Polarization-Insensitive Silicon Nitride Photonic Receiver Based on Thin Waveguides for Optical Interconnects at 1$\mu$m

This article demonstrates with simulations two polarization independent wavelength division multiplexing receiver platforms based on thin silicon nitride waveguides for optical interconnects at 1 <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m. The chosen waveguide base geometry (width = 900 nm × height = 160 nm) is a good tradeoff between mode confinement and propagation loss. We first propose a design using a polarization splitter with an 1×4 demultiplexer based on an arrayed waveguide grating (AWG). This receiver has a reduced size and requires only one etching step. We later propose another simplified receiver design using a polarization splitter-rotator with two identical 1×4 demultiplexers based on cascaded Mach-Zehnder interferometers. The rotator is based on a thicker waveguide (width = 500 nm × height = 400 nm) and is partially etched to rotate the electric field by 90<inline-formula><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula>. Thus, it requires the use of mode size converters at the in/output ports. To keep the fabrication complexity as low as possible for the second design, we limited ourselves to only two etching steps. Therefore, the thickness of the slab of the mode converters and of the rotator is the same as for the main 900 nm (wide) × 160 nm (thick) waveguide. The simulated extinction ratio of the polarization splitter at 1035 nm is 18 dB and the calculated TM-TE and TE-TM polarization conversion efficiency of the polarization rotator at 1035 nm is 99.9<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula>.


Polarization-Insensitive Silicon Nitride Photonic
Receiver Based on Thin Waveguides for Optical Interconnects at 1µm Alexander Caut and Magnus Karlsson , Fellow, IEEE Abstract-This article demonstrates with simulations two polarization independent wavelength division multiplexing receiver platforms based on thin silicon nitride waveguides for optical interconnects at 1 µm.The chosen waveguide base geometry (width = 900 nm × height = 160 nm) is a good tradeoff between mode confinement and propagation loss.We first propose a design using a polarization splitter with an 1×4 demultiplexer based on an arrayed waveguide grating (AWG).This receiver has a reduced size and requires only one etching step.We later propose another simplified receiver design using a polarization splitter-rotator with two identical 1×4 demultiplexers based on cascaded Mach-Zehnder interferometers.The rotator is based on a thicker waveguide (width = 500 nm × height = 400 nm) and is partially etched to rotate the electric field by 90 • .Thus, it requires the use of mode size converters at the in/output ports.To keep the fabrication complexity as low as possible for the second design, we limited ourselves to only two etching steps.Therefore, the thickness of the slab of the mode converters and of the rotator is the same as for the main 900 nm (wide) × 160 nm (thick) waveguide.The simulated extinction ratio of the polarization splitter at 1035 nm is 18 dB and the calculated TM-TE and TE-TM polarization conversion efficiency of the polarization rotator at 1035 nm is 99.9%.Index Terms-Optical interconnects, silicon nitride, arrayed waveguide grating, Mach-Zehnder interferometer, coupling loss, polarization dependence, fiber misalignment, manufacturing tolerance.

