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OmniSim

Omni-directional photonic simulations

A 1x2 M.M.I. (Multimode Interference Coupler)
with Butterfly Geometry

OmniSim 2D FDTD simulation

OmniSim can be used to model and simulate the propagation of light through a 1x2 MMI. In this example, we use OmniSim’s FDTD engine to calculate the transmissions and reflections of an 1x2 MMI with butterfly geometry at different phase differences, and compare its results to a paper published by A.J. Millan-Mejia et al. [1].

Design of the structure

The 2D structure of an MMI with butterfly geometry is represented below. Instead of allowing parasitic reflections to disrupt the functionality of the MMI, butterfly geometry allows the unwanted light to escape. Optimized angles ensure that the unnecessary light is redirected away from the main propagation path and out of the MMI. Moreover, the implementation of butterfly geometry in MMIs was originally proposed by E. Kleijin [2]. In this example, the waveguide (background) has a refractive index of 2.729, while the etched areas (blue) have a refractive index of 1.00. This structure is parameterized using variables that can easily be changed in the OmniSim software.

The structure below is an approximate sketch of the butterfly geometry MMI on OmniSim. In this particular graphic, the etched areas are in red, and have a refractive index of 1.00. Using Kallistos, the parameters of the structure can be optimized

 

Unoptimized MMI with butterfly geometry  

1x2 MMI with butterfly geometry on Omnisim, not optimized (Transmission 91.42%, Reflection 3.19%)

Optimization of parameters using Kallistos

The critical parameters are optimized using Photon Design’s Kallistos tool which is an automatic optimization tool that can be used to find both local and global extrema.

The Kallistos user can easily re-optimize the MMI as (s)he sees fit, choosing the variables (s)he wishes to vary and adding upper and lower bounds that are within the proper dimensions of geometry.

Here we wish to optimize two quantities: maximise transmission and minimise reflection.

The structure below is a 1x2 MMI with butterfly geometry that has been optimized by Kallistos. Notice that the wedges on the right have drastically decreased in length, and have almost become triangular. Also notice that the polygons on the left have become smaller, perhaps allowing more light to escape the device in order to minimize reflection.

Optimized 1x2 MMI with butterfly geometry  
A labelled diagram of the 1x2 MMI with butterfly geometry on OmniSim,
optimized (Transmission 91.70%, Reflection 0.0879%)

The following graphic shows the propagation of light through the optimized MMI. Notice how part of the pulse is able to escape the MMI and disperse elsewhere without negatively affecting the functionality of the MMI.

FDTD simulation of butterfly 1x2 MMI  
OmniSim FDTD simulation of Butterfly 1x2 MMI – two partly out-of-phase optical pulses are injected from right.
Light of incorrect phase can be seen directed out of the MMI and away from the main propagation path

Comparing results of OmniSim calculations with the results of Millan-Mejia et al.

The following graphic is a graph of the unoptimized MMI on Omnisim. This has a rather high, undesireable reflections of ~3%.

Unoptimized transmission/reflection of 1x2 MMI butterfly  
Effect of phase difference on the transmission (blue) and reflection (green) of a 1x2 MMI with butterfly geometry in OmniSim,
produced using OmniSim’s Scanner Tool (unoptimized)

The following graphic is a graph of the optimized MMI on Omnisim, which indicates both transmission and reflection based on the phase difference of the light source, ranging from 0° to 180°.

Optimized transmission/reflection of 1x2 MMI butterfly  
Effect of phase difference on the transmission (blue) and reflection (green) of a 1x2 MMI with butterfly geometry in OmniSim, produced using OmniSim’s Scanner Tool (optimized)

The next graph details the results from A.J. Millan-Mejia et al.

Effect of phase difference on transmission/reflection  

Effect of phase difference on the transmission (blue) and reflection (orange) of a 1x2 MMI with butterfly geometry [1]

Displaying the Kallistos’s optimisation map (see figure), you can readily see the areas that would yield the best transmission or reflection values. Many other optimisers will give you just one “optimum” design. However Kallistos’s design will give you also the 2nd, 3rd etc best designs too – this is important because sometimes the “best” design may be bad for other reasons, e.g. difficult to manufacture.

Kallistos Optimisation Map of the MMI  
Kallistos Optimisation Map of the MMI (the more red the point is, the better its value).
This map shows variations against 2 design parameters but the optimisation varied other parameters too
for which additional maps are available.

Both the results from Millan-Mejia et al. [1] and from Omnisim indicate a positive correlation between the reflections of the MMI and the phase difference of the light source. Moreover, both the transmission and reflection of each graph exhibits similar trends, with transmission decreasing and reflection increasing when the phase difference increases.

The OmniSim MMI reflection results are a little different since Kallistos was told to focus on focused on minimising out of phase transmission rather than minimising out of phase reflection. This can be easily remedied by altering the Objective Function given to the Kallistos Optimizer.

Reference

[1] A.J. Millan-Mejia et al., 1x2 Multimode interference coupler with ultra-low reflections in membrane photonic integrated circuits, 19th European Conference on Integrated Optics Proceedings

[2] E. Kleijin et al., Multimode interference couplers with reduced parasitic reflections, IEEE PTL, Vol. 26, No. 4.