Edwin Jan Klein - Universiteit Twente

Chapter 3
3.1 Introduction
The most important question that needs to be addressed when designing a microresonator
or a component comprised of multiple micro-resonators is: “For what will
the resonators be used ?”. Micro-resonators are often considered as the basic building
blocks for optical circuitries of the future and, like their electronic counterpart, the
transistor, have to be designed specifically for a certain task where its suitability for
that task often makes it less suitable for another.
An interesting example of this can be found in the field of all optical switching. The
basic concept of all optical switching is that one optical signal can switch another
optical signal because it brings about a change in the material (e.g. in index or losses)
in which both signals propagate. In general this requires the switching signal to be of
a very high intensity. One solution to achieving these high intensities is through the
use of a micro-resonator where the intra-cavity intensities can be many orders of
magnitude above the input intensities.
The intra-cavity power of a micro-resonator at full resonance can be found by setting
2
φr=2π in Equation (2.14) and dividing the result by κ 2 :
2
PCav
_ Max κ1
χ r
=
2
PIn
( 1−
µ 1µ
2χ
r )
(3.1)
In Figure 3.1 the intra cavity power of a micro-resonator has been plotted as a
function of the field coupling coefficient with the intra-cavity losses as a parameter.
P Cav_Max (dB)
80
60
40
20
0
0.0 0.2 0.4 0.6 0.8 1.0
Field coupling coefficient
Figure 3.1. Intra-cavity power as a function of the field coupling coefficient for several
resonator roundtrip losses.
40
0.03 dB
0.06 dB
0.16 dB
0.31 dB
0.62 dB
1.25 dB
The Figure shows that in a resonator the highest power enhancement is only possible
for very low field coupling coefficients and low cavity losses. For instance, for
resonator roundtrip losses of 0.03 dB (equivalent to a resonator with a radius of 50
µm and waveguide losses of 1 dB/cm) a maximum enhancement of ≈70 dB is
achieved at κ1=κ2=0.06. The same resonator, however, will achieve only 20 dB
enhancement for the moderately higher value of κ1=κ2=0.2. From the perspective of
all optical switching it therefore makes sense to optimize the micro-resonator for very
low losses and very small coupling coefficients. In literature such optimized