## 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)

doesnt 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 its applications in the telecommunication

sector.