In nature, wave phenomena of both a material and field nature are extremely widespread. Despite the variety, they all exhibit common features and are described by the same laws of physics. Among these phenomena is wave diffraction. This is a universal property inherent in waves of any origin, and here we will pay attention to some of its aspects, in particular, how it manifests itself and what role it plays in various physical processes.
The essence of the phenomenon
In a broad sense, wave diffraction is a deviation of the oscillatory process propagating in space from a number of principles that form the basis of geometric optics. These include postulates that affirm the rectilinear and independent propagation of rays and the addition of illuminances when they converge.
In a narrow, traditional sense, diffraction is understood as wave enveloping any obstacle. When it deviates from the straight path at the obstacle, if its dimensions are comparable with the wavelength, the surface of the wave front is curved, due to which the wave falls into the region of the geometric shadow created by the obstacle. For example, acoustic waves freely bend around a tree trunk, because their length is comparable to the thickness of the trunk, and light waves can penetrate only into a small area of the shadow created by the tree.
There is a simple relation that allows one to evaluate the strength of the manifestation of the diffraction effect. The wavelength λ in this ratio is associated with the width of the wavefront d limited by the obstacle: λ / d. Obviously, diffraction manifests itself the stronger, the shorter the wavefront and the longer the wave.
Huygens principle
A description of how the wave changes direction during diffraction gives the Huygens principle. He considers the motion of the wave as the continuous excitation of secondary waves at each point that the moving wave front reaches. If a wave encounters an obstacle, for example, a screen with a hole that limits the width of its front, then this section can also be represented as a set of sources of spherical (characteristic for an isotropic medium) secondary waves.
The line enveloping the surface of these waves will be curved the more, the smaller the size of the hole in the screen. The directions along which the waves propagate are the normals to this line, the curvature of which leads to their divergence. Consequently, with a decrease in the size of the hole, the wave goes further into the geometric shadow.
Wave interference when they are deflected
The Huygens principle does not tell us anything about the intensity of the diffracting wave, since it does not concern the question of what happens to its amplitude. A corresponding addition was made by O. Fresnel, pointing out the fact of interference of secondary waves. According to the Huygens-Fresnel principle, such waves are coherent, and their amplitude and phase are proportional to those of a wave incident on an obstacle. The diffraction wave pattern is the result of the superposition of these secondary waves, that is, it gives an interference effect.
If we observe light, then when it is diffracted at the observation point (on a special screen located at some distance from the obstacle), a characteristic system of alternating amplitude maxima and minima will be visible. Thus, the interference and diffraction of waves are phenomena inextricably linked.
Fresnel zones
Fresnel solved the problem of interference by breaking the surface of the wave front into the so-called half-wave zones. These are sections whose boundaries are distant from the observer by distances that differ by half the wavelength of the incident wave. It is clear that secondary waves emanating from neighboring zones oscillate in antiphase and therefore cancel each other out. At the same time, the amplitudes of waves excited by sources separated by one Fresnel zone, on the contrary, are added. The result is an interference wave pattern.
Of great importance is the angle between the direction of the observer and the normal to the front of the incident wave. The larger it is, the smaller the amplitude, and therefore the intensity, becomes.
Diffraction of electromagnetic waves
These waves, which are not oscillations of particles of any material medium, but the propagation of perturbations of the electromagnetic field, are fully exposed to the phenomenon of interest to us. Electromagnetic waves are characterized by an extremely wide range of lengths, and therefore their diffraction is very different in conditions and manifestation.
So, the radio waves are deflected by large obstacles. The phenomenon of diffraction of long radio waves on the curvature of the earth's surface is well known , due to which they are able to envelope its convexity. But the short-wave X-ray diffracts only on very small objects, such as elements of crystal lattices - molecules and atoms.
Let us dwell in more detail on the optical range, due to the visibility of the picture, which is convenient for studying wave diffraction.
Diffraction of light on various obstacles
In the case of a linear form of an obstacle (it can be a hair, a thread, a screen with a narrow slit or a straight edge of the screen), the diffraction pattern has the form of parallel light stripes alternating with dark ones. Light areas correspond to the maximum amplitude of vibrations, dark ones arise where interfering secondary waves cancel each other out.
When a light wave passes through a circular hole, the diffraction result looks like a system of concentric rings. Its appearance is determined by the number of Fresnel zones falling into the hole section. If it is even, then the center of the diffraction pattern turns out to be dark, with an odd number of zones it will be bright.
If we observe the deviation of light waves on a disk or a ball, a bright amplitude maximum will almost always appear in the center, unless the obstacle is too large and covers many Fresnel zones.
An interesting manifestation of diffraction is also the expansion of the waves in the spectrum. If you illuminate an obstacle with white light (that is, not monochromatic), then the concentric rings acquire a multi-colored color.
Diffraction behavior of a mechanical wave
It is very easy to observe the diffraction of mechanical waves on the surface of the reservoir when the waves bend around an obstacle protruding from the water - a stone, a piece of wood, etc. If you install a partition with a small hole in the path of the waves, you can clearly see the change in the shape of the wave front: from the gap will be a circular wave diverges, as from a point source. With large slit sizes, the wave front bends only at the edges, allowing it to penetrate into the space closed by the partition.
Acoustic waves are also mechanical. Due to diffraction, the sound “bypasses”, for example, the corners of buildings, the edges of walls in window and door openings and other obstacles. To the diffraction effects in acoustics, a phenomenon such as reverberation, or after-sounding, which manifests itself in sonar, is also partly related. This gradually decaying sound appears during the diffraction of an acoustic wave propagating in water on an uneven bottom relief or on inhomogeneities such as air bubbles in the water itself.
Particle diffraction
Elementary particles - electrons, protons, neutrons - these are quantum objects that exhibit wave properties in some processes. Their behavior is determined by quantum-mechanical probability waves (de Broglie waves), which in the same way experience diffraction as circles on water, sound or light. As applied to particles, wave diffraction is scattering by electron shells or atomic nuclei.
The first diffraction pattern from electron beam scattering on nickel crystals was obtained in 1927 by K. Davisson and L. Jermer, and in 1948, Soviet physicists V. Fabrikant, L. Bieberman and N. Sushkin experimentally proved that the wave nature is not unique to beams particles, but also to single electrons.
About the role of diffraction
Here are some striking examples of the negative and positive role of this phenomenon in different areas.
Light diffraction imposes a fundamental restriction on the resolution of optical systems, not allowing a clear image of very distant or small objects. The diffraction of sound and ultrasound is an obstacle to the operation of sonar devices. With regard to radio waves, this phenomenon can cause a signal to fall — the “fading” of a radio wave due to diffraction from the clouds — and impede directional radio transmission or radar operation.
However, diffraction phenomena bring great benefits. So, the frequency separation of light rays caused by them is used in spectroscopy, where special diffraction gratings are created for these purposes, which make it possible to study the features of the fine structure of the spectra. The diffraction of X-rays and electrons by crystals and molecules has become the basis of X-ray diffraction analysis and electron diffraction — methods for studying the structure of matter widely used in science, medicine, and manufacturing. Electron microscopes also use diffraction of electron beams on microobjects.
Wave diffraction is a universal phenomenon. This circumstance explains the importance that it has in many processes, as well as the variety of methods of its application.