The maximum wavelength that a grating can diffract is equal to twice the grating period, in which case the incident and diffracted light will be at ninety degrees to the grating normal. The groove period must be on the order of the wavelength of interest the spectral range covered by a grating is dependent on groove spacing and is the same for ruled and holographic gratings with the same grating constant. Gratings are usually designated by their groove density, the number of grooves per unit length, usually expressed in grooves per millimeter (g/mm), also equal to the inverse of the groove period. The efficiency of a grating may also depend on the polarization of the incident light. The incident angle and wavelength for which the diffraction is most efficient are often called blazing angle and blazing wavelength. By controlling the cross-sectional profile of the grooves, it is possible to concentrate most of the diffracted energy in a particular order for a given wavelength. The grating equation shows that the angles of the diffracted orders only depend on the grooves' period, and not on their shape. The higher the spectral order, the greater the overlap into the next order. The diffracted beams corresponding to consecutive orders may overlap, depending on the spectral content of the incident beam and the grating density. In the first positive order ( m = +1), colors with increasing wavelengths (from blue to red) are diffracted at increasing angles. The order m = 0 corresponds to a direct transmission of light through the grating. This is visually similar to the operation of a prism, although the mechanism is very different.Ī light bulb of a flashlight seen through a transmissive grating, showing three diffracted orders. Each wavelength of input beam spectrum is sent into a different direction, producing a rainbow of colors under white light illumination. The wavelength dependence in the grating equation shows that the grating separates an incident polychromatic beam into its constituent wavelength components, i.e., it is dispersive. The grating equation applies in all these cases. direction of optical axis (optical axis gratings).reflectance (reflection amplitude gratings).transparency (transmission amplitude gratings).Gratings can be made in which various properties of the incident light are modulated in a regular pattern these include The detailed distribution of the diffracted light depends on the detailed structure of the grating elements as well as on the number of elements in the grating, but it will always give maxima in the directions given by the grating equation. However, the relationship between the angles of the diffracted beams, the grating spacing and the wavelength of the light apply to any regular structure of the same spacing, because the phase relationship between light scattered from adjacent elements of the grating remains the same. This derivation of the grating equation has used an idealized grating. Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam. The other maxima occur at angles which are represented by non-zero integers m. The light that corresponds to direct transmission (or specular reflection in the case of a reflection grating) is called the zero order, and is denoted m = 0. Thus, the diffracted light will have maxima at angles θ m given byĭ sin θ m = m λ. This occurs at angles θ m which satisfy the relationship dsin θ m/λ=| m| where d is the separation of the slits and m is an integer. However, when the path difference between the light from adjacent slits is equal to the wavelength, λ, the waves will all be in phase. Generally, the phases of the waves from different slits will vary from one another, and will cancel one another out partially or wholly. The light in a particular direction, θ, is made up of the interfering components from each slit. When a plane wave of wavelength λ, is incident normally on the grating, each of the point slits in the grating acts as a set of point sources which propagate in all directions. When a wave propagates, each point on the wavefront 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.Īn idealized grating is considered here which is made up of a set of long and infinitely narrow slits of spacing d. The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation.
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