Shallow etched diffraction grating couplers

When space of the chip is vital and expensive as the case of MPW and when access to the edge of the chip is not available, another structure is needed to couple light into the chip. This structure is called diffraction grating couplers (DGC) or also commonly known as grating couplers. These structures can bend the light 90 degrees from a vertical SMF into the planar horizontal waveguide. They can be fabricated anywhere on the chip, as close as required, and their size is as big as the SMF core, about 10 × 10 μm² so there is a good match between fields. However, another element is required to scale down the optical mode to fit into a nano waveguide. Fortunately, this element can be easily fabricated on chip, and is called a taper. The simplest taper is the linear taper that requires about 100 μm to efficiently convert the mode in a 10 μm wide waveguide to a 500 nm waveguide. Other variations exist such as the parabolic taper [45], focused taper [46] and other unique shapes [47] that decrease the required length of the taper. For the out coupling element, a similar structure is used but in reverse order.

DGC also removes the constraint of having extra-long waveguides to access one single device, and the necessity to polish the edges. Unfortunately, the 3 dB bandwidth of light they can couple is reduced to about 70 nm, they are polarization dependent and the insertion loss is increased to a couple of dB per DGC. The polarization and bandwidth problem can be solved by using several designs of DGC, each for a unique set of wavelengths and polarization. Even by duplicating the number of DGC, we can save more footprint area using this approach than routing the waveguides to the end of the chip. The additional insertion loss is not easily solved. There have been many efforts from several research groups to increase the coupling efficiency using mirrors [48], apodized structures [49], multiple layers [50], and metamaterial structures that are not periodical [51].

Nevertheless, their loss is higher than SCC, but they are very useful for fast prototyping of photonic devices.

There are two different types of DGC, shallow etched and fully etched. First, we will introduce the shallow etched DGC and then extend our discussion to the fully-etched DGC. A shallow DGC top view SEM image is shown in Figure 2-4 (left) with its lateral profile in the right. From the lateral profile, we can identify that the DGC consists of a

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periodical corrugation in the silicon thickness. In this specific case, there are two heights of Si, 220 nm and 160 nm.

Figure 2-4(Left) A SEM image of a shallow etched DGC (right) lateral refractive index profile

Now, supposing that there is an input lightwave coming from the left as shown by the arrow, the periodical structure will either diffract the light into the air, the substrate, reflect it or propagate it. It is important to say that the DGC is completely reciprocal, this means that we could suppose that the input light is coming from the air and we get the same results. For this reason, the in-coupler and the out-coupler can be designed with the same equations and methodology. A detailed explanation of such couplers have been extensively researched and they can be found in [51]. As in this work, we are interested in experimentally comparing the performances of the different couplers, we only state the most important equations. The 2D coupler is governed by the following equation where the main parameter is the wavelength to be diffracted.

𝑚𝜆 = 𝛬(𝑛_𝑒𝑓𝑓 − 𝑛_{𝑐𝑙𝑎𝑑}𝑠𝑖𝑛 𝜙_{𝑐𝑙𝑎𝑑}) (2.1) Where 𝑛_𝑒𝑓𝑓 is the average effective refractive indices of the silicon heights, 𝑛_{𝑐𝑙𝑎𝑑} is the refractive index of the cladding and 𝜙_{𝑐𝑙𝑎𝑑} is the angle in which the light will be diffracted. In order to calculate the average effective refractive index of the structure, the fill factor is required as well as the etching depth. We have that

𝑛_𝑒𝑓𝑓 = 𝑒𝑓𝑛_{𝑒𝑓𝑓160}+ (1 − 𝑒𝑓)𝑛_{𝑒𝑓𝑓220} (2.2) And 𝑒𝑓 is the etch factor or in other words, the percentage of the period that is shallow-etched . For the shallow shallow-etched type DGC, we can use a 2D model of the 3D structure as the x direction can be ignored because the length of the grating coupler is much longer than the wavelength. To get the effective refractive index of the different silicon heights, a mode solver and the dispersion of silicon are needed. The structure is like that in the right of Figure 2-4 where the refractive indices of the cladding, waveguide and substrate are 1, 3.47 and 1.44 respectively for the 1550 nm wavelength.

We calculated the dispersion of the effective refractive indices for the two different heights and the results are shown Figure 2-5 (top). As it can be seen from the design equation, the Bragg wavelength depends on the effective refractive index, and the effective refractive index also depends on the Bragg wavelength. Thus, it is easier to solve

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both equations using a graphical method, where the intersection of the lines give us the expected Bragg wavelength as shown in the bottom of the same figure.

Figure 2-5 (Top) Effective refractive index for Si slab waveguides of 220 nm and 160 nm for TE polarization (Bottom) Graphical method to solve for the Bragg wavelength for different periods

When designing DGC, there are parameters fixed by the fabrication process, and the rest can be tuned – to a certain degree – to meet the required emission wavelength. The parameters set by the fabrication process are the Si thicknesses, which in our cooperation with AIST, they were fixed to 220 nm and the etching depth to 60 nm, (which sets the second height of Si to 160 nm). This etching depth is usually in the range of 60 to 90 nm as it is the same etching depth used to fabricate rib waveguides. Also, the cladding material needs to be known before designing the coupler. Then, the most important variable that has to be decided is the period of the structure. There are other variables that can be adjusted during the measurements and are tilt angle of the SMF. As default, the tilt angle, is set to match our L shape fiber holder that had an angle of 10°.

