An ultrasonic grating is a type of diffraction grating [1] produced by the interference of ultrasonic waves in a medium, which alters the physical properties of the medium (and hence the refractive index) in a grid-like pattern. The term acoustic grating is a more general term that includes operation at audible frequencies.
An ultrasonic wave is a sound wave at a frequency greater than 20 kHz. The human ear cannot recognize ultrasonic waves, but animals such as bats and dogs can. Ultrasonic waves can be produced by the piezoelectric effect and magnetostriction.
When ultrasonic waves are generated in a liquid in a rectangular vessel, the wave can be reflected from the walls of the vessel. These reflected waves are called echoes. The direct and reflected waves are superimposed, forming a standing wave. The density of the liquid at a node is more than the density at an antinode. Hence, the liquid acts as a diffraction grating to a parallel beam of light passed through the liquid at right angles to the wave.
The diffraction grating formed in this way is analogous to a conventional diffraction grating with lines ruled on a glass plate. The less dense antinodes refract light less and are analogous to the transmitting slits of a conventional grating. The denser nodes refract light more and are analogous to the opaque part of a conventional grating.
The grating element is equal to the wavelength of the ultrasonic waves—denoted by . If is the wavelength of the light passed through the grating that is diffracted by an angle , then the nth order of the maximum is given by:
or
If is the velocity of the ultrasonic wave in the liquid we can calculate the velocity of the wave with:
or,
where is the frequency of the wave.
The Debye–Sears method determines the wavelength of monochromatic light using an acoustic or ultrasonic gratings. This method utilises the concept of piezoelectricity to obtain a grating.
The phenomenon of diffraction of light using an ultrasonic grating was first observed by Debye and Sears in 1932. When ultrasonic waves are propagated in a liquid, the density varies from layer to layer due to periodic variation of pressure. This grating can determine the wavelength of monochromatic light and the speed of waves.
If is the wavelength of a monochromatic light source, and is the wavelength of the ultrasonic waves, then applying the principle of diffraction, we get
Where is the angle of diffraction.
Thus we can calculate either or if the other is known. We need not worry about the grating element since the nodes themselves act as slits, hence the distance between two slits are equal to the ultrasonic wave wavelength.
This method determines the velocity of ultrasonic waves using monochromatic sources like sodium vapour lamps. The medium is usually a piezoelectric crystal such as quartz, tourmaline, or Rochelle salt. A mechanical stress is produced along an axis of the crystal using an RF oscillator. By adjusting the frequency of the oscillator, we can determine the velocity of the ultrasonic waves by using
where is the frequency of the oscillator.
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.
Frequency, most often measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: f = 1/T.
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
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 the physical sciences, the wavenumber, also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time or radians per unit time.
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific heat in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box in contrast to the Einstein photoelectron model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence of the heat capacity of solids, which is proportional to – the Debye T 3 law. Similarly to the Einstein photoelectron model, it recovers the Dulong–Petit law at high temperatures. Due to simplifying assumptions, its accuracy suffers at intermediate temperatures.
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.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance from the object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and is given by the Fresnel diffraction equation.
An acousto-optic modulator (AOM), also called a Bragg cell or an acousto-optic deflector (AOD), uses the acousto-optic effect to diffract and shift the frequency of light using sound waves. They are used in lasers for Q-switching, telecommunications for signal modulation, and in spectroscopy for frequency control. A piezoelectric transducer is attached to a material such as glass. An oscillating electric signal drives the transducer to vibrate, which creates sound waves in the material. These can be thought of as moving periodic planes of expansion and compression that change the index of refraction. Incoming light scatters off the resulting periodic index modulation and interference occurs similar to Bragg diffraction. The interaction can be thought of as a three-wave mixing process resulting in sum-frequency generation or difference-frequency generation between phonons and photons.
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.
Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.
Diffraction processes affecting waves are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as a proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations.
An acousto-optic deflector (AOD) is a device that uses the interaction between sound waves and light waves to deflect or redirect a laser beam. AODs are essentially the same as acousto-optic modulators (AOMs). In both an AOM and an AOD, the amplitude and frequency of different orders are adjusted as light is diffracted.
Volume holograms are holograms where the thickness of the recording material is much larger than the light wavelength used for recording. In this case diffraction of light from the hologram is possible only as Bragg diffraction, i.e., the light has to have the right wavelength (color) and the wave must have the right shape. Volume holograms are also called thick holograms or Bragg holograms.
A blazed grating – also called echelette grating – is a special type of diffraction grating. It is optimized to achieve maximum grating efficiency in a given diffraction order. For this purpose, maximum optical power is concentrated in the desired diffraction order while the residual power in the other orders is minimized. Since this condition can only exactly be achieved for one wavelength, it is specified for which blaze wavelength the grating is optimized. The direction in which maximum efficiency is achieved is called the blaze angle and is the third crucial characteristic of a blazed grating directly depending on blaze wavelength and diffraction order.
Quantum mechanics was first applied to optics, and interference in particular, by Paul Dirac. Richard Feynman, in his Lectures on Physics, uses Dirac's notation to describe thought experiments on double-slit interference of electrons. Feynman's approach was extended to N-slit interferometers for either single-photon illumination, or narrow-linewidth laser illumination, that is, illumination by indistinguishable photons, by Frank Duarte. The N-slit interferometer was first applied in the generation and measurement of complex interference patterns.
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.
In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.
Littrow expansion and its counterpart Littrow compression are optical effects associated with slitless imaging spectrographs. These effects are named after austrian physicist Otto von Littrow.
