Diffraction (1)

As light or sound waves travel through the world, they encounter obstacles and openings that can cause them to bend and interfere with one another. This phenomenon, known as diffraction, was first described by Italian scientist Francesco Maria Grimaldi in the 17th century. According to the Huygens-Fresnel principle, each point on a wavefront can be thought of as a collection of small, spherical waves that spread out in all directions. When a coherent wave, such as a laser, encounters an obstacle or opening that is roughly the same size as its wavelength, these small wavelets can add together in a way that causes the wave to bend around the obstacle. This is why a light wave passing through a narrow slit will produce a characteristic pattern of light and dark bands on a surface behind it. If there are multiple, closely spaced openings, the diffraction pattern can become much more complex.

Diffraction is not limited to electromagnetic waves like light and sound. It can also occur with gravitational waves, water waves, and other types of waves. Even matter itself can exhibit wave-like properties and undergo diffraction, as described by quantum mechanics. The amount of diffraction that occurs depends on the size of the gap or obstacle relative to the wavelength of the wave. When the gap is similar in size to the wavelength, the waves passing through it become more circular in shape.

The phenomenon of diffraction, or the bending and interference of waves as they pass around obstacles or through openings, was first studied in detail by Francesco Maria Grimaldi in the 17th century. Grimaldi's observations were eventually published in 1665 and showed that light could be broken up into different directions as it passed through certain openings or encountered certain obstacles. Isaac Newton also studied diffraction and attributed it to the inflection of light rays, but it was not until Thomas Young conducted a famous experiment in 1803 involving interference from two closely spaced slits that the wave nature of light was more fully understood. Augustin-Jean Fresnel carried out further research and calculations on diffraction, which he made public in the early 19th century, and his work provided strong support for the wave theory of light put forward by Christiaan Huygens and revived by Young, as opposed to Newton's particle theory.

In classical physics, diffraction occurs due to the way in which waves propagate, as described by the Huygens-Fresnel principle and the principle of superposition. This can be visualized by considering each particle in the transmitting medium as a point source for a secondary spherical wave. The total wave displacement at any subsequent point is the sum of these secondary waves, and the resulting diffraction pattern will have a series of maxima and minima depending on the relative phases and amplitudes of the individual waves. In the modern, quantum mechanical understanding of light propagation, each photon has a wavefunction that is determined by its surroundings and initial conditions. When light passes through a slit or multiple slits, a diffraction pattern is created by the probability distribution of the photons, with the presence or absence of light in certain areas corresponding to the likelihood of detecting photons in those areas. There are various analytical models that can be used to calculate the diffracted field, including the Kirchhoff-Fresnel diffraction equation and the Fraunhofer and Fresnel diffraction approximations. In general, it is not possible to solve diffraction problems analytically, but numerical solutions can be obtained through finite element and boundary element methods. A basic understanding of diffraction can often be gained by considering how the relative phases of the secondary wave sources vary, particularly when the phase difference is half a cycle, leading to wave cancelation. In many cases, the problem can be reduced to two dimensions, such as with water waves or light shining through small circular holes, although three-dimensional problems may also arise.

Diffraction is a phenomenon that can be observed in everyday life in a variety of ways. For example, the closely spaced tracks on a CD or DVD act as a diffraction grating to create the rainbow pattern that is commonly seen when looking at these discs. This principle can be used to design gratings with structures that produce any desired diffraction pattern, as can be seen in the hologram on a credit card. Diffraction can also cause a bright ring to be visible around a bright light source like the sun or moon when small particles are present in the atmosphere. Shadows of solid objects may also show small fringes around their edges when light from a compact source is used. The speckle pattern that is observed when laser light hits an optically rough surface is also a diffraction phenomenon, as is the iridescent appearance of deli meat, which is caused by diffraction off the meat fibers. These effects are all consequences of the wave nature of light.

Diffraction can occur with any type of wave, including ocean waves that diffract around obstacles like jetties and sound waves that can diffract around objects. This is why it is possible to hear someone calling even when hiding behind a tree. In technical applications, diffraction can set a fundamental limit on the resolution of cameras, telescopes, and microscopes.

According to the Huygens-Fresnel principle, when a narrow slit is illuminated by light, the resulting diffraction pattern will be a series of circular waves with a cylindrical wavefront of uniform intensity. If the slit is wider than a single wavelength, interference effects will be present in the space downstream of the slit. These interference effects can be calculated by considering the slit as if it were made up of a large number of point sources with the same phase, spaced evenly across its width. If the incident light is coherent, the relative phases of the contributions from these point sources will vary, leading to minima and maxima in the diffracted light. The angle at which the first minimum appears can be determined by considering the path differences between the point sources and the resulting destructive interference. This analysis only applies in the far field, or a distance much larger than the width of the slit. The intensity profile of the diffracted light will depend on the width of the slit and the incident angle of the light. If the width of the slit is much smaller than the wavelength, the intensity will have little dependence on the angle, resulting in a cylindrical wavefront with azimuthal symmetry. If the width of the slit is much larger than the wavelength, the intensity will be concentrated near zero angle, resulting in a wavefront similar to that of geometrical optics. When the incident angle of the light is non-zero, the intensity profile in the far field will be modified according to the angle and the width of the slit.