Cross-polarization effects in sheared 2D grating couplers in a photonic BiCMOS technology

We investigate numerically and experimentally sheared 2D grating couplers in a photonic BiCMOS technology with a focus on their splitting behavior. Two realization forms of a waveguide-to-grating shear angle are considered. The cross-polarization used as a figure-of-merit is shown to be strongly dependent on the grating perturbation strength and is a crucial limitation not only for the grating splitting performance, but also for its coupling efficiency.


Introduction
Intra data center optical communication systems rely exclusively on low-cost technologies using a direct detection scheme. However, the increasing demand on even higher data rates poses the question on the adoption of coherent systems based e.g. on single-or dual-polarization quadrature phase shift keying (QPSK) or more generally on quadrature amplitude modulation (QAM). Such modulation formats feature the advantage of a better spectral efficiency. 1) On the other hand, coherent systems in data centers will require a technology, which is able to reduce their total cost to a reasonable level. For that reason, silicon photonics keeps receiving a strong interest from both industry and research, as it makes use of existing CMOS or BiCMOS foundries and promises for a cost-effective co-integration of electronics and photonics. 2,3) Monolithically integrated QPSK receivers have already been demonstrated for both single-and dual-polarization operation. 4,5) In dual-polarization (DP) QPSK or QAM receivers, the utilization of two-dimensional grating couplers (2D GC) is of particular interest, as they enable simultaneous coupling and polarization splitting of an optical signal with two polarization states. However, the first attempts for their realization were lacking a good coupling efficiency, reaching 20 % -25 % corresponding to an insertion loss between -7 dB and -6 dB. [6][7][8] Since then, many attempts * E-mail: galina.georgieva@tu-berlin.de have been made to reduce the coupling loss. 2D GCs with -3.2 dB were demonstrated, 9) which could be further improved up to around -2 dB by the adoption of a double-SOI substrate acting as a Bragg mirror 10) or -of a backside metal mirror. 11

) Without bottom reflection mirrors, 2D
GCs in 220 nm silicon-on-insulator (SOI) technology typically show an insertion loss between -5 dB and -4 dB. 12,13) Another thoroughly examined issue in 2D GCs is the polarization-dependent loss (PDL).
A possibility for its minimization was proposed by the adoption of a phase shifter. 14) Luxtera introduced first a modified 'clover' scatterer shape, 15) which inspired multiple investigations on the impact of the scatterer shape on the PDL in both C-and O-bands. [16][17][18] Also a 2D GC with fabrication tolerant stretched cylinders was shown. 19) The PDLs reported are as low as 0.2 -0.3 dB.
While the 2D GC coupling efficiency and PDL have been a subject of a strong interest, effects concerning the 2D GC splitting performance remained eclipsed. In early publications 6,7) the 2D GC splitting behavior was reported in terms of crosstalk. The values reached were below -15 dB. However, the crosstalk was not examined on any parameter dependence. In a more recent publication, the impact of the scatterer shape was discussed. 20) Our work here aims to conduct a thorough analysis on the splitting performance of 2D GCs, taking into account multiple dependencies. Our figure-of-merit -the cross-polarization (short: cross-pol.) is defined as the portion of power of one of the polarizations (e.g. the y-polarization), which is converted to the other one (e.g. the x-polarization) by the 2D GC. Hereby, it is of particular interest (a) how much of the cross-pol. power is coupled from a single-mode fiber (SMF) into the 2D GC and vice versa and (b) how much of the 2D GC power loss is attributed to the cross-pol.
The examined 2D GCs are here referred to as sheared 2D GCs. In the literature, a waveguide-to-grating shear angle has been often reported in 2D GCs. 8,17,18,20,21) Previously, we described a systematic design procedure of 2D GCs with a shear angle, 22) which is used for the designs considered here. We distinguish two types of sheared 2D GCs, in dependence on how the shear angle is practically realized. Previously, we investigated numerically and experimentally the cross-pol. in one of the two types in its dependence on two parametersthe shear angle and the etch depth, which is a measure for the grating perturbation strength. 23) Our work is here extended with the same analyses on the other type of sheared 2D GCs. In addition, we provide a more comprehensive explanation of the basic theory and the simulation results as well as of the principle of our experiment. We further discuss the possible impact of the cross-pol. on system level.
In Sec. 2 we first briefly describe the design of BiCMOS integrated sheared 2D GGs and the working principle of the device fabricated for the experimental evaluation of the crosspol. In the following Sec. 3, numerical results outline our expectations on the sheared 2D GCs splitting behavior, depending on their type, shear angle and etch depth. Next, statistical experimental results are used to confirm our observations. The test samples used here are fabricated in a full photonic BiCMOS flow based on 220 nm SOI, using a 248 nm deep UV lithography and comprising the complete backend of line stack. In addition, we analyze the potential impact of different cross-pol. levels on a system using DP QAM modulation formats.
The results finally summarized in Sec. 4 point out the importance of a deep understanding of the cross-pol. effects for both 2D GC design and low bit-error-rate (BER) coherent transmission.

