Optimal design of photonic crystals 52

λ
h
CL,1
λ
h
WG,1
λ
h
WG,2
0.8
1
1.2
1.4
0.8
1
1.2
1.4
0.8
1
1.2
1.4
||H
2
(β
1
)||
2
−
||H
2
(β

1
)||
2
^
||H
2
(β
2
)||
2
−
||H
1
(β
1
)||
2
^
Figure 5.6: β
2
= 2. The figures in the columns from left to right each represent
the case: (left)initial configuration, with band width J
h
= 0.0036 (
ˆ
β
1
= 1.9367);
(middle) optimal configuration when only cladding is optimized, with band width
0.0307 (

ˆ
β
1
= 1.9385); (right) optimal configuration when both cladding and
core are optimized, with band width J
h
= 0.1113 (
ˆ
β
1
= 1.7807). The first
row illustrates the PCF cross-sections. The second row shows the corresponding
dispersion relations between [
ˆ
β
1
, β
2
]. From the third row to the last, the magnetic
field intensities at both
ˆ
β
1
and β
2
are shown in 3D surf plots.
130
λ
h
CL,1

λ
h
WG,1
λ
h
WG,2
0.16
0.18
0.2
0.12
0.14
0.16
0.18
0.2
0.12
0.14
0.16
0.18
0.2
0.12
0.14
||H
2
(β
1
)||
2
−
||H
2

(β
1
)||
2
^
||H
2
(β
2
)||
2
−
||H
1
(β
1
)||
2
^
Figure 5.7: β
2
= 0.8. The figures in the columns from left to right each repre-
sent the case: (left)initial configuration, with band width J
h
= 0.014 (
ˆ
β
1
= 0.79);
(middle) optimal configuration when only cladding is optimized, with band width

J
h
= 0.074 (
ˆ
β
1
= 0.74); (right) optimal configuration when both cladding and
core are optimized, with band width J
h
= 0.1 (
ˆ
β
1
= 0.72). The first row illus-
trates the PCF cross-sections. The second row shows the corresponding disper-
sion relations between [
ˆ
β
1
, β
2
]. From the third row to the last, the magnetic field
intensities at both
ˆ
β
1
and β
2
are shown in 3D surf plots.
131