Lect. 13: Total Internal Reflection - Yonseitera.yonsei.ac.kr/class/2016_1_1/lecture/Lect 14...
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E&M 2 (14/1) W.-Y. Choi Lect. 13: Total Internal Reflection i E i x y z 0 0 2 , t θ r θ r E t E t H r H i H 0 0 , (Cheng, 8-10.1)
Transcript of Lect. 13: Total Internal Reflection - Yonseitera.yonsei.ac.kr/class/2016_1_1/lecture/Lect 14...
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
iE
i
x
y z
0 02 , tθrθ
rEtE
tH
rH
iH
0 0,
(Cheng, 8-10.1)
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
1 2Snell's Law: sin sini tn n
i
r t
1medium 2medium
z
x1 2From B.C.'s, and i r x x
1 2If , i tn n
What happens when ? i c
When ,i c 2 2 2
2 2 2Since ,x z 2
2 < 0 z
2Let , z j
2 22~ x xzj x j xj z ztE e e e e
Total Internal Reflection
12 2 2 2
1 0 2 0[( sin ) ]in k n k 2 22 2 x
2 2 22 2so that x
2
1
= 90 when sint inn
(Critical angle, )c
2 1x x 2
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
Theta=50 deg Theta=70 deg
-11 2 1 2 c
12 , , sin ( ) 452
2 22~ x xzj x j xj z ztE e e e e
Evanescent wave, Surface wave
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
Optical fiber for optical communication
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
2 1
2 1
1 1cos cos1 1
cos cos
t i
t i
n n
n n
What is for TIR?
/ cos / cos2 1/ cos / cos2 1
t it i
From Snell’s Law: :1 2sin sini tn n
2 2 2 21
2
cos 1 sin 1 ( ) sint t inn
2 2 1/ 21( )
2
cos 1 ( ) sint inn
2 2 1/211 2
2
2 2 1/211 2
2
cos (1 ( ) sin )
cos (1 ( ) sin )
i i
i i
nn nnnn nn
1 2
1 2
cos coscos cos
i t
i t
n nn n
2 1
2 1
1 1cos cos
1 1cos cos
t i
t i
2 1/22
1
2 1/22
1
cos ( sin )
cos ( sin )
i i
i i
nnnn
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
12 2 2
21
2 2 2 1
cos sin with
cos sin
i i
i i
n nnnn
12 2 2
12 2 2
cos sin
cos sin
i i
i i
j n
j n
1,
je
1 12 2 2 22 2-1 -1(sin ) (sin )=tan ( ) ( tan ( ))
cos cosi i
i i
n n
It can be shown for parallel polarization,
||
12 2 2-1
|| || 2
(sin ), = + 2tan ( )cos
j i
i
nen
1 12 2 2 22 2 Let sin sini in j n
12 2 2-1 (sin )2tan ( )
cosi
i
n
Since sin , c n sin for TIRi n
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
i r
t
1 1.44n
2 1.0n
inE rE
tE
E&M 2 (14/1) W.-Y. Choi
Lect. 13: Total Internal Reflection
Beam SplitterDielectric Mirror
- Use of TIR: Dielectric waveguide
