Edwin Jan Klein - Universiteit Twente

3.6 Lateral resonator design
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Design
The laterally coupled micro-resonator, although being easier to fabricate than the
vertically coupled resonator, is more complicated to design.
The higher complexity is due to the fact that both the resonator and port waveguides
are defined in the same optical layer and therefore inherently have the same
waveguide thickness. The only variable that therefore makes the difference between a
resonator and a port waveguide is their width. For a resonator the width is generally
chosen large to reduce its bending losses. The width of the port waveguides on the
other hand has to be small enough to ensure mono-modality. Increasing the width of
the resonator, however, can only reduce the bending losses by a limited amount.
Therefore, if after widening the waveguide the losses are still too high for a certain
desired radius, the only option is to increase the layer thickness. This will in turn
require a reduction in de width of the port waveguides so that these remain monomodal.
Although this balancing act works to a certain degree it is ultimately limited
by the fabrication technology that places a lower limit on the width of the
waveguides.
Additional complexity is added to the design process when the laterally coupled
micro-resonator is a true ring-resonator. In such a resonator the phase matching
between the resonator and port waveguides has to be considered in the design. This
complicates the design task because the resonator and port waveguides have the same
height and can therefore only be varied in width to keep the difference between their
refractive indices as low as possible.
The problem of the phase matching can be avoided altogether by choosing a racetrack
instead of a ring resonator. As was previously mentioned in Section 3.3.1 this type of
resonator has slightly higher roundtrip losses due to the overlap losses between the
bend and straight waveguide sections that make up the resonator. By careful design,
however, these losses can remain low and in many devices the additional losses can
be compensated for by an increase of the coupling coefficients. In high index devices
made in, for instance, silicon this might not even be necessary since the overlap losses
are typically very small for these devices.
For this reason all the lateral resonators presented in later chapters are of the racetrack
type. An additional reason for doing so was the fact that the lithography at the
MESA+ Research institute [111] simply cannot reliably define gaps smaller than 0.7
µm. Midrange coupling coefficients (≈0.5) would therefore simply not be possible for
a small-radius ring-resonator.
The design of the laterally coupled racetrack resonator, like that of the vertically
coupled resonator, can be described in three phases. These can be summarized as:
• Decide in which material system the resonator will be fabricated.
• Design the resonator and the port waveguides such that the desired radius is
reached at acceptable roundtrip losses, the port waveguides are monomodal
and the overlap losses are small.
• Set the field coupling coefficients to their required values. For the racetrack
resonator this is achieved by choosing an appropriate length of the straight
waveguide section of the racetrack.