I. INTRODUCTION
P OLARIZATION independence is a crucial factor for the receiver side of an optical interconnect as the polarization of the out-coupled light from a single-mode fiber is unknown and eventually drifts with time.Several ways exist to achieve polarization tolerance and the simplest one consists in designing square waveguides to obtain equal effective indices for the fundamental TE 00 and TM 00 modes.However, the use of square single mode waveguides results in a strong interaction of the propagating mode with the sidewalls [1].As one of the main source of propagating loss in a waveguide is the sidewall roughness, there is a tradeoff between thick polarization insensitive waveguides and thin low loss waveguides [1], [2], [3].In addition, the use of square waveguide could still result in polarization diversity as fabrication deviations in the core geometry occur [4].In [1], two single-mode waveguides had been designed: one had a dimension of 800 nm × 740 nm (width × height) and another 1500 nm × 200 nm.The measured propagation loss was 30 dB/m for the quasi-square waveguide and 4.1 dB/m for the thin waveguide.This makes the thin waveguide more attractive for low loss operation.However, in such waveguide design, the guided mode is much less confined and leads to a higher critical bending radius [1], [2], [3].In addition, thin waveguides are polarization sensitive and require additional components such as polarization splitters and rotators to make the receiver polarization independent [5], [6].This would increase the size of the whole integrated receiver with respect to one based on square waveguides.Despite this, thin waveguides are of interest as a receiver based on square waveguides would require good tolerance to fabrication defects which could potentially lead to unwanted polarization diversity.In [7], a TE/TM polarization shift of 1.6 nm was observed in the cascaded Mach Zehnder interferometer based on a 600 nm × 600 nm waveguide for a channel spacing of 20 nm.
In our envisioned receiver platform, the wavelengths are demultiplexed into photodiode arrays, flip-chipped over grating couplers which are more tolerant to misalignment than edge couplers [3].With the recent development of efficient GaAs VCSEL emitting at 1060 nm [8], [9], [10] and the reduced dispersion and propagation losses in optical fibers at this wavelength [11], the 1 µm band (1015-1055 nm) would allow a reduction of cost and power consumption [3].This article further extends the research done in our previous work [3], [12] and focuses on the receiver side, and to the best of our knowledge, investigation of polarization independent receivers at 1 µm is still missing.Silicon nitride (Si 3 N 4 ) is the material of choice as it is transparent from the visible to the mid infrared [13] and presents a good tradeoff between footprint and phase errors compared to other technologies based on silicon and silica due to its moderately low refractive index contrast [14].In addition, Si 3 N 4 is CMOS compatible.
For the demultiplexing device (DEMUX), arrayed waveguide gratings (AWGs) could be considered due to their small footprint [15].One common approach to make the AWG insensitive to polarization variations is the use of a polarization splitter at the input waveguide of the device [16].Another innovative possibility is to insert polarization rotators in the arrayed waveguides of the AWG, making the device insensitive to polarization change [17].In this work, we propose two polarization independent receiver designs based on a thin waveguide.The selected dimension of the waveguide is 900 nm × 160 nm (width × height).This geometry was already selected in our previous work for 1 µm components [3].Demultiplexers based on AWGs and cascaded Mach-Zehnder interferometers (MZIs) at 1 µm with a channel spacing of 25 nm were demonstrated in [15].In this work, we envision on the transmitter side VCSELs manufactured in the same array to significantly reduce the footprint and to increase the bandwidth density [12].However, since the gain bandwidth of the VCSEL is limited [10], the channel spacing has to be reduced.Therefore, an array containing 4 VCSELs emitting at different wavelengths needs to have a channel separation of 8 nm.The wavelengths of the VCSELs are located at 1023, 1031, 1039 and 1047 nm.
The article is organized as follows: Section II describes a polarization independent receiver design based on a polarization splitter and an arrayed waveguide grating (AWG).Then Section III further exploits the polarization splitter by proposing another design based on a polarization splitter-rotator and two identical cascaded MZIs.Finally, Section IV presents discussions followed with conclusions.

