Biomedical Engineering Reference
In-Depth Information
20
18
16
14
d
1
12
10
8
d
1
d
0
6
4
d
0
2
0
1
3
5
7
9
11
13
15
17
N
D
(#/cm
3
) × 10
17
FIGURE 5.1
Cutoff thickness versus substrate doping for λ
0
= 1.3 μm.
2
+
2
2
ε
m
ω π
⎛
⎜
1
⎞
⎟
0
N N
−
≥
(5.5)
3
1
2
2
2
4
e
2
π
d
/
λ
+
1
/(
n
−
n
)
0
2
3
In general, the carrier compensation necessary for guiding the TE
1
(1-th
order) mode is given by the expression
2
2
+
2
2
ε
m
ω π
1
2
⎛
⎜
1
⎞
⎟
⎛
⎜
⎞
⎟
0
N N
−
≥
1
+
(5.6)
3
1
2
2
2
4
e
2
π
d
/
λ
+
1
/(
n
−
n
)
0
2
3
Figures 5.1 through 5.3 illustrate representative cutoff thickness versus sub-
strate doping curves for three wavelengths of interest. The assumption is
made that essentially complete carrier compensation will occur in the wave-
guide fabrication process.
5.2 Comparisonof“Exact”andNumerical
ChannelWaveguideTheories
A number of workers have analyzed lossless dielectric waveguide structures
including Marcatili, Goell, Schlosser, Bartling, and Shaw [2]. Goell repre-
sented the radial variation of the longitudinal electric and magnetic fields of
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