Our target is to obtain a Bragg wavelength of 1520 nm, as is in the middle of our laser range. Then, from our dispersion curves of the effective refractive indices for both heights, we found that the effective refractive index of a 220 nm slab waveguide is 2.849, and for a 160 slab waveguide is 2.585. If we assume a 50% duty cycle, the 𝑛_𝑒𝑓𝑓 of the complete structure is 2.717. The last variable we solved for was the period keeping in mind that the cladding is air 𝑛_{𝑐𝑙𝑎𝑑𝑑} = 1 and we get a period 600 nm for an emission angle of 10°. This

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is our main design and we fabricated some variations of it by increasing / decreasing the period in 50 nm steps. Then, the expected Bragg wavelengths can be found from the intersection of the lines with the Ref line.

Here, it is important to say that we assumed that the emission angle is the same as the tilt angle of the fiber. However, we do not use polished fibers, so there is an additional loss due to the un-matching coupling integral. Nevertheless, the additional loss is acceptable if we can simplify the setup by using 90 degrees cleaved fibers instead of polished fibers.

We experimentally evaluated the performance of such DGC in terms of insertion loss and 3 dB bandwidth, and the results are in good agreement with the Bragg wavelength from our calculated values. In order to correctly measure the insertion loss of the grating couplers, we first measured the back-to-back losses of the setup, meaning the losses from the SMF and polarization controller. Then, the extra losses from this value after inserting our device come from two grating couplers and waveguide loss. This extra loss is then divided by two to obtain the loss from a single grating coupler and half the losses of the waveguide, and this is measured to be 6 dB at 1520 nm wavelength. Figure 2-6 shows the transmission spectrum for the three different periods.

Figure 2-6 Transmission spectrum of the shallow etched DGC for TE polarized light for different periods

From the figure, we can see that the Bragg wavelength (maximum power) for the 550 nm period grating coupler is barely seen around 1440 nm wavelength. For the 660 nm, the Bragg wavelength is around 1524 nm, and for 650 nm it is around 1600 nm. By using Figure 2-7 (Bottom) we are able to calculate a Bragg wavelength of 1430 nm for a period of 550 nm and 1620 nm for a period of 650 nm. The experimental results match to a certain extent the expected Bragg wavelength and due to the limitation of our laser to 1440 nm, we are not able to see the Bragg wavelength of the shortest period. The 20 nm difference may be due to a thinner Si height, other fabrication tolerances or a semi-exact model. The theoretical values are given in Table 2-1 for an easier comparison.

Other than insertion loss and Bragg wavelength, the other important figure is the 3 dB bandwidth of the couplers. Ideally, the bandwidth is desired to be as wide as possible, but due to the fact that only certain wavelengths that meet the Bragg grating phase matching condition are efficiently coupled, the bandwidth is reduced to tenths of nanometers. For

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our devices, the bandwidth of the structure is about 70 nm as shown in the same graph for the period of 600 nm. As the wavelength increases, so does the dispersion and thus, the bandwidth is reduced.

As it was said earlier, the DGC are polarization sensitive, due to the fact that silicon is highly birefringent with these dimensions. Therefore, different periods are needed for the TE case and for the TM case to match the same diffraction wavelength. We also designed a grating coupler for TM polarized light following the same procedure as stated before, with the main modification in the period due to the complete different numerical values of the effective refractive index as shown in Figure 2-7 (Top). We found that the period had to be updated to 1000 nm to achieve a diffraction wavelength of 1550 nm with the same conditions as before because the refractive indices are 1.933 and 1.512, thus, an average index of 1.722. The same graphical procedure can be used and is shown in Figure 2-7 (Bottom).

Figure 2-7 (Top) Effective refractive index for Si slab waveguides of 220 nm and 160 nm for TM polarization (Bottom) Graphical method to solve for the Bragg wavelength for different periods

Again, three different periods were fabricated and the normalized transmission for the DGC for TM polarized light is shown Figure 2-8. The interesting result regarding the Bragg wavelength is that they are not shifted as much as the TE case because the effective refractive index of the 160 nm slab waveguide is already approaching the cut-off value, so its numerical value is quite stable. Also, from both intersection graphs, we can see that the TM mode intersects the Ref line in shorter spans which is confirmed with our

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experimental results. Again, there is a small discrepancy of about 20 nm between theory and experiment.

Figure 2-8 Transmission spectrum of the shallow etched DGC for TM polarized light for different periods

The efficiency is deteriorated about 1 dB compared to the TE mode, but the 3 dB bandwidth is increased about 10 nm. The following table shows the theoretical and experimental results for shallow etched grating couplers for the TE and TM polarization.

Pol Λ [nm] ef % λB λB exp. BW [nm] Loss [dB]

TE 550 0.54 1430

TE 600 0.50 1520 1526 72 5.88

TE 650 0.46 1620 1600 60 6.98

TM 950 0.42 1510 1490 85 9.86

TM 1000 0.40 1550 1534 92 7.7

TM 1050 0.38 1600 1570 58 7.4

Table 2-1 Theoretical and experimental results for the shallow etched DGC

Although there are other parameters that can be modified to tune the transmission spectrum, we are not going to include those results in this thesis, as the main drawback of these DGC is that two etching steps are required, which is not a problem in most cases, as rib waveguides are commonly used in the same chip. However, this process is not easily implemented at NTRC, where we only have one etching step. Therefore, we would like to define all the structures, including the DGC in a single etching step. This problem is common to various research groups, and the most common solution is to use fully-etched diffraction grating couplers (FE-DGC) as they will be studied in the next section.