Flat-Top Fourth Order MZI Filter

1 Flat-Top Fourth Order MZI
Filter

In telecommunication applications such as high speed links, there are
challenges like in-band ripples which can cause unwanted signal
distortions and/or power variations induced by wavelength drifts of the
light sources (in the absence of thermal control). These challenges can
be mitigated by using the optical filters having a flat-top transmission
response. This article present a fourth order MZI filter [1] with the
use of Multimode Interferometers (MMIs) splitters, designed using the
building blocks developed by VLC Photonics, based on the silicon nitride
(SiN) technology, establised and running at CNM (Centro Nacional De
Microelectronica). Due to their broadband operation and tolerance to
fabrication errors, MMI splitters are preferred over the other splitter
types. SiN material these days is commonly used in CMOS platform and has
an edge over traditional silicon (Si) and III-V material due to its wide
index contrast and relatively low thermal oxide coefficient.

2 Theory

Figure 1 shows a doubly point-symmetric configuration where the
building block, composed of a type A coupler and half-type B coupler, is
repeated point symmetrically which results in a ABA structure. This
structure is repeated point symmetrically to give the desired result.
The angular expression of the amplitude coupling ratio [2] of a coupler
is defined by:

[begin{equation}
phi(lambda) = kappa(lambda)[L + delta L (lambda)]
end{equation}]

where,

(kappa(lambda)) is the coupling
per unit length in the straight part of the coupler

(delta L(lambda)) accounts for
the contribution of the input and output curves

While designing the filter, these two quantities are assumed to be
same for all the couplers and also assume any dependence of (phi) on (lambda) to be negligible. Then the fourth
order MZIs based filter with the flat-top response can be designed based
on analytic equations [3] to determine the coupling angles (phi^A) and (phi^B) as follows:

[begin{eqnarray}
phi^A = frac{pi}{16} + (m+k)frac{pi}{8} \
phi^B = frac{pi}{8}+(m-k-t)frac{pi}{4}
end{eqnarray}]

If t=k=0 and m=1, then

[begin{eqnarray}
phi^A = frac{3pi}{16} \
phi^B = frac{3pi}{8} = 2phi^A
end{eqnarray}]

which requires a single point-symmetric configuration. (phi^B) exactly matches the coupling angle
of an 85/15 MMI [1] whereas, (phi^A)
doesn’t match any simple MMI design. So, the two (phi^A) at the edges of the filter require
a double MMI approach to mimic the functionality of an equivalent
directional coupler. Whereas, the two (phi^A) splitters in the middle can be
combined in a single splitter of angle (2phi^A = frac{3pi}{8} = phi^B). So,
the couplers with coupling angle (phi^B) are replaced with the MMI having
85/15 splitting ratio i.e. three 85/15 MMIs at the center. At the input
and output edges, a double MMI 50/50 is used to acquire the desired
splitting ratio. The proposed flat-top fourth order interleaver filter
is shown in figure 2.

A (frac{pi}{2}) phase is added
at the end of each double MMI 50/50 to make sure the output phase is
correct. In between the double MMI 50/50, an additional (frac{5pi}{8}) phase shift is required to
have accurate splitting ratio. This phase shift is slightly different in
this particular example since the MMI ratios are not ideal. The orange
color in the arms of the asymmetrical MZIs in figure 2 represent the
delay length ((Delta L)).

3 Design

To design and simulate the flat-top filter shown in figure 2,
building blocks from the VLC-CNM PDK and from the OptiSPICE device
library are selected. The filter is build and simulated using the
simulation tool S-edit from SIEMENS Tanner. The devices used from the
VLC-CNM PDK are: cnmMMI2x2BB_TE (MMI 50/50), cnmMMI8515BB_TE (MMI
85/15), cnmWaveguideDE_TE (straight waveguide). All these devices are
made of deep etched waveguide and are TE polarized. A complete circuit
for the simulation can be seen in figure 3, where a three port laser
sends in a signal (freq = 210 THz) at the input of the filter, and the
output response, is measured using the optical probes.

The phase shift of (frac{pi}{1.99}) and (frac{pi}{1.848}) is added in between the
double MMI 50/50 at the input stage and the output stage, respectively.
The (Delta L) for the MZI arms is 40
um. The additional phase shift of (+frac{pi}{2}) and (-frac{pi}{2}) is added to the (Delta L) as shown in figure 3.

4 Simulation and Results

An AC analysis is carried out and the laser frequency is swept from
200 THz to 220 THz. The flat-top transmission response of the filter is
shown in figure 4. The probe ‘OTerminator4’ shows the frequency response
in the bar state and ‘OTerminator3’ shows a frequency response in cross
state. The measured FSR is 2.35 THz, and the extinction ratio from the
plot is measured to be >20dB. The wide bandwidth of the MMIs allow to
cover the E-band of the telecom wavelength spectrum.

Thus, a fourth order interleaver filter based on the point symmetric
configuration [1] is presented in this article using the MMI 50/50, MMI
85/15 and waveguide building blocks from the VLC-CNM PDK showing a
flat-top filter, which finds it’s applications in the telecommunication
sector.