Edwin Jan Klein - Universiteit Twente

Chapter 2
differences between the filters become even more pronounced. The dropped power of
the single order MR is more than 12 dB below that of the cascaded MR. This large
difference is due to the very small coupling coefficients required for the single order
MR to achieve the 33 dB SRR. Combined with the high losses this only allows a small
power fraction to be dropped. Again the best filter of choice is the second order filter
with 1 dB more power dropped than the cascaded filter. Although this may seem to
implicate that, when a single order resonator is no longer sufficient for a specific task,
second order MR or even higher order filters are preferred over cascaded filters this is
largely dependent on the available technology. This is because the resonators in the
serially coupled higher order filters couple directly with each other. Due to the
circular geometry in the coupling region, however, the gap size between the
resonators may have to be quite small in order to achieve the required coupling
between the resonators. The choice between the filter types may therefore ultimately
be made based on the available lithography.
Table 2.2. MR Filter parameters required for SRR≈33 dB at αdB =10 dB/cm.
Single MR Cascaded MR Second order MR
κ1 0.09 0.48 0.57
κ2 0.09 0.48 0.57
κ21 0.48
κ22 0.48
κ3 0.19
Radius MR1 (µm) 50 50 50
Radius MR2 (µm) 50 50
ng 1.84 1.84 1.84
Instead of cascading the MRs in series they can also be placed in parallel [60-66] as
shown in Figure 2.17. This offers certain (fabrication) advantages over a series
coupled filter. In a series coupled filter the resonance wavelengths of all MRs have to
be identical for optimal performance. However, in a parallel MR filter the optical
signal goes through all MRs simultaneously which relaxes this strict requirement.
Also, because the resonators are all coupled directly to the port waveguides in stead of
each other, the lithographical requirements are more relaxed because no (typically
small) coupling gaps are present between the resonators. The disadvantage, however,
is that the distance Lc between the resonators is a highly important parameter in the
performance of these filters and should typically be as close to a small odd multiple of
a quarter wavelength [60] for optimum filter performance.
Figure 2.17. Second order serial MR.
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