Edwin Jan Klein - Universiteit Twente

Chapter 2
The figure shows that it can be very difficult if not impossible to create a single ring
resonator that achieves a high rejection ratio as well as a large bandwidth. Assuming
for instance that a resonator with an effective radius of ≈87 µm, similar to that of the
basic resonator building block presented in later chapters, is used in a device with
bandwidth requirements of 40 GHz then an SRR of at most 20 dB can be achieved.
While this may be sufficient in some cases, typical telecom applications often require
rejection ratios at least an order of magnitude higher.
Decreasing the radius of a resonator can be a possible solution to this problem. In
most cases, however, the minimum radius of the resonator is limited by the choice of
materials and the fabrication technology. An attractive alternative is then offered by
higher order filters, which will be discussed in the next paragraph.
2.6 Multiple-resonator filters
Similar to the higher order filters well known from the field of electronic engineering
multiple resonators can also be combined to form more complex filters. Although the
higher number of resonators requires more space on-chip or, in some cases, is more
technologically demanding, the resulting filter characteristics can often be very
rewarding. Figure 2.12 shows two of the most common filter implementations. These
are the first order resonator cascade and second order serial filter in Figures 2.12a and
2.12b respectively.
Figure 2.12a. First order MR cascade. Figure 2.12b. Second order serial MR.
The first order cascade filter in Figure 2.12a already has significant advantages over a
single micro-resonator. It is created by using multiple resonators of equal geometry
where each resonator has its own set of port waveguides that guide light from one
resonator to the next. Because this type of filter is based on multiple copies of the
basic single resonator geometry it is relatively straightforward to calculate the
response. The filter function is given by:
n
Drop
P
P
In
⎛ H
= ⎜
⎝1
+ FC
⋅sin
(
24
2
ϕr
/ 2)
where n is the number of resonators in the cascade.
⎞
⎟
⎠
n
(2.32)