Edwin Jan Klein - Universiteit Twente

Chapter 2
light Icav2 in the cavity and the light in the port waveguide Iin. At this point no
additional power can be transferred from Iin and the resonator is operating in a steady
state condition. The power in the through port Ithrough is now at its lowest level while
the power in the drop port Idrop is at its highest level. The resonator has thus
effectively transferred power from the input to the drop port.
2.1.2 Transient resonator behavior
As described in the previous section all the power that is transferred from the (first)
input waveguide into the resonator is dropped to the second port waveguide (for a
loss-less the resonator). The transient drop response of a micro-resonator in full
2
resonance, which can be found from the intra-cavity power using I drop = κ 2 ⋅ I cav1,
is
shown in Figure 2.3a. In this Figure the transient buildup of power and the stable
equilibrium phase where the dropped power no longer fluctuates can be identified.
Figure 2.3b shows the transient step response of a resonator that is near full
resonance. In this case the roundtrip phase of the light in the cavity is not exactly
2 ⋅ mπ
, but constructive interference within the resonator cavity, and thus power
buildup, can still occur. However, the maximum attainable intra-cavity power is
reduced and as a result the maximum dropped power level is lower compared to that
of a resonator in full resonance.
Power (a.u.)
1.0
0.8
0.6
0.4
0.2
0.0
0 10 20 30
Time
40 50 60
Figure 2.3a. Transient drop response at
full resonance.
In a resonator that is completely off
resonance the roundtrip phase of the
light in the resonator cavity is equal to
(2.m+1).π. It will therefore interfere
destructively with the light that enters
the cavity. This has the effect that the
power of the light that enters the
cavity is reduced below its initial
2
value of κ 1 ⋅ Iin
, thereby blocking the
transfer of power from the input to the
drop port. This is also visible in
Figure 2.3c where, after an initial peak
in power, the drop power converges to
a significantly lower value.
Power (a.u.)
14
0.5
0.4
0.3
0.2
0.1
0.0
0 10 20 30 40 50 60
Time
Figure 2.3b. Transient drop response near
full resonance.
Power (a.u.)
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0 10 20 30
Time
40 50 60
Figure 2.3c. Transient drop response at offresonance.