Lect. 13: Dielectric Waveguide (2)

Lect. 13: Dielectric Waveguide (2)
E(y) profile: n 1 =1.5, n 2 =1.495, d=10μm, λ=1μm
TE 1
TE
1 TE 2
Optoelectronics (10/2)
W.-Y. Choi

Lect. 13: Dielectric Waveguide (2)
E(y) profile: n 1 =1.5, n 2 =1.495, d=10μm, λ=1μm
TE 1
TE 3
TE
1 TE 2
Optoelectronics (10/2)
W.-Y. Choi

Lect. 13: Dielectric Waveguide (2)
Wave is not entirely confined within core: Confinement factor
Power inside core
Γ= =
Total Power
d
y= 2
2
∫
d
y=−
2
y=∞
∫
y=−∞
E( y)
E( y)
2
dy
dy
For higher modes, how does Γ change
Optoelectronics (10/2)
W.-Y. Choi

Lect. 13: Dielectric Waveguide (2)
Partitioning of input field into different guided modes.
n 2
E ( ) in
y
n 1
+ +
Ein( y) ≅ ∑ amEm( y)
n 2
For a , use the fact that E ( y)'s are orthogonal.
m
∫ ∫∑
E ( y ) E ( y ) dy ≈
a E ( y ) ⋅
E ( y )
dy
in m n n m
n
= ∫
∫ in m
∴ am
=
2
∫ E y dy
a E
m
E ( y) E ( y)
dy
m
( )
m
2
m
( y)
dy
m
Optoelectronics (10/2)
W.-Y. Choi

Lect. 13: Dielectric Waveguide (2)
ω
Slope = c/n 2
Sl / Slope = c/n 1
TE 3
TE 2
TE 2
ω cut-off
TE 1
β m
Schematic dispersion diagram, ω vs. β for the slab waveguide for various TE m . modes.
ω cut–off Group corresponds velocities to V are = π/2. different The group for velocity different v g modes at any => ω is modal the slope dispersion of the ω vs. β
curve at Need that frequency. a single-mode waveguide in order to avoid signal distortion.
How do you design a single mode waveguide
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Optoelectronics (10/2)
W.-Y. Choi

Lect. 13: Dielectric Waveguide (2)
n 3
cladding
b-V diagram for TE mode
d
n 1
core
n 2
1
2 2 2
0
(
1 2
)
V = kd( kdn − n )
(Normalized k)
b =
⎛β
⎜
⎝ k
n
2
⎞
⎟ − n
⎠
0
2 2
1
−
n
2
2
2
(Normalized β )
b
a =
n
− n
2 2
2 3
2 2
n1 − n2
(Asymmetry factor)
V
Optoelectronics (10/2)
W.-Y. Choi