For diffracted light traveling left-to-right, θ m ≥ 0, whereas for diffracted light traveling right-to-left, θ m ≤ 0. Incident light is shown traveling left-to-right, for which the angle θ ≥ 0. Note the sign conventions for the angles. This 0 th order is typically not considered a diffracted order since it does not provide any angular dispersion (change in angle with change in wavelength). Referring to Figure 2, there will be three diffracted orders ( m = –2, –1, and +1) along with the specular reflection ( m = 0). As an example, suppose a HeNe laser beam at 633 nm is incident on an 850 lines/mm grating.
The larger the period Λ, or the lower the frequency f, the more orders there are. (2) A graphical example of the grating equation: Figure 2 In terms of f the grating equation becomes Often gratings are described by the frequency of grating lines instead of the period, where f (in lines/mm) is equal to 10 6/Λ (for Λ in nm). For a given angle of incidence, θ, it gives the angle of diffraction θ m for each “order” m for which a solution to (1) exists. Since AB = Λsinθ m and A’B’ = Λsinθ, where Λ is the grating period and θ m and θ are the angles of diffraction and incidence, respectively, relative to the surface normal, the condition for constructive interference is Mathematically, the difference between paths AB and A’B’ is a multiple of the wavelength when AB – A’B’ = mλ, where m is an integer and λ is the wavelength of light (typically stated in nm).
If the difference between adjacent green-blue ray paths diffracted off of identical locations on adjacent periods is equal to a multiple of the wavelength of light, the two blue rays interfere constructively. The light is diffracted in many directions, only one of which is indicated by the blue rays. Referring to Figure 1, imagine a beam of light represented by the two green rays incident on the binary (rectangular profile) grating shown. Constructive interference leads to the grating equation: Figure 1
#Reflection grating series#
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. Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference.
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