted them in 1885. Contents 1 Description 2 Isotropic body ... Wikipedia
Love waves- Love waves are an elastic wave with horizontal polarization. It can be both volumetric and superficial. Named after Love, who studied this type of waves in application to seismology in 1911. Contents 1 Description ... Wikipedia
Surface acoustic waves- A typical SAW device based on an anti-comb converter used as a bandpass filter. A surface wave is generated on the left through the application of an alternating voltage through the pro... Wikipedia
Books
- Wave phenomena in media with dispersion, Kuzelev M.V.. The book consistently presents the fundamentals of physics wave phenomena in dispersive media, including dissipative and nonequilibrium ones. Based on the concepts of dispersion function and dispersion...
Surfactants can exist near the free surface of a solid or near the interface between two different bodies. There are five types of surfactants.
Rayleigh waves, theoretically discovered by Rayleigh in 1885, can exist in a solid body near its free surface bordering the vacuum. The phase velocity of such waves is directed parallel to the surface, and the particles of the medium oscillating near it have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. During their oscillations, these particles describe elliptical trajectories in a plane perpendicular to the surface and passing through the direction of the phase velocity. This plane is called sagittal. The amplitudes of longitudinal and transverse vibrations decrease with distance from the surface into the medium according to exponential laws with different attenuation coefficients. This leads to the fact that the ellipse is deformed and the polarization far from the surface can become linear. The penetration of the Rayleigh wave into the depth of the sound pipe is on the order of the length of the surface wave. If a Rayleigh wave is excited in a piezoelectric, then both inside it and above its surface in a vacuum there will be a slow electric field wave caused by the direct piezoelectric effect.
Waves of Stoneleigh(or Stonley), named after the scientist who discovered them in 1908, differ from Rayleigh waves in that they can exist near the interface of two solid media in acoustic contact. When a Stoneley wave propagates, particles of both media participate in the oscillations. At the same time, just like in a Rayleigh wave, they perform an elliptical movement in the sagittal plane. The penetration depths of Stoneley waves into contacting media are on the order of the surface wave length.
Gulyaev - Bluestein waves(Blyukshtein) were discovered in 1968 in the USSR by Yu.V. Gulyaev. and independently in the US by Bluestein. They have two characteristic signs. Firstly, they exist only in piezoelectric crystals near the free boundary and, secondly, the particles of the medium experience purely transverse vibrations in a direction parallel to the surface (“horizontal” polarization). Gulyaev-Blustein waves penetrate into the oscillating medium more deeply than Rayleigh and Stoneley waves. The depth of their penetration into the volume of a solid body is of the order of magnitude λ sound ε / k 2
, where ε- the dielectric constant, k
- electromechanical coupling coefficient (see below). Thanks to the direct piezoelectric effect, the Gulyaev-Blustein wave is accompanied by a slow electric field wave in a vacuum above the surface of the piezoelectric.
Waves of Marfeld - Tournois, discovered in 1971, differ from Gulyaev-Blustein waves in that they can exist near the interface of two contacting piezoelectrics. These surfactants are also purely shear and have “horizontal” polarization.
Love waves (1926) spread in a thin (about λ sound) a layer of a substance deposited on a substrate in which the speed of sound is greater than in the layer. These purely shear waves have “horizontal” polarization and penetrate the substrate to a depth of the order of λ sound. They have dispersion; their speed lies between the speeds of sound in the layer and in the substrate.
1.3. Guided and channeled waves. Representatives waveguide acoustic modes are waves in thin plates or films, both surfaces of which are free, and the thickness is of the order of the length elastic wave. In this case, the plate performs the functions of a planar waveguide, and the waves themselves are essentially normal waves in it. The latter were called Lamb waves after the scientist who discovered them in 1916. The displacement vector in a Lamb wave has both longitudinal and transverse components, with the transverse component being normal to the surfaces of the waveguide.
Other representatives of waveguide modes are normal acoustic waves in thin rods of various profiles (round, rectangular, etc.). Channeled acoustic waves are those waves that can propagate both through channels along grooves and protrusions of various profiles (rectangular, triangular, semicircular, etc.) made on the free (not necessarily flat) surface of a solid body, as well as along the spatial angle formed by two faces sound pipes. For practice, they are attractive because they can be used in acoustic integrated circuits.
