![]() To verify this claim, consider the following example. Blazing is not necessary for single-order gratings: However, this intuition is not accurate when the wavelength of light is comparable to or larger than the grating period. It might seem reasonable that the highest possible diffraction efficiency in one order should occur when the grating equation permits only a single nonzero order and the groove profile is blazed according to the law of reflection as shown in Figure 1. The most effective way to channel as much light as possible into a single order is to make the grating period Λ small enough to eliminate all other nonzero orders as solutions to the grating equation (see Figure 7 in ). When interference permits multiple diffracted orders, even a perfectly optimized groove profile is not sufficient to achieve nearly 100% DE into a single order. ![]() Figure 1 Achieving maximum diffraction efficiency in a single order:įor many gratings, especially those designed for use with lasers, it is desirable for all of the incident light to be diffracted into a single order to minimize loss in the overall system. Referring to the example of a reflection grating in Figure 1, to direct as much light as possible into a specific order –M, the grating should be blazed as shown in the figure with the blaze angle chosen so that the incident and –M th order rays obey the law of reflection (equal angles relative to the normal to the surface of reflection). Formally, the diffraction efficiency (DE) associated with an order m is the ratio of the optical power P m that propagates away from the grating in order m to the optical power P inc incident on the grating, orįor larger-period or lower-frequency gratings in which many orders exist, the choice of groove profile to direct light into a particular order is intuitive. In other words, the profile of the grating grooves dictates the efficiency with which light diffracts into each of the orders. How much light diffracts into each direction is determined by the principle of diffraction at a microscopic level. The PGL Technical Note “The Grating Equation” describes how to predict the different directions light propagates from a grating using optical interference. Diffraction from the groove profile determines efficiency in each order: If the surface irregularity is periodic, such as a series of grooves etched into a surface, light diffracted from many periods in certain special directions constructively interferes, yielding replicas of the incident beam propagating in those directions. When light is incident on a surface with a profile that is irregular at length scales comparable to the wavelength of the light, it is reflected and refracted at a microscopic level in many different directions as described by the laws of diffraction. Therefore, the wavelength of light will ne 146.7 nano meter.Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference. In this formula, \(\theta\) is the angle of emergence at which a wavelength will be bright. This is known as the DIFFRACTION GRATING EQUATION. Constructive interference will occur if the difference in their two path lengths is an integral multiple of their wavelength \(\lambda\) i.e., The formula for diffraction grating:Ĭonsider two rays that emerge making the angle \(\theta\) with the straight through the line. Diffraction is an alternative way to observe spectra other than a prism. ![]() Also, if peaks fall on peaks and valleys fall on valleys consistently, then the light is made brighter at that point. If a peak falls on a valley consistently, then the waves cancel and no light exists at that point. Here Huygens’ Principle is applicable.Īccording to it every point on a wavefront acts as a new source, and each transparent slit becomes a new source so cylindrical wavefront spread out from each. ![]() Rays and wavefront form an orthogonal set so the wavefront will be perpendicular to the rays and parallel to the grating. 2 Solved Examples Diffraction Grating Formula Concept of the diffraction gratingĪ parallel bundle of the rays will fall on the grating. ![]()
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