II. RECEIVER BASED ON AN AWG WITH A POLARIZATION SPLITTER
This section focuses on TM-TE polarization conversion based on edge coupling between the fiber and the thin waveguide.We explore the polarization splitter, the polarization rotator and the different combinations with a demultiplexer and grating couplers to obtain a polarization independent platform.
Integrated receivers play a key role in data communication and WDM is crucial for high network capacity.WDM photodiodes with high-speed output of 100 Gbit/s have been demonstrated and feature low-loss AWGs based on Silicon technology [18].In our previous work, we designed and demonstrated SiN integrated devices in the 1 µm band based on a 900 nm × 160 nm (width × thickness) waveguide [3].The measured propagation loss was below 0.3 dB/cm [3] and mainly arise from sidewall roughness and fabrication quality.In this work, we chose to conserve the same waveguide dimensions as they present a good tradeoff between propagation loss, mode confinement and reduced footprint.The effective indices for the TE 00 and TM 00 modes are respectively 1.567 and 1.491 and the simulated differential group delay with Finite Difference Time Domain (FDTD) was estimated to be 6.5 × 10 -4 ps/µm, which corresponds to a delay of 1.3 ps for a 2 mm-long receiver.The buried oxide SiO 2 layer can be thermally deposited on top of a silicon wafer, with a thickness of 3 µm.The 160 nm thick Si 3 N 4 can be deposited with a low-pressure chemical vapor deposition (LPCVD) method.The top SiO 2 cladding can be deposited with LPCVD with a thickness of 3 µm.
One common approach is the use of an AWG with two inputs, each corresponding to one specific polarization.As the effective index differs between the fundamental TE and TM modes, they will have a different initial phase at the input of the 1st free propagation region (FPR).Therefore, to compensate this initial difference and to make the AWG polarization independent, the TM input is angularly shifted from the TE input, which will result in a matching between the two spectra.Thus, the AWG requires a polarization splitter prior to the device to separate the TE and TM modes and guide them at their assigned input.The design presented is conventional and directional coupler-based.As the TE 00 mode is more confined than the TM 00 mode, it can be guided in curved waveguides with a bending radius below 50 µm with minor losses.The TM 00 mode however, requires a bending radius above 200 µm to be properly confined.Fig. 1(a) shows the scheme of the receiver based on a polarization splitter and the AWG.The TE and TM input of the AWG are angularly shifted.Since grating couplers are polarization dependent, and that the propagating mode coming from each channel could be either TE or TM polarized, edge couplers are only considered.Fig. 1(b) shows a scheme of the polarization splitter.The TE and TM polarization are guided into the bar and cross output respectively.The device was designed and optimized with FDTD simulations.Fig. 1(c) and (d) show the electric field profiles of the polarization splitter when the input polarization is TE and TM respectively.Fig. 1(e) presents the transmission of the polarization splitter when the input is a TE 00 or a TM 00 mode.The blue and orange continuous curves represent the transmitted power of the TE polarization at the bar and cross output respectively.The blue and orange dashed curves on the other hand represent the transmitted power of the TM polarization at the bar and cross output respectively.The device has a good transmission for both polarizations: -0.1 and -0.3 dB for the TE and TM polarization respectively at 1035 nm.
The extinction ratio (ER) of the device is defined as [19], [20] ER Bar = log 10 TE Bar TM Bar (1) ER Cross = log 10 TM Cross TE Cross (2) The ER of the polarization splitter is plotted in Fig. 1(f).The simulated ER for the bar and cross output is 16 and 18 dB respectively.The crosstalk and wavelength dependence of the device can be reduced by curving the waveguides but at the cost of increasing significantly the device's footprint.
Fig. 1(g) shows the simulated response of the AWG for the TE (continuous curve) and the TM polarization (dashed curve).The simulations were carried out with 2D Beam Propagation Method (2D BPM).The base length difference between the arrayed waveguides is 18.6 µm and the designed free spectral range (FSR) is 32 nm.The separation between the TE and TM input waveguides at the interface of the input free propagation region (FPR) is 2.6 µm.However, the output waveguide spacing is larger on the second FPR and is set at 4.6 µm.The length of both FPRs is 51.4 µm and the separation between them is 800 µm.The AWG has a footprint of 800 µm × 700 µm excluding the input and output waveguides and the whole receiver an estimated footprint of 1800 µm × 1300 µm.The device works reasonably well with a slight channel mismatch of around 1 nm which is due to polarization dispersion in the FPRs and in the arrayed waveguides [16].The method proposed in [16] consists in adapting the width of the arrayed waveguides so that the effective and group index change from TE to TM polarization compensates that of the effective index in the FPR region.
Unfortunately, meeting this condition with a waveguide thickness of 160 nm is not possible as the width would be too small to guide the TE 00 and TM 00 modes.One possibility to solve the channel mismatch problem due to polarization dispersion consists in cascading a polarization splitter with a rotator at the cross output port, allowing only the TE polarization to thrive.This approach will be investigated in next section.