Methods
In this section, we describe the specifics of the platform, which the proposed 2D GCs are intended for. Afterwards, the numerical design procedure is outlined, followed by an explanation of our experimental approach for the cross-pol. characterization.

Integration Platform
Many research groups investigating GCs work with optimized buried oxide or top cladding layers. The results achieved in such cases, however, are not automatically applicable to a (Bi)CMOS foundry. In addition, experimental evidence is often based on measurements of a single device, which raises questions regarding repeatability. The devices shown in our paper have the advantage of being fully integrated in a photonic BiCMOS 24) fabrication flow. They meet the requirements of the used platform. Moreover, we are able to perform a statistical analysis of their behavior and discuss the large-scale repeatability of the obtained results.
The photonic BiCMOS platform 24) used here integrates monolithically bulk-Si electronics in parallel with SOI photonics in the frontend of line (FEOL). Both electronic and photonic components are covered by a backend of line (BEOL) stack of about 13 µm height, which mainly comprises multiple SiO 2 layers of different thickness and optical properties. In addition, the platform offers five metal layers, which can be used to realize the shortest interconnects between photonics and electronics. On the electronic side, very fast SiGe:C heterojunction bipolar transistors (HBT) can be designed for the accomplishment of high-speed electronicphotonic systems. The fixed BEOL top stack is of huge importance for a GC design and is here taken into account in all simulations. Another aspect is the fixed minimal feature size, determined by the 248 nm deep UV lithography used. The latter defines the optimization limits of the GC scatterers size and shape.

