Edwin Jan Klein - Universiteit Twente

Chapter 4
As demonstrated by these two second order micro-resonator filter examples the
current simulation method is very sensitive to optical circuits with loops of differing
optical path lengths. This sensitivity is largely due to the currently used call-insertion
algorithm of which the time required for insertion scales with the number of calls in
the call-list as T ( n)
∈ O(
n)
. However, the use of more efficient algorithms, such as
the B-Tree [121], the Binary tree [122] or Skip lists [123] that scale according to
T ( n)
∈ O(log
n)
, can greatly reduce this sensitivity and easily improve the simulation
time by an order of magnitude for complex optical circuits.
4.5.5 Simulations on complex structures
The strength of Aurora and other similar tools [124, 125] is that optical circuits can be
evaluated with a minimum in effort and often in a fraction of the simulation time
required by more rigorous methods. This also allows a user to quickly test a new idea
and even stimulates “play-time”: just try random optical circuits and see if any
interesting effects occur.
4.5.5.1 The hyper-resonator
One optical circuit that emerged form this “play” is the “Hyper-resonator” which
features on the cover of this thesis and shown again here in Figure 4.32a. While this
device may seem quite simple at first glance, closer inspection reveals a highly
complex high-order filter device in which light propagates in two directions in all
waveguide sections. The complex behavior for such a seemingly simple geometry
made this device a prime candidate for simulation in Aurora as such devices might
display interesting and perhaps useful filter properties.
A simulation was therefore created as shown in Figure 4.32b. Although the ratio of
the resonators radii in Figure 4.32a is by definition given by:
3 + 2 3
ROuter = RInner
≈ 2.
15RInner
(4.31)
3
a ratio of 3 was chosen instead. This ratio is more realistic from the perspective of
fabrication and removes any wide-range Vernier effects between the resonators that
may obfuscate some of the more interesting effects in this device.
In
Reflected
Figure 4.32a. “Hyper-resonator”
layout.
Figure 4.32b. Aurora simulation circuit to simulate the
hyper-resonator. All lengths are in micrometers.
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