Edwin Jan Klein - Universiteit Twente

25
The Micro-Resonator
In a higher order serial filter [53-58], of which the second order variant is shown in
Figure 2.12b the intermediate waveguide between the micro-resonators is omitted and
light is coupled directly between the resonators. This causes the light not only to
resonate in the individual resonators but also between the resonators. This can also be
seen in Figure 2.13b that shows the drop port model of the second order resonator in
Figure 2.13a. In this model the feedback loops that account for the resonance in the
individual resonators (short dash boxes) are supplemented by an additional feedback
loop (long dash) that creates an additional resonance.
Figure 2.13a. Model parameters for a second order serial MR filter.
In
Figure 2.13b. Simplified drop-port model of a second order serial MR filter.
It is this additional feedback loop that gives the response of this filter some interesting
properties when compared with the cascade filter. The drop response of this filter can
be derived from Figure 2.13b and is given by:
− j(
ϕ
2
1 + ϕ 2 )
2
Drop
jκ1κ
2κ3
⋅ e χr1χ
r 2
= − jϕ1
− jϕ
2
− j(
ϕ1
+ ϕ 2 )
PIn
1− µ 1µ
2 ⋅ e χr1
− µ 2µ
3 ⋅ e χr
2 + µ 1µ
3 ⋅ e χr1
⋅ χr
2
P
-jκ1
µ1
µ1
+
e
e
e
IIn
−
jϕr 2 −αr
2 2
. e
− jϕr1 −αr
2 2
. e
− jϕr1 −αr1
2 2
. e
1
2
α2, φ2
α1, φ1
IThrough
where αn and φn are the loss and phase terms of the respective resonators.
κ3
κ2
κ1
µ2
− jϕr 2 −αr
-jκ2 2 2
-jκ2
µ2
+
e
e
e
. e
− jϕr 2 −αr
2 2
. e
− jϕr 2 −αr
2 2
. e
2
2
2
µ3
µ3
-jκ3
Drop
(2.33)