Numerical Design of Sheared 2D GCs
A 2D GC must be designed in such a way, that two orthogonal polarizations from two silicon waveguides are in-or out-coupled into the two polarizations of a SMF mode by diffraction.
All sheared 2D GC designs here are intended for a silicon rib waveguide with 220 nm Si on 2 µm SiO 2 , where the rib etch depth is the same as the grating etch depth. The simulations are performed in the C-band. The waveguide and the grating need to be integrated in the previously described photonic BiCMOS and covered by the full BEOL stack. A waveguide schematic is shown in Fig. 1 together with the two types of sheared 2D GC design, depending on how the waveguide-to-grating shear angle is realized. Type I gratings have perpendicular waveguides and rhombus shaped grating area, while Type II have angled waveguides and square shaped grating. The existence of a shear angle is for the reason of improving the mode field overlap between the polarizations of the two waveguides and the SMF mode. A shear angle introduces a second degree of freedom along with the grating period, which allows for a change of the mode propagation direction in both ϕ and ϑ direction (see the coordinate system in Fig. 1). This is necessary, as a SMF must be placed at the symmetry plane ϕ = 45 • between the two waveguides. In our previous work, 22) we described the working principle of sheared gratings and derived a 2D diffraction condition, which is used here for all designs. The condition states, that certain combinations (α, Λ) correspond to certain radiation patterns (ϕ = 45 • , ϑ). We showed further that the choice of larger shear angles α leads to a larger angle ϑ in the symmetry plane for a desired wavelength.
The coupling angles and the determination of the grating parameters depend on the grating effective refractive index n eff . Because of the complexity of integrated gratings, which have a specific covering pattern, n eff is determined out of the simulated field components, by applying a 2D spatial Fourier transform. For a grating with optimized etch depth and scatterer size, corresponding to a certain n eff , the 2D Fourier transform delivers the actual radiation angles (ϕ, ϑ) and n eff can be calculated from the diffraction condition. If the angles require an adaption, the grating period can be afterwards adjusted without a further change of the scatterers dimensions and n eff .
For the numerical analysis of the cross-pol., we use a commercial time-domain solver by Simulia CST, which implements the finite-integration-technique. 25) We consider an outcoupling 2D GC with only one waveguide polarization excited, here the y-polarization (short: y-pol.). The radiated fields are evaluated at a tilted plane (ϕ = 45 • , ϑ), according to the coordinates in Fig. 1. We assume a standard SMF and calculate the power, which is properly coupled into its y-pol. The portion of power coupled into the x-polarization (short: x-pol.) is then referred to as a cross-pol. As the in-and out-coupling is reciprocal, the difference between the calculated y-and x-pol. powers in dB at a wavelength of interest corresponds to the 2D GC split ratio. A large split ratio indicates that the 2D GC is a good splitter. Because in practical measurements it is difficult to determine exactly the maximal transmission wavelength, we evaluate the mean split ratio in a wavelength range of 15 nm around the y-pol. maximal transmission. In this interval, the transmission changes by no more than 0.3 dB, which is typically the accuracy limit in transmission measurements.
Furthermore, we are interested also in the question whether the 2D GC is an efficient coupler, and consider for a wavelength of interest the power that remains inside the 2D GC without being radiated. We again calculate how much of this power loss is caused by the cross-pol.
Exact absolute values of the split ratio are challenging to simulate, because they depend on the numerical accuracy. Generally, a large amount of grid cells per wavelength is required for results with high accuracy, which is however connected to an extremely long simulation time.
Nevertheless, all results are calculated with the same accuracy (15 grid cells per wavelength) and allow for comparison of the structures with each other. It is important to note that 2D GCs of Type I and Type II require a different kind of mode excitation. While the waveguide mode in Type I can be calculated by a mode port, Type II has angled waveguides and an angled port is not supported by the time-domain solver. In that case, a waveguide mode is calculated externally and afterwards imported and tilted under the desired shear angle. Minor, differences in the numeric results between the two types of 2D GCs may thus result because of the different simulation procedure. MMI coupler split ratio is wavelength dependent, but the variation is small. The device working principle is the following -the 2D GC splits an incident wave of an arbitrary polarization into the two waveguide arms. If we denote these amplitudes as a 1 and b 1 , the ratio of their squares corresponds to the grating split ratio f , i.e to the power ratio between the polarizations in the two waveguides. We further normalize the amplitudes to the 2D GC input power

Device for a Cross-Polarization Measurement
We choose such coordinates that the split ratio here is defined as the y-to x-pol. power ratio similar to the simulated case. After the delay line and the MMI, the two signal paths interfere constructively or destructively at the outputs, depending on the wavelength and the corresponding phase delay ∆φ in the delay line. The ratio between the maximal and minimal signal transmission is known as an extinction ratio (ER) and can be measured after out-coupling with a 1D GC.
From the ER we are able to estimate the 2D GC split ratio by using a simple matrix model. 26) The relation between the input waves a 1 and b 1 and the output waves a 2 and b 2 can be mathematically written as a multiplication of a matrix T MMI describing the MMI coupler and a matrix T ∆φ describing the delay line: If we take e.g. the first output, the power measured there is proportional to the square of the wave amplitude a 2 P out ∼ |a 2 | 2 = 1 2 The maximum and the minimum of P out can be obtained by maximizing or minimizing sin ∆φ and their ratio results in the ER. If we further replace a 1 and b 1 through their split ratio f , we Measured ERs can be easily translated into split ratios. It is still an open question, how we determine if the 2D GC splits the polarizations well. The answer is illustrated by two examples, which do not consider the GCs filter spectra. In Fig. 2 (b), the incident polarization is such that the signal is equally split between the two waveguides. The split ratio is therefore 1 and from (4) we obtain an ER of infinity. The ER is, however, limited in real systems, so we consider another case in Fig. 2 (c). This time, the incident polarization is such that all the power is coupled in one of the waveguides. The example is chosen to match the simulated case. The split ratio is now f → ∞ and the ER is 1, which means that minimal and maximal levels are the same and no resonances result. In our experiment, we look therefore for a polarization, which leads to a minimal ER. Ideally, smooth transmission without resonances should result. Out of the minimal ER, we can estimate the best achievable split ratio of the considered structure.
The principle of our measurement may first look rather complicated, but as we perform manual measurements, it has two obvious advantages. First, the signals at the two MMI coupler outputs are the same and only phase shifted. Thus, it is sufficient to measure only one of the outputs, which reduces the time for the measurement and/or the setup complexity. Second, if we measure on two outputs, we need to guarantee that they are equally well coupled, which is practically very difficult in manual measurements. In this experiment, the in-and out-coupling efficiency has no impact on the determined split ratios. Also the mechanical coupling stability during the long wavelength sweep (typically 3-4 minutes) is less crucial.