III. RECEIVER BASED ON A POLARIZATION SPLITTER-ROTATOR AND TWO IDENTICAL CASCADED MZIS
Another solution consists in inserting a rotator at the TM output port of the input polarization splitter [20] to rotate the electric field by 90 • , thus converting the TM 00 input mode into a TE 00 mode.Hence, the main factor to consider is the polarization conversion efficiency, which is defined as the ratio between the proportion converted into a TE mode and the input TM mode.A compact device that could split and rotate the polarization was demonstrated in [21].The design principle was based on modifying the width of one of the two waveguides so that the effective index of the TE 00 of the smallest waveguide matches with that of the effective index of the TM 00 of the largest waveguide.A similar design was also demonstrated in [22] based on silicon.However, to perform a successful polarization conversion, the material of the top cladding needs to differ from that of the bottom one [21], [22].Regarding the demultiplexing device, a polarization rotator was inserted in each waveguide in the array section of an AWG in [17] to limit the footprint of the WDM.But this is at the cost of increasing the manufacturing complexity of the PIC.In this section, we propose a solution that decreases the manufacturing complexity of the circuit by using only one rotator at the input.
In this polarization independent receiver design, we consider a polarization splitter-rotator.A demultiplexer based on a cascaded MZI is placed at both outpout ports of the polarization splitter as shown in Fig. 2(a) and (b).The cascaded MZI was selected due to its high performance and good tolerance to fabrication deviations [12].The demultiplexers are identical and designed for the TE polarization.The polarization rotator is placed at the TM output port of the polarization splitter.As only the TE 00 mode is propagating through the MZIs, the grating coupler could be considered for the output as illustrated in Fig. 2(a).A receiver design with two 4-wavelength arrays of photodiodes instead of one can be exploited to avoid possible interferences from unwanted signals, as well as compensating for polarization dependent losses in the electric domain, after photodetection.The total footprint of the receiver is estimated to be 2200 µm × 1300 µm, which is slightly larger than the first receiver design proposed in Section II.To obtain a channel spacing of 8 nm, the base length difference between the MZI arms on the first stage is 37.7 µm.The power splitters used are multimode interferometers (MMIs).The simulated transmission of the cascaded MZI is plotted in Fig. 2(c) and was carried out with 2.5D-FDTD (varFDTD).
For this receiver platform, we exploit the polarization splitter design from Section II and then add a rotator at the TM output port as illustrated in Fig. 3.However, such device is more efficient with thick waveguides [17] and would require input and output mode converters [20].Several techniques exist to rotate the polarization.One of them consists in etching the thick waveguide asymmetrically as in [17], [23].A device based on silicon was manufactured and performed an extinction ratio of 15 dB with an insertion loss of less than 1 dB in TM-TE conversion [24].However, the effect of over-and under-etching can degrade the performance of the device [25].Therefore, another approach consists in a two-layer design [20], [25], enabling fabrication robustness.A slot layer made of SiO 2 is inserted between the two silicon layers in [25].The effect of misalignment is minimized as slots waveguides serve as an etch stop layer in the final etching process [20].However, the overall length of this design can exceed 1 mm [20].Another polarization rotator reported in [5] used a two-core design, the main core made of Si being inserted in another, larger, made of Si 3 N 4 .
The architecture used in this work is similar to the designs in [17], [26], [27].However, designing a rib-rotator based on a 160 nm thick Si 3 N 4 is challenging.Therefore, we decided to increase the thickness of the device.For comparison, the rotator in [17] also based on Si 3 N 4 material in the O-band uses a 700 nm (wide) × 600 nm (thick) core with a 350 nm thick slab.To reach a TM-TE conversion efficiency above 90%, the waveguide dimensions need to be properly optimized.The best found waveguide had a width of 500 nm and a thickness of 400 nm.Then, the thickness of the slab also plays a significant role in the conversion efficiency.Here, the selected thickness for the slab is the same as that of the main 900 nm (wide) × 160 nm (thick) waveguide to limit the number of etching steps.Hence, to be adapted for our PIC based on a 900 nm × 160 nm, mode converters must be inserted at the input/output of the rotator.This feature was chosen to limit the propagation loss through the PIC, even though it increases the complexity of the circuit.The other approach, simpler, would be designing the entire PIC based on the 500 nm × 400 nm, but at the cost of higher propagation loss.As the WDM receiver based on the 900 nm × 160 nm waveguide would require only two etching steps and that the accuracy can Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.be controlled with a deviation of a few nm only, we believe that the design is not limited by the fabrication.Therefore, we opted for this design based on the 900 nm × 160 nm waveguide requiring the use of mode converters.However, with respect to the receiver design in Section II, since Si 3 N 4 is deposited with LPCVD, crack barriers and thermal cycling process would be required as cracks can occur for Si 3 N 4 films with thicknesses above 350 nm [28].Indeed, the mode converters and polarization rotator are 400 nm thick after the second etching step.
Figs. 4 and 5 illustrate the mode converter and the rotator respectively with the insets of the electric fields of the guided mode through the devices.The length of the tapered section of the mode converter is selected to ensure an adiabatic transition between the waveguides.The length of the input converter, which is adapted for the TM polarization, is 100 µm-long.The output mode converter however, is only 25 µm-long as it is designed for the TE polarization, resulting in a more confined mode in this case.Fig. 5(c) presents the simulated electric field profiles at different section of the rotator for an input TM 00 mode.A successful rotation can be observed when comparing the first and last electric fields.The main parameters of the device (lengths of the tapering sections, width w 2 of the nanowire) were optimized with EingenMode Expansion (EME) simulations.The optimizations start with a selection of a sufficiently large width w 2 to minimize the insertion loss and primary values for L 1 , L 2 and L 3 .The lengths are then swept one by one to maximize the conversion efficiency.Fig. 6 presents the impact of etching on the insertion loss of the input (a) and output (b) mode converters, for the TM and TE polarization respectively.Overall, the results show that the mode converters are robust to deviations in the etching depth, with the input converter showing insertion losses within 0.8 dB and the output converter within 0.1 dB.The loss is higher for the input converter due to the far weaker confinement of the TM 00 mode in the 900 nm × 160 nm waveguide, leading to a less effective adiabatic transition into the 500 nm × 400 nm waveguide.Fig. 7 shows the simulated conversion efficiency of the polarization rotator when the device is properly etched at 240 nm.The obtained conversion efficiency at 1035 nm is 99.9% and an extinction ratio of 40 dB at 1015 nm and 32 dB at 1055 nm.In addition, the TM-TE and TE-TM conversions show a bandwidth large enough to work at wavelengths between 800 and 1200 nm, but the extinction ratio is lower than 20 dB at these wavelengths.The high wavelength dependence of the device is due to the wavelength dependence of the effective index and thus of the modal confinement of the injected mode.To avoid effective index crossing between the TE 00 and TM 00 modes [17], we decided to make the nanowire section represented by the parameter w 2 (300 nm) in Fig. 5(a) significantly smaller the device's thickness, which was 400 nm.Shifting the notche's dip towards the center of the bandwidth of interest would require further enlarging w 2 but the extinction ratio's level at 1055 nm (-32 dB) in Fig. 7(b) is good enough for our system, which requires a maximum crosstalk level of -20 dB [12].A similar TM-TE conversion efficiency higher than 99% was obtained in [17].The calculated extinction ratio between the two polarizations is 38 dB.In Section II, we saw that the polarization splitter has an extinction ratio of 18 dB in the cross output, (where the rotator is placed) when the input polarization is TE.This signal will then be converted into a TM 00 mode by the rotator and then transmitted to the demultiplexing device in Fig. 2.However, as the demultiplexer is based on a cascaded MZI which is specifically designed for the TE polarization, this signal will be further attenuated.
Fig. 8 shows the simulated impact of the etching depth on the device's performance.The rotator shows good robustness to etching variations.In Fig. 8(a), we observe that the TM-TE conversion remains almost unchanged while the TM-TM conversion increases by 9 dB when under-etched by 5 nm and by 14 dB when over-etched by 5 nm.The zoom on the TM-TE conversion efficiencies in Fig. 8(b) shows that a ±5 nm etching variation has a negligible impact as the efficiency decreases by 0.017 dB in the worst case.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

