opto-electronics and photonicstera.yonsei.ac.kr/class/2020_2_1/lecture/lecture 8...
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Opto-Electronics and
Photonics
Woo-Young Choi
Dept. of Electrical and Electronic EngineeringYonsei University
Lecture 8: Normal Incidence at Dielectric Interface
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
0 1exp( ) ,iE yE j zb= -
Unknowns:
rE
11
11
,,hbme
iE22
22
,,hbme
tE
x
zy
rH =
iH =
tE =
rE =
22
exp( )ttEH x j zbh
= - -
0s =
(Cheng 8-8)
01
1
exp( )Ex j zbh
- -
11
exp( )rEx j zbh
Er, Et
1exp( ) ,ryE j zb
2exp( ) ,tyE j zb-
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
0 1exp( ) ,iE yE j zb= -
1) Etan should be continuous at z=0
rE
11
11
,,hbme
iE22
22
,,hbme
tE
: reflection coef.: transmission coef .t
G
x
zy
11
exp( )rrEH x j zbh
=
01
1
exp( )iEH x j zbh
= - -
2exp( ) ,t tE yE j zb= -
1exp( ) ,r rE yE j zb=
22
exp( )ttEH x j zbh
= - -
0 r tE E E+ =
0 0Define , and r tE E E Et= G =
1 tÞ + G =
B.C.’s
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
2) Htan should be continuous at z=0
2 1( )n sa H H J´ - =
i r tH H H+ =
12
2
12
12 2, ηηητηη
ηη+
=+-
=G
0=
rE
11
11
,,hbme
iE22
22
,,hbme
tE
11
exp( )rrEH x j zbh
=
01
1
exp( )iEH x j zbh
= - -
22
exp( )ttEH x j zbh
= - -
0
1 1 2
trE EEh h h
- + = -
1 1 2
1 ,th h h
G\- + = - (1 )t+ G =
0s =
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
rE
11
11
,,hbme
iE22
22
,,hbme
tE
G =
mhe
=
12
2
12
12 2, ηηητηη
ηη+
=+-
=G
In dielectric materials,
0m m= e = 0re e2
0n e=
n: refractive index1me
=0 0
1n m e
2 1
2 1
2 1
2 1
m me em me e
-
-
2 0 1 0
2 0 1 0
1 1 1 1
1 1 1 1n n
n n
e e
e e
-=
+
1 2
1 2
,n nn n
-=
+1
1 2
2nn n
t =+
0nb w me b= =
-
Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
rE
1n
iE
2n
tEMax. :G
:t
1, 1 2n n>>
Min. :G:t
-1, 1 2n n
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
Incident and Transmitted waves
Reflected and Transmitted waves
rE
1 1n =
iE
2 2n =
tE
1 2
1 2
n nn n
-G =
+13
= -
1
1 2
2nn n
t =+
23
=
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
Total waves
rE
1 1n =
iE
2 2n =
tE
1 2
1 2
n nn n
-G =
+13
= -
1
1 2
2nn n
t =+
23
=
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
Total E-field for z
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
1 0 1 00( 0) ( )
jn z jn ztotalE z yE e e
b b-< = + G
totalE =
G+1
G-1
z02λ-
1 0 1 020 (1 )
jn z j n zyE e eb b-= + G
1 020 1
j n zE e b+ G
Im
)0(1
=G+
zG-1
0
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
Total H-field for z
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Opto-Electronics and Photonics (2020/2) W.-Y. Choi
Lecture 8: Normal Incidence at Dielectric Interface
Homework (Due 9/28)
1( Re )2av
P E H *é ù= ´ë û
Determine the vector expression for the average power density propagation.