Experimental Approach and Setup
The experimental verification of the numerically predicted behavior is carried out by manual

Results and Discussion
In this section, numerical and experimental results are used to discuss the impact of different design parameters on the cross-pol. effects in sheared 2D GCs. The 2D GC tilt angle is fixed to ϑ = 8 • , so we can compare different devices only around different central wavelengths. The constant angle is necessary to ensure similar coupling conditions in all measurements. In the last subsection, we move from device to a system aspect investigation of the cross-pol. effects by taking them into account in DP QAM transmission simulations.   be preferred. However, other than the shear angle, the etch depth has a strong impact on the grating out-coupled power. If the perturbation strength is too weak, a large amount of power remains guided and is not radiated by the grating. We consider this kind of loss and compare how much of the normalized input power remains inside the structure for the two different etch depths. Consider the numerical example in Fig. 4. On the left hand side, we have an input mode, which is purely y-pol. While this mode is propagating through the 2D GC, a portion of its power is coupled out towards a SMF. The geometries are such that the out-coupling angles are ϕ = 45 • , ϑ = 8 • for a wavelength of 1590 nm and an etch depth of 90 nm or for a wavelength of 1550 nm and an etch depth of 120 nm. Power losses are caused by radiation towards the substrate (not represented) and by the power guided in the structure.

Numerical Results
In Fig. 4, we clearly see that in both cases the further propagating mode has an y-pol. part  Finally, we have a look over the split ratio variation, if the fabricated grating holes show an asymmetry and have elliptical instead of circular shape. This would lead to a different wavelength shift of the spectra of the y-pol. and the cross-pol. If the holes are stretched or shrunk by 20 nm in y-direction we have around ∓1 dB variation of the split ratio. The variation is small compared to the expected split ratio difference for different etch depths, but of similar order with the expected split ratio difference between 2D GCs of different types or shear angles.

