Grating diffraction angle7/30/2023 ![]() The apparently optimal blaze profile would incorporate the reflective surface inclined at an angle of 38º relative to horizontal. According to the grating equation, the only solutions are m = 0 and m = –1, and the –1 st order is diffracted at –22º (blue rays). Suppose light from a Ti:Sapphire laser at 800 nm is incident at 54º on a 1480 lines/mm gold reflection grating, as illustrated by the green rays in Figure 2. 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. Why would weaker diffraction cause a pattern further from the center? Center means "no diffraction", so "a tiny bit of diffraction" should translate to "a tiny bit from the center", and "a lot of diffraction" should translate to "a large distance from the center".Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference. However, it kind of feels intutive that a weaker diffraction should produce a interference pattern that is FURTHER from center (ie opposite of reality) Smaller wavelengths require a smaller path difference, and thus a smaller angle $\theta$, for constructive interference. Gratings have diffraction peaks for certain wavelengths whenever the optical difference between neighboring slits in the grating is a full wavelength, so constructive interference appears. Where $d$ is the spacing of the grooves in the grating, $\theta$ is the angle off the center, $\lambda$ is the wavelength and $m$ is the order of the peak, it is quite obvious. If you look at the formula for the diffraction peaks of a single wavelength
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