Experimental results

We fabricated the devices at NTRC using our previously explained process with fully-etched DGC to input and output the light. Our results show the normalized transmission when taking as reference a straight nanowire waveguide. The following section shows the experimental characterization of the device in the following order: gap, cavity size, coupling length and finally, the same analysis is performed for the TM polarization. We begin with the analysis of the fabricated device based on the simulation for comparison.

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Figure 4-5 Experimental results for the previously simulated device (Left) complete range (Right) Zoom in the spectrum.

By fabricating the same design as the simulation, we are able to confirm the experimental behavior of the system. The transmission spectrum is found to have several power dips in the order of 2 dB, and in the same wavelengths, there is a sharp increase of power in the drop R port. These wavelengths meet the resonant condition. The extinction ratio of the device is intrinsically low because the coupling length is long and the device is wide. This means that in order to obtain high extinction ratios, we would need to satisfy the phase matching condition through the whole coupling length. This is relatively easy to achieve with traveling wave resonators, but it is very difficult to achieve with square resonators as there is power coming from both sides. Thus, it is easier to examine the drop-port, and as both ports contain the same information, the conclusions that we obtain from the drop R port also refer to the drop L port.

The first immediate result we see is the existence of two high Q factors denoted by A-B, or C-D. In between these two resonances, there are some other low power resonances that are not easily distinguishable. For example, when we show a magnification of the spectrum of resonances D and C, we are able to see some other low Q factor peaks, which are not completely spectrally resolved, and thus, they broaden the resonant peak as is the case of C. Nevertheless, the spacing between both peaks is in the order of 4.3 nm as is the case of the simulation. The FSR of the peaks, meaning from D to A or from C to B is 14 nm. In general, simulation and experiment match with small differences due to dispersion.

As we know, the group index is wavelength dependent, and for higher wavelengths, the value is greatly decreased. As both resonances have different values of group index, we found that there is a point that their group index matches, and that is where we are not able to see two resonances anymore, but rather only one resonance. This effect is seen in the fact that the left resonance D, or A, approach the right resonance C or B as the wavelength is further increased. In the simulation, we didn’t take any dispersion into account, and thus, the separation of the two high power resonances is always constant which is the main difference.

The next step was to change the gap size of the resonator, the idea behind the gap is to achieve something similar to the critical coupling case of the ring resonator. In general, there are three cases, the over-coupling, the under-coupling and the critical case. Usually, the over-coupling and the under-coupling are not easily distinguishable as they have a very similar response in terms of the absolute value of the Q factor. However, for the critical case, we expect to obtain the closest case to critical coupling, which will give us the highest Q value. The experimental case for the case of a gap of 160 nm, 200 nm and

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300 nm are shown in Figure 4-6 and their respective Q values are 4200, 10000, 13000 respectively.

Figure 4-6 Effect of the gap size for the rectangular resonator

By looking closely at the results, a higher gap size in the system gives us a higher Q value at the expense of power. For the case when the gap is 200 nm, the Q is increased to 10,000 and all the resonances can be easily identified. Then, when we increase the gap size to 300 nm, we observe that the Q value is also increased to 13000 for resonance labeled as C. However, the resonance labeled as D is not resolved anymore due to the lack of power. This is the biggest tradeoff we have to compromise, increasing the Q value, or getting more power in the drop port, and this decision is application dependent. For our case, a Q of 10000 is enough to create a good sensor. There have been some different proposed ways to increase this value, either by cutting the corners of the square [101], reducing the size [102], opening holes in the center and some other methods [103].

However, the highest reported value is of 4200 [104], so we managed to increase the Q value by optimizing the coupling parameters and reported for the first time a Q value of 13000.

Then, we changed the coupling length between the bus waveguide and the cavity. In our proposed device the maximum coupling length is given by the rectangle length. From this length, we can only decrease it to zero. In order to decrease it, we set the coupling length as a straight waveguide, and then bend it with the tightest radius allowed before incurring in additional loss. This bent radius is 5 μm and we do not consider the additional coupling length due to the bending radius. Therefore, for a 20 × 10 μm², we changed the coupling length to be 10, 5 and 0 μm. The results are shown in Figure 4-7.

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Figure 4-7 Effect of the coupling length for a rectangular resonator

As we expected, the overall behavior is the same for the resonant wavelengths.

However, as the coupling length is decreased so is the coupled power. This is also seen in directional couplers, where the length is important to transfer the power from one side to the other side. The transfer power requires a long coupling length more than 5 μm.

Below this value, not enough power is detected at the drop ports. On the other hand, when the coupling length is very long, we have a transfer of power back and forth, and then we end up with more power in the bus waveguide than in the cavity. For this reason, the coupling length of 10 μm is able to obtain a higher Q value than the 20 μm case and is about 10000. As it is also seen in Figure 4-7, there is not much power coupled when the length is less than 10 μm, and for this reason, resolving the resonances is a bit more difficult and the Q value is not determined due to the noise level of our system. So, our minimum coupling length that we would like to use is 10 μm for a 20 μm long cavity.

The next study we performed was regarding the size of the resonator. From the equations we presented before, by changing the size of the resonator, we also change the FSR and the Q. Even though, there will be different optimal parameters for each case, we used the best results for the 20 × 10 μm² case, which are a coupling length equal to the cavity length, a gap of 160 nm and a waveguide width of 500 nm. The results are given in Figure 4-8.