2. EQUATIONS DESCRIBING ELECTROMECHANICAL
PROCESSES IN PIEZOELECTRICS
Surface acoustic waves (SAW) are widely used in the development of filters and delay lines used in radio engineering devices. IN Lately Surfactants are also used in the development of measuring transducers.
Several types of surfactants are known; Rayleigh waves are most often used in practice. Displacement of solid particles during Rayleigh wave propagation in the direction of the axis X illustrated in Fig. 2-22, A. As can be seen from Fig. 2-22, A, waves propagate near the boundary of a solid body and attenuate almost completely at a distance z from the surface, approximately equal to wavelength l. One of the main reasons for the growing interest in surfactants is precisely the concentration of energy in thin layer, since thanks to this, only one requirement is imposed on the surfactant element manufacturing technology - careful processing of the working surface along which the acoustic wave propagates.
To excite the surfactant, combs of back-to-back electrodes are applied to the surface of the piezoelectric element (Fig. 2-22, b), which are an interdigital converter (IDC) having a pitch l 0 = l. When voltage is connected to the IDT electrodes, underneath them, due to the inverse piezoelectric effect, particle displacements occur and a surfactant appears, propagating in both directions. If the wavelength coincides with the IDT pitch, then due to the superposition of oscillations arising under each pair of electrodes, the total SAW energy reaches a maximum; if the wavelength does not coincide with the IDT pitch, the SAW energy decreases and at a certain ratio between l and l 0 wave outside the IDT can be completely extinguished.
To receive surfactant energy, a second IDT is used, which also has a pitch equal to length waves. Due to the direct piezoelectric effect, charges arise on the electrodes of the receiving IDT and voltage appears. The delay line consists of an input and output IDT. To a first approximation, both IDTs can be considered as local electrodes located at a distance L, equal to the distance between geometric centers VShP. The delay time t is equal to the time of passage of the acoustic wave between the IDTs, i.e.
t = L/u,
where u = – surfactant propagation speed; E ij– elasticity constant; r is the density of the material.
In quartz Y-cut speed of surfactant propagation is equal to u= 3159 m/s; thus, with L= 10 mm the delay time is about 3 µs. The wavelength l is determined by the propagation speed u and the wave excitation frequency and is l= u /f. Modern technology provides the ability to create IDTs with steps up to l 0 = 10 µm; thus, the operating frequencies of SAWs can be in the range of up to 300 MHz.
The surfactant structure can be used as a frequency-setting element of a self-oscillator (Fig. 2-22, V); in this case, as follows from the phase balance condition (phase shifts in electrical circuits neglected), along the length L an integer number of waves must fit. The phase-frequency characteristic of the delay line is defined as j (w)= –wt. The value of the equivalent quality factor is determined by the formula:
and amounts to Q eq = pw 0 t L/(2l).
Length L limited by the size of the surfactant structure and the attenuation of the surfactant energy and does not exceed L= 500l ; thus, the quality factor is equal to Q eq » 10 3 .
Changing the delay time of the surfactant structure under the influence of external factors is used in measuring converters with frequency output. When t changes, the relative change in the generator frequency is
Dw/w 0 =–Dt/t 0 .
Change in delay time t = L/u determined by change in length L and phase velocity u is equal to
Dt/t= D LIL–DE ij /(2Eij) + Dr/(2r).
A change in the delay time can occur due to mechanical deformation of the surfactant structure, under the influence of temperature, when loading the surface with thin films (film thickness h" < 0,1 l), при изменении зазора d между поверхностью распространения ПАВ и токопроводящим экраном (d < 1). Accordingly, converters for measuring mechanical quantities(Dt/t–up to 1%), temperature (Dt/t–up to 1%), micro-displacements, for micro-weighing and studying the parameters of thin films (Dt/t–up to 10%). With a non-contact excitation system, SAW transducers can also be used to measure the movement of an object that causes movement of one of the IDTs and leads to a change L.
