Concept of Diffraction Gratings - EMPossibleDiffraction from Gratings Slide 4 The field is no longer...
Transcript of Concept of Diffraction Gratings - EMPossibleDiffraction from Gratings Slide 4 The field is no longer...
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Advanced Electromagnetics:
21st Century Electromagnetics
Concept of Diffraction From Gratings
Fields are Perturbed by Objects
Slide 2
A portion of the wave front is delayed after travelling through the dielectric object.
inck
The rest of the wave front is not delayed.
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Fields in Periodic Structures
Slide 3
Waves in periodic structures take on the same periodicity as their host.
k
1,trnk
2,trnk
3,trnk
4,trnk 5,trnk
x
x
Diffraction from Gratings
Slide 4
The field is no longer a pure plane wave. The grating “chops” the wave front and sends the power into multiple discrete directions that are called diffraction orders.
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Reason for Discrete Diffraction Orders (1 of 2)
Slide 5
The field must be continuous so only discrete directions are allowed. The allowed directions are called the diffraction orders.The allowed angles are calculated using the famous grating equation.
Allowed Not Allowed Allowed
Reason for Discrete Diffraction Orders (2 of 2)
Slide 6
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Grating Lobes
Slide 7
If the power exiting a periodic structure is plotted as a function of angle, the following would be obtained. The power peaks are called grating lobes or sometimes side lobes. The power minimums are called nulls.
Grating Lobe Level
Main Beam (Zero‐order mode)
inc incincr,avg 2 2
j k K r j k K rjk r A AA e e e
Field in a Periodic Structure
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r r,avg cosr K r
A wave 𝐸 𝑟 propagating through this grating takes on the same symmetry as the grating.
incjk rAE r er
incr,avg cos jk rA K r e
Wave 1 Wave 2 Wave 3
The dielectric function 𝜀 𝑟 of a sinusoidal grating can be written as
2K
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Grating Produces New Waves (1 of 7)
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A wave 𝑘 enters the diffraction
grating defined by grating vector 𝐾…
Grating Produces New Waves (2 of 7)
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…and splits into three waves.
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Grating Produces New Waves (3 of 7)
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Then each of these splits into three waves…
Grating Produces New Waves (4 of 7)
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…and each of these splits into three waves…
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Grating Produces New Waves (5 of 7)
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…and so on.
Grating Produces New Waves (6 of 7)
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Grating Produces New Waves (7 of 7)
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All possible directions are defined by
inc
any integer
k m k mK
m
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