Figure 4-8 Transmission spectrum for different sizes of resonator

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We can see the clearest effect that is the change of FSR of the devices. The FSR of the biggest rectangle is 14 nm, followed by 22 nm of the 10 × 10 and 44 nm of the 5 × 5 rectangle. Also, the Q value is affected as it was foreseen by the equation, and a low Q values of 1000 is for the smallest rectangle followed by 4100 for the 10 × 10 μm² and ending with 4200 for the biggest one that is the 20 × 10 μm². From the spectrum we notice two things, first, there are more resonances coupled to the 10 × 10 square and we can easily identify three different ones. For the 5 × 5, we are able to identify two resonances as for the case of the 20 × 10. Next, we studied a bit more in detail this point. From the ray optics approach, we can see that there are several angles that meet the TIR requirement for 𝑘_{𝑟𝑒𝑐𝑡}. It has been shown that when the angle inside the cavity matches the angle of the waveguide, strong coupling occurs [105]. When there is a bigger mismatch, a weaker coupling takes place. For example, if the angle of the waveguide is 45 degrees, and the angle of the bounces is 44 degrees, then, we will obtain a very strong coupling. If another angle is 33 degrees inside the cavity, the coupled power will be very less as there is a big mismatch between them. Therefore, for the case where the square is 10 × 10 μm long, there are three bouncing trajectories that meet the waveguide front, and have a similar angle to the propagating bus angle.

It is important to say that the dispersion effect is clearly seen in all cases. As the wavelength increases, all the resonances tend to merge into one. From this analysis, we can think that it is possible to select only one resonance by adjusting the bouncing angle of the cavity to match the waveguide. We can try to achieve this by either changing the coupling angle between the waveguide and cavity, i.e., tilting the bus waveguide some degrees, or we can modify the waveguide width as this is the parameter that sets the 𝑘_𝑤𝑔. This is equivalent to changing the coupling angle of the prism or fiber when using a discrete element method [106].

Therefore, for our next experiment we set the waveguide width to 350, 400 and 450 nm to see how preferential coupling can be achieved. The fixed parameters are a gap of 160 nm and a cavity of 20 × 10 μm². From our mode solver, we can confirm that those waveguide widths can guide the fundamental mode and the results are shown in Figure 4-9.

Figure 4-9 Preferential coupling in integrated rectangular resonators (left) width of 350 nm (center) width of 400 nm (right) width of 450 nm

We see that for the narrowest case, the 350 nm, there is high losses as a bigger fraction of the mode is propagated along the sidewalls of the cavity. In this particular case, we are not able to distinguish any resonances. The next case is for the waveguide width of 400 nm, the loss problem is improved and we are able to see the resonances from the transmission and dropped port. Nevertheless, the losses are still high enough that for certain wavelengths, it is difficult to spectrally resolve them. Here, it is important to say

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that only one set of resonances is easily seen and for some wavelengths, the power is higher in the dropped port. This means that for these special wavelengths, the angles match very well and so there is a big power transfer between ports across the cavity. For the next case, when the waveguide width is 450 nm, we can see a very well-resolved spectrum where only one set of resonances appears in the transmission and the drop port.

The Q value is increased to 5600 and no more over coupling is seen throughout the whole spectral range. This means that we are able to see the preferential coupling inside the rectangular cavity meaning that only one resonance is selected from the previous two resonances. This is the first time this effect is shown in an integrated system. However, this effect was already demonstrated when using a different coupling mechanism such as prism coupling in silica rectangles [107].

From the geometry of the proposed device, it is important to confirm if a standing wave appears inside the cavity, so both end ports of the device have to be monitored at the same time. Additionally, it is interesting to notice that the system seems to be symmetrical, and thus, the bus waveguide can be placed on any side of the square. By using this idea, we can place four bus waveguides, instead of two, one at each side of the square. As we would like to keep the system as simple as possible, we do not want to cross the waveguides. Therefore, we have to bend the waveguides after a minimum coupling length of 10 μm so that they are separated enough to avoid any kind of cross talk but still get power inside the cavity. From the previous results, we found a good performance was obtained when the cavity size was 20 × 10 μm, and the coupling length was set to 10 μm. Taking advantage of this property, we designed a square cavity of 20 × 20 μm², and placed four bus waveguides with a gap of 160 nm and coupling length of 10 μm as shown in Figure 4-10. The closest distance between the bus waveguides at any given point was 2 μm to avoid cross-coupling. A SEM image of the eight port device is shown in Figure 4-10 left and then experimental results are also shown in the right.

Figure 4-10 Eight Port devices to prove the symmetry and standing wave resonator

In the experiment, the input is set at the top left port and at first two other fibers were used to collect the power from the C and D port simultaneously. We can confirm that the spectrum is almost identical, and there are a minor power differences, due to perhaps the fabrication differences between the C and D ports. By confirming this issue, we can say that a standing wave appears inside the cavity because the same amount of power is going to the C and the D ports at the same time. Then, we added a third fiber and tested the case

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where the input was excited on top-right, and the A, B and C ports were monitored with three power meters at the same time. For this, it was necessary to build two extra stages to couple the additional fibers. All fibers were independently mounted on their respective stages and then one by one, they were aligned to their respective grating couplers. The computer program that was written controlled the laser wavelength and it recorded the power read by the three photo-diodes, then, it stepped the laser and repeated the measurements from the three photo-diodes. The results are shown in the right of that figure.

Our main interest is in confirming if all the ports had the same amount of power at the same time however, we can also confirm the effect of the FSR as the size of the cavity is larger. We found that the same resonant wavelengths out couples to all the ports regardless of the port we are measuring. This is an interesting result, because we understand the reason why the power in the drop port was so less. It is because the energy is lost in all the sides of the rectangle. Therefore, it will be interesting to study the same device from the point of view of switches and signal routers. The next study that was in turn was to repeat the same but for TM polarized light.