IV. CONCLUSION
We proposed two integrated receivers based on a thin waveguides.The first design uses an AWG with a polarization splitter based on a straight directional coupler.The receiver has a polarization dependent loss of 1-2 dB depending on the channel and suffers from a slight channel shift of 1 nm in the worst case.This receiver design has an estimated size of 1800 µm × 1300 µm and only requires one array of photodiodes.In addition, only one etching step is required for this receiver.However, it was found in [12] that AWGs are more prone to fabrication defects with respect to MZIs and that the writing time was at least seven fold for a system with 4 channels.Finally, if this receiver only requires one array of photodiode, output edge couplers are more sensitive than grating couplers to possible misalignments between the array and the waveguides of the output channels.Advanced edge coupling designs using multilayers or subwavelength grating structures could be considered to reduce both the coupling and misalignment loss [29].
The second receiver design combines the polarization splitter used from the first design with a partially etched polarization rotator.Since the rotator is based on a 500 nm (width) × 400 nm (thickness) waveguide, which differs from the 900 nm × 160 nm base waveguide, this device requires partially etched mode size converters at the input and at the output ports.The interest of this receiver is the reduction of the fabrication complexity with selecting the thickness of the slab sections of the rotator and of the converters the same as the 900 nm × 160 nm base waveguide.Therefore, only two etching steps are required.The loss from the converters are 0.06 dB for the TE polarization and 0.6 dB for the TM polarization.The devices show in addition good tolerance to deviations in the etching depth.The polarization rotator has a TM-TE conversion efficiency of 99.9% and an extinction ratio between 30 and 40 dB.The rotator also good robustness to overand under-etching.To avoid possible interferences coming from unwanted signal, this receiver requires twice the amount of photodiodes with respect to the first design, which increases the cost of manufacturing, but this is compensated by the low complexity of the cascaded MZIs and the relaxed tolerance to misalignment offered by the grating couplers.However, advanced designs with a bottom reflector [3] or using a staircase profile [30] should be considered to reach high coupling efficiencies.Finally, the estimated size of this receiver is 2200 µm × 1300 µm, which is close to the first proposed design.