Fig. 5.
Exemplary measured interferometric curves of devices with sheared 2D GCs used for the comparison of the split ratio of three cases for two types of gratings -t1 (Type I with rhombus-shaped grating area) and t2 (Type II with angled waveguides).
The structures discussed in the previous subsection are now experimentally investigated. Fig. 5 shows on example interferometric curves for each of the devices considered. The polarization is chosen such, that a minimal ER results. The transmission includes the coupling losses at the input and the output. Compared to our previous results 23) we managed to further minimize the ER for each of the structures, by scanning more precisely the PoincarÃľ sphere. This does not change our general observations. Another difference here is the wider wavelength range of 15 nm around the maximal transmission. We also repeated our previous measurement on the Type I 2D GCs, in order to make the two types of 2D GCs comparable to each other. It is important to note that split ratios below 20 dB, which correspond to ERs of below 1.5 dB become very difficult to measure, because other effects like Fabry-Perot resonances and noise start to predominate and make the determination of the ER difficult. In Tab. II the averaged split ratios in a 15 nm wavelength range for each of the cases are summarized. The mean split ratio results from the averaging over 10 chips and the standard deviation σ is given as well. All structures, which are directly compared to each other, show a similar standard deviation. The differences between structures of Type I and Type II vary from one structure to another and we cannot generally state that one of the types has an advantageous splitting behavior. The lack of systematic difference can be caused by variations of the hole shapes, causing various 2D GC asymmetries. Such variations can make differences between the gratings with the different shear angles α = 2 • , 3 • also difficult to be observed.
Being difficult to distinguish from other fabrication variations, the differences between the 2D GCs of different types or with different shear angle appear to be of minor importance.
The split ratio for a certain etch depth appears to be of similar order, independent of the particular 2D GC geometry. Compared to the simulations, the difference between the split ratios for d = 120 nm and d = 90 nm is lower -between 1 dB and 3 dB and better pronounced for the 2D GCs of Type I. The deviations from the simulation can be caused again by different asymmetry variation of the gratings. Nevertheless, the distinction between structures with different etch depths is still measurable, which shows that the grating perturbation strength has the most pronounced impact on the 2D GC splitting performance.
If we discuss the absolute values of the split ratios, we have to point out that they depend on the channel width around a wavelength of choice. We consider only a narrow channel around a maximal transmission wavelength. The estimated split ratios obtained by the experiment reach levels that are better than predicted numerically. This can result from several reasons. The first one is the previously mentioned limited accuracy of the numerical results, because of the chosen wavelength and spatial resolution. Another reason can be the fact that in simulations the impact of the tapers is not taken into account. The desired polarization and the crosspol. do not have generally the same coupling angles (ϕ, ϑ), which is evident by their shifted coupling spectra. Thus, it is possible that the cross-pol. has a higher taper loss, especially if it enters the taper under a non-perpendicular angle. In future, the possible impact of tapers and waveguides needs to be investigated in more detail. In an integrated DP coherent detection receiver, a 2D GC cross-pol. resulting in a limited polarization split ratio can be expressed as a crosstalk between two data streams with the same source. The system behavior in such a case is comparable to the in-band crosstalk, discussed in long haul transmission systems. 27) We perform an exemplary simulation, where the split ratio is varied and the SNR penalty for reaching the forward error correction (FEC) limit of BER = 10 −3 is determined. A 28 Gbaud transmission using a laser with a linewidth of 100 kHz is assumed (local oscillator effects are neglected). Polarization mode dispersion (PMD) is not taken into account. Fig. 6 shows the SNR penalty over the 2D GC split ratio for different QAM formats. If we permit a 1 dB penalty (corresponding to the red dashed line in Fig. 6), we can estimate the minimal split ratio required for the desired QAM format. The results shown in this example correspond closely to the findings in the case of a fiber transmission link. 27) For QPSK, 8-PSK, 16-QAM, 32-QAM and 64-QAM, the required split ratios are 16.5 dB, 21.5 dB, 23.5 dB, 26.5 dB and 29 dB. The 2D GC designs discussed here reach mostly split ratios better than 16.5 dB, which make them suitable for DP QPSK. However, for higher order modulation formats the limited split ratio becomes more critical. Therefore, the suppression of cross-pol. effects in 2D GCs is crucial for the realization of integrated higher order DP QAM systems.

Conclusions
We analyzed numerically and experimentally cross-polarization effects in sheared 2D grating couplers. The focus was set on the gratings splitting behavior, but the grating coupling efficiency was shown to be affected by the cross-polarization as well.
Numerical results predicted small differences in the splitting performance of sheared 2D GCs of different types or with different shear angles. Experimentally, such differences could not be systematically measured. Their strength is therefore of the same order like effects because of fabrication deviations on the wafer. Thus, the choice of a 2D GC type or a shear angle plays a less significant role for the 2D GC splitting functionality.
A comparison between 2D GCs with a variable etch depth corresponding to a variable perturbation strength showed both numerically and experimentally that deeply etched gratings have a worse splitting performance. In addition, simulations showed that increased perturbation strength leads to a large amount of power loss, caused by a cross-polarization further propagating in the grating. The cross-polarization restricts therefore the maximal achievable out-coupled power, which is an important limitation for the 2D GC coupling efficiency.
Finally, we estimated the potential impact of different levels of cross-polarization, when a 2D GC is used as a part of a DP QAM receiver. For a QPSK modulation, the demands on the SNR penalty for a desired BER can be met by the current 2D GCs. The adoption of higher order modulation formats requires further improvement of the 2D GCs splitting functionality.
Experimentally, the splitting performance was less affected by cross-polarization effects than numerically predicted. In future, the cross-polarization propagation behavior and the influence of other components like tapers, waveguides and bends are to be studied in more detail. Furthermore, possibilities for optimizing the 2D GC perturbation strength to achieve both high efficiency and low cross-polarization are to be investigated.