Topic 3 Dielectric Waveguides and Optical Fibers 2-1 Symmetric ...

α B (m -1 ) for 10 cm of bend
10 2
10 −1
10 −2
10 −3
901 37500 光電導論 ?1999 S.O. Kasap, Optoelectronics (Prentice Hall)
901 37500 光電導論
10
1
λ = 633 nm
V ≈ 2.08
λ = 790 nm
V ≈ 1.67
0 2 4 6 8 10 12 14 16 18
Radius of curvature (mm)
Measured microbending loss for a 10 cm fiber bent by different amounts of radius of
curvature R. Single mode fiber with a core diameter of 3.9 μm, cladding radius 48 μm,
Δ = 0.004, NA = 0.11, V ≈ 1.67 and 2.08 (Data extracted and replotted with Δ correction
from, A.J. Harris and P.F. Castle, IEEE J. Light Wave Technology, Vol. LT14, pp. 34-
40, 1986; see original article for discussion of peaks in αB vs. R at 790 nm).
77
Example 2.9.1: Rayleigh scattering limit
What is the attenuation due to Rayleigh scattering at around the
λ = 1.55μm window given that pure silica (SiO 2 ) has the following
properties: T f = 1730°C (softening temperature);
β T = 7 x 10 -11 m 2 N -1 (at high temperatures);
n = 1.4446 at 1.5μm.
α
≈
3
=
R
8π
≈
3λ
3
4
2 ( n −1)
3
8π
2 2 −11
−23
( 1.
4446 −1)
( 7×
10 )( 1.
38×
10 )( 1.
730 + 273)
−6
4
( 1.
55×
10 )
3.
27×
10
−5
Attenuation
α
dB
= 4.
34α
m
R
−1
=
2
=
β
T
k
B
T
3.
27×
10
f
−2
km
−1
−2
−1
−1
( 4.
34)(
3.
27×
10 km ) = 0.
142dBkm
79
Example 2.9.1: Rayleigh scattering limit
What is the attenuation due to Rayleigh scattering at around the
λ = 1.55μm window given that pure silica (SiO 2) has the following
properties: T f = 1730°C (softening temperature);
β T = 7 x 10 -11 m 2 N -1 (at high temperatures);
n = 1.4446 at 1.5μm.
901 37500 光電導論
Example 2.9.2: Attenuation along an optical fiber
The optical power launched into a single-mode fiber from a laser
diode is approximately 1 mW. The photodetector at the output
required a minimum power of 10 nW to provide a clear signal (above
noise). The fiber operates at 1.3μm and has an attenuation coefficient
of 0.4 dB km -1 . What is the maximum length of fiber that can be used
without inserting a repeater (to regenerate the signal)?
α
dB
1
L =
α
901 37500 光電導論
1 ⎛ P
= 10log
L ⎜
⎝ P
dB
in
out
⎛ P
10log
⎜
⎝ P
in
out
⎞
⎟
⎠
−3
⎞ 1 ⎛10
⎞
⎟ = 10log
= 125km
8
0.
4 ⎜
10 ⎟ −
⎠ ⎝ ⎠
The signal has to be amplified after a distance of about 50 ~
100km, and eventually regenerated by using a repeater.
78
80