Fig. 1 .
Fig. 1.(a) Scheme of the whole PIC including an AWG and output grating couplers designed for one specific polarization.(b) Scheme of the polarization splitter.The length L of the straight section is 74 µm and the gap between the waveguides is 300 nm.FDTD simulation of the E-field profile of the polarization splitter for (c) TE and (d) TM polarizations.(e) Output transmission of the polarization splitter for TE and TM polarizations.(f) Extinction ratio of the splitter.(g) Simulations of the AWG for TE (continuous lines) and TM (dashed lines) polarizations.Each color corresponds to one specific output channel centered at a specific wavelength: λ 1 = 1023 nm, λ 2 = 1031 nm, λ 3 = 1039 nm and λ 4 = 1047 nm.

Fig. 2 .
Fig. 2. (a) Scheme of the full receiver based on two identical cascaded MZIs designed for the TE polarization.(b) Side view of the receiver with the SiN waveguides encapsulated in the SiO 2 cladding.The red arrows represent the light coming from the fiber and coupled into the array of photodetectors.(c) Transmission of the cascaded MZIs.Each color corresponds to one specific output channel.

Fig. 3 .
Fig. 3. (a) Scheme of the full polarization splitter/rotator.(b) Zoom on the polrization rotator with the mode size converters.

Fig. 4 .
Fig. 4. (a) Top view of the mode size converter.The input and output mode converters have different dimensions denoted as L and w.The length L of the upper linear taper is 25 µm for TE 00 (output) and 100 µm for TM 00 (input).The width for both input and output tapers is w = 100 nm.(b) Cross section of the device.The slab is 160 nm thick and the total height is 400 nm.(c) Onsets of the electric field profiles for both polarization.

Fig. 5 .
Fig. 5. (a) Top view of the polarization rotator.The optimum values found with eigenmode expansion (EME) simulations are L 1 = 100 µm, L 2 = 60 µm, L 3 = 20 µm and w 2 = 300 nm.(b) Cross section of the device.The thickness of the slab is the same as for the mode converters and the total height is 400 nm.(c) Onsets of the electric field profile of the guided mode at different sections of the device.The cyan and red arrow respectively represent the direction of the electric and magnetic fields.

Fig. 6 .
Fig. 6.Insertion losses of the TM (a) and TE (b) mode converters for different etching depths.The TM mode converter is placed at the input port of the rotator and the TE mode converter is placed at the output port.

Fig. 7 .
Fig. 7. (a) EME simulations of the polarization rotator.The dashed vertical lines represent the bandwidth of interest.(b) Simulation of the rotator within the bandwidth of interest.

Fig. 8 .
Fig. 8. (a) EME simulations of the impact of the etching depth on the performance of the rotator.(b) Zoom on the simulated TM-TE conversion efficiencies for different etchings.