# Integrated polarization beam splitters in the silicon nitride platform for 950 and 1300 nm wavelengths

Zindine Mokeddem, William Fraser, Martin Vachon, Winnie N Ye, Laurent Vivien, Delphine Marris-Morini, Eric Cassan, Carlos Alonso-Ramos, Dan-Xia Xu, Jianhao Zhang, et al.

► To cite this version:

Zindine Mokeddem, William Fraser, Martin Vachon, Winnie N Ye, Laurent Vivien, et al. Integrated polarization beam splitters in the silicon nitride platform for 950 and 1300 nm wavelengths. Optics Letters, 2025, 50 (7), pp.2310-2313. 10.1364/OL.560110. hal-04758322v2

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# Integrated polarization beam splitters in the silicon nitride platform for 950 and 1300 nm wavelengths

ZINDINE MOKEDDEM<fnref n="1" />,*, WILLIAM FRASER<fnref n="4" />, MARTIN VACHON<fