Opto-Electronics and

Photonics

Woo-Young Choi

Dept. of Electrical and Electronic Engineering

Yonsei University

Lecture 14 : Diffraction Gratings

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 14: Diffraction Grating

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

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

● ● ●

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

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 14: Diffraction Grating

sind m

Width for each diffracted beam?

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 14: Diffraction Grating

Finite grating length

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

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

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

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

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

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 14: Diffraction Grating

2-D Diffraction Grating

Take x and y separately

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 14: Diffraction Grating

Homework (11/1)