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Opto-Electronics and
Photonics
Woo-Young Choi
Dept. of Electrical and Electronic Engineering
Yonsei University
Lecture 14 : Diffraction Gratings
![Page 2: Lecture 14 Diffraction Gratings - Yonseitera.yonsei.ac.kr/class/2020_2_1/lecture/Lecture 14... · 2020. 10. 27. · Microsoft PowerPoint - Lecture 14 Diffraction Gratings Author:](https://reader036.vdocuments.us/reader036/viewer/2022071418/6116bfa0cc826146aa14e01c/html5/thumbnails/2.jpg)
Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
![Page 3: Lecture 14 Diffraction Gratings - Yonseitera.yonsei.ac.kr/class/2020_2_1/lecture/Lecture 14... · 2020. 10. 27. · Microsoft PowerPoint - Lecture 14 Diffraction Gratings Author:](https://reader036.vdocuments.us/reader036/viewer/2022071418/6116bfa0cc826146aa14e01c/html5/thumbnails/3.jpg)
Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
sin2
2
y
y
ak
ak
slit shape (y) far-field (ky)
Fourier Transform
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
a
d
● ● ● ● ● ● *
×
FourierTransform
● ● ●● ● ●
2
d
yk
a
ya
d
Diffracted light from periodic opening
(Assume infinitely many for simplicity)
==> Far-field only for discrete ky's
yk yk
(Diffraction Grating)
yk 2
md
sink
d
● ● ●
y
● ● ●
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
a
d
2yk m
d
Grating equation
2 2sin m
d
sind m
yk
(Bragg Condition)
William Lawrence Bragg(1890-1971)
William Henry Bragg(1862-1942)
Nobel Prize in Physics (1915)
W. L. Bragg is the youngest Nobel Physics winner
The only father-son joint Nobel winner
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
sind m
Width for each diffracted beam?
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
Finite grating length
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
i
Input with tilted angle
(sin sin )ijkytotal
AE e dy
R
(2)
(1)y
R
sin sini ijky jkyAe e
R
sinjkyAe
R
sinjkytotal
AE e dy
R
siny
sin iy
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
Normal Incidence on Grating
msinsind isind m
Tilted incidence on Grating
sinjkytotal
AE e dy
R
(sin sin )ijky
total
AE e dy
R
![Page 10: Lecture 14 Diffraction Gratings - Yonseitera.yonsei.ac.kr/class/2020_2_1/lecture/Lecture 14... · 2020. 10. 27. · Microsoft PowerPoint - Lecture 14 Diffraction Gratings Author:](https://reader036.vdocuments.us/reader036/viewer/2022071418/6116bfa0cc826146aa14e01c/html5/thumbnails/10.jpg)
Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
Reflection-type grating
R=1
R=0
Grating realized with periodic shaping of reflection surface
sin sin id m Same diffraction equation
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
sin sinout ind m
2 2sin sinout in m
d
,y outk
Grating shifts ky,in by integer multiples of 2/d
2 2 2sin sinout in m
d
K-vector perspective?
,y ink 2 m
d
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
Grating imposes BC on the incident wave
( 0, )x ( )inE x y f y( 0, )rE x y
Far-Field Diffraction:
( )f y 2
exp( )mm
a jm yd
F.T. of ( 0, )x ( )inE x y f y
( )y outE k ( ) y inE k
,y outk ,y ink 2 m
d
Spatial modulation Sidebands formation
● ● ●
ky2
d
● ● ●
*
y
x
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
2-D Diffraction Grating
Take x and y separately
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 14: Diffraction Grating
Homework (11/1)