Mode conversion is the transformation of a wave at an interface into other wave types (modes). [1] [2]
Mode conversion is the transformation of a wave at an interface into other wave types (modes). [1] [2]
Mode conversion occurs when a wave encounters an interface between materials of different impedances and the incident angle is not normal to the interface. [1] Thus, for example, if a longitudinal wave from a fluid (e.g., water or air) strikes a solid (e.g., steel plate), it is usually refracted and reflected as a function of the angle of incidence, but if some of the energy causes particle movement in the transverse direction, a second transverse wave is generated, which can also be refracted and reflected. Snellius' law of refraction can be formulated as: [1]
This means that the incident wave is split into two different wave types at the interface. If we consider a wave incident on an interface of two different solids (e.g. aluminum and steel), the wave type of the reflected wave also splits.
Besides these simple mode conversions, an incident wave can also be converted into surface waves. For example, if one radiates a longitudinal wave at a shallower angle than that of total reflection onto a boundary surface, it will be totally reflected, but in addition a surface wave traveling along the boundary layer will be generated. The incident wave is thus converted into reflected longitudinal and surface wave.
In general, mode conversions are not discrete processes, i.e. a part of the incident energy is converted into different types of waves. The amplitudes (transmission factor, reflection factor) of the converted waves depend on the angle of incidence. [3]
In seismology, a wave conversion specifically refers to the conversion between P and S waves at discontinuities. [4] Body waves are reflected and refracted when they hit a boundary layer within the earth. Here, P-waves can be converted into S-waves (PS-wave) at interfaces, as well as vice versa (SP-wave). [5] Here applies analogously for an incident P-wave:
The change in amplitudes can be described with the zoeppritz equations.
Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.
In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. The angle is named after the Scottish physicist Sir David Brewster (1781–1868).
In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light into several beams traveling in different directions. The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or distance between adjacent diffracting elements on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high-precision motion control and wavefront measurement.
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.
In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source. Even when there is a propagating electromagnetic wave produced, one can still identify as an evanescent field the component of the electric or magnetic field that cannot be attributed to the propagating wave observed at a distance of many wavelengths.
In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.
Etendue or étendue is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, and the AΩ product. Throughput and AΩ product are especially used in radiometry and radiative transfer where it is related to the view factor. It is a central concept in nonimaging optics.
In geophysics and reflection seismology, amplitude versus offset (AVO) or amplitude variation with offset is the general term for referring to the dependency of the seismic attribute, amplitude, with the distance between the source and receiver. AVO analysis is a technique that geophysicists can execute on seismic data to determine a rock's fluid content, porosity, density or seismic velocity, shear wave information, fluid indicators.
The contact angle is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interface at their intersection. It quantifies the wettability of a solid surface by a liquid via the Young equation.
A prism coupler is a prism designed to couple a substantial fraction of the power contained in a beam of light into a thin film to be used as a waveguide without the need for precision polishing of the edge of the film, without the need for sub-micrometer alignment precision of the beam and the edge of the film, and without the need for matching the numerical aperture of the beam to the film. Using a prism coupler, a beam coupled into a thin film can have a diameter hundreds of times the thickness of the film. Invention of the coupler contributed to the initiation of a field of study known as integrated optics.
X-ray reflectivity is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers. It is a form of reflectometry based on the use of X-rays and is related to the techniques of neutron reflectometry and ellipsometry.
In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.
In geophysics and reflection seismology, the Zoeppritz equations are a set of equations that describe the partitioning of seismic wave energy at an interface, due to mode conversion. They are named after their author, the German geophysicist Karl Bernhard Zoeppritz, who died before they were published in 1919.
Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, increasing reflection at some wavelengths and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections.
Seismic site effects are related to the amplification of seismic waves in superficial geological layers. The surface ground motion may be strongly amplified if the geological conditions are unfavorable. Therefore, the study of local site effects is an important part of the assessment of strong ground motions, seismic hazard and engineering seismology in general. Damage due to an earthquake may thus be aggravated as in the case of the 1985 Mexico City earthquake. For alluvial basins, we may shake a bowl of jelly to model the phenomenon at a small scale.
