IEEE Solid-States Circuits Magazine - Summer 2021 - 26

BW is limited (to the megahertz level
or lower) [14].
SiP and CMOS Circuits
Passive Circuits
Microring Resonator
Figure 4 shows a microring resonator
(MRR). It includes a straight waveguide,
a looped waveguide, and directional
couplers to access the loop. The directional
coupler couples the incoming
light into the looped waveguide with
a 90° phase shift. The waves in the
loop accrue phase shift or delay as
they go around the loop and then
another 90c when they couple back
to the through port. If the phase shift
in the looped waveguide equals an
integer times 2 ,r the waves destructively
interfere at the through port,
and the cavity is in resonance at a
wavelength
mre .s A plot of normalInput
-i
-i
M
= neff
φ = 2 Mπ
L
λres
at Resonance
Through
-10
-20
-30
-40
-50
1,500
1,550
Wavelength (nm)
FIGURE 4: An MRR with a through port and its normalized transmission (in decibels) as a
function of wavelength. MRR: microring resonator.
1,600
ized transmission, defined as the
ratio of the through port to input
power versus wavelength, shows a
response similar to that of a sharp
notch filter. But the curve is periodic
with wavelength. Recall that one full
wavelength is equivalent to 2r of
phase shift. If the circumference of
the loop is L, it can be shown that
different values of M lead to different
resonant frequencies, as shown
in Figure 4. The wavelength range
between two resonances is called the
free spectral range.
When the MRR is coupled to two
IL
Input
-i
-i
Through
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Drop
Wavelength (nm)
FIGURE 5: An MRR with through and drop ports and its normalized transmission (T) as a function
of wavelength. IL: insertion loss; ER: extinction ratio; FWHM: full-width at half-maximum.
ER =
FWHM
Q =
FWHM
λres
Through
Drop
FSR
Tmax
Tmin
waveguides, the incident field is
partly transmitted to the drop port
(Figure 5). Because of round-trip
losses in the ring and directional
coupler, there is a finite insertion
loss (IL) at both the through port
and drop port. The full-width at halfmaximum
(FWHM) is defined as the
spectral width when the transmission
is 50%. The quality factor, Q, is
therefore defined as the ratio of the
central resonance wavelength resm
to the FWHM. Very large values of
Q (~50,000) can be achieved in SiP;
thus, we can build very high-Q optical
bandpass and notch filters. Finally,
the extinction ratio (ER) is defined
as the ratio of maximum transmission
(Tmax) to minimum transmission
(Tmin) and can be defined at both the
drop and through ports.
Ei
Ei
√2
Ei
√2
φ
Eo =
Io =
FIGURE 6: An MZI, ignoring losses. MZI: Mach-Zehnder interferometer.
26 SUMMER 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
Eieiφ
√2
Eieiφ + Ei
2
Ii
2
[1 + cosφ]
Mach-Zehnder Interferometer
Figure 6 shows a Mach-Zehnder
interferometer (MZI) built using a
Y-branch splitter and combiners. If
the light has the same optical path
length in both branches, we anticipate
constructive interference at
the output waveguide,
EE .oi
= If the
light has a 018 c excess phase shift
between the two optical paths, we
anticipate destructive interference
at the output waveguide. Then what
happens to the light? The light couples
into higher-order modes and
radiation modes.
Normalized Transmission
Normalized Transmission (dB)
ERt
ERd
1,530
1,535
1,540
1,545
1,550
1,555
1,560
1,565
1,570

IEEE Solid-States Circuits Magazine - Summer 2021

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