Diffraction grating

In optics, a diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. The emerging coloration is a form of structural coloration. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are commonly used in monochromators and spectrometers. In optics, a diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. The emerging coloration is a form of structural coloration. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are commonly used in monochromators and spectrometers. For practical applications, gratings generally have ridges or rulings on their surface rather than dark lines. Such gratings can be either transmissive or reflective. Gratings that modulate the phase rather than the amplitude of the incident light are also produced, frequently using holography. The principles of diffraction gratings were discovered by James Gregory, about a year after Newton's prism experiments, initially with items such as bird feathers. The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse, who strung hairs between two finely threaded screws. This was similar to notable German physicist Joseph von Fraunhofer's wire diffraction grating in 1821. In the 1860s, gratings with the lowest line-distance d were created by Friedrich Adolph Nobert (1806-1881) in Greifswald, then the two Americans Lewis Morris Rutherfurd (1816-1892) and William B. Rogers (1804-1882) took over the lead, and by the end of the 19th century, the concave gratings of Henry Augustus Rowland (1848-1901) were the best gratings available. Diffraction can create 'rainbow' colors when illuminated by a wide spectrum (e.g., continuous) light source. The sparkling effects from the closely spaced narrow tracks on optical storage disks such as CDs or DVDs are an example, while the similar rainbow effects caused by thin layers of oil (or gasoline, etc.) on water are not caused by a grating, but rather by interference effects in reflections from the closely spaced transmissive layers (see Examples, below). A grating has parallel lines, while a CD has a spiral of finely-spaced data tracks. Diffraction colors also appear when one looks at a bright point source through a translucent fine-pitch umbrella-fabric covering. Decorative patterned plastic films based on reflective grating patches are very inexpensive, and are commonplace. The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation. According to the Huygens–Fresnel principle, each point on the wavefront of a propagating wave can be considered to act as a point source, and the wavefront at any subsequent point can be found by adding together the contributions from each of these individual point sources. Gratings may be of the 'reflective' or 'transmissive' type, analogous to a mirror or lens, respectively. A grating has a 'zero-order mode' (where m = 0), in which there is no diffraction and a ray of light behaves according to the laws of reflection and refraction the same as with a mirror or lens, respectively. An idealised grating is made up of a set of slits of spacing d, that must be wider than the wavelength of interest to cause diffraction. Assuming a plane wave of monochromatic light of wavelength λ with normal incidence (perpendicular to the grating), each slit in the grating acts as a quasi point-source from which light propagates in all directions (although this is typically limited to a hemisphere). After light interacts with the grating, the diffracted light is composed of the sum of interfering wave components emanating from each slit in the grating. At any given point in space through which diffracted light may pass, the path length to each slit in the grating varies. Since path length varies, generally, so do the phases of the waves at that point from each of the slits. Thus, they add or subtract from each other to create peaks and valleys through additive and destructive interference. When the path difference between the light from adjacent slits is equal to half the wavelength, λ/2, the waves are out of phase, and thus cancel each other to create points of minimum intensity. Similarly, when the path difference is λ, the phases add together and maxima occur. The maxima occur at angles θm, which satisfy the relationship d sinθm/λ = | m |, where θm is the angle between the diffracted ray and the grating's normal vector, and d is the distance from the center of one slit to the center of the adjacent slit, and m is an integer representing the propagation-mode of interest. Thus, when light is normally incident on the grating, the diffracted light has maxima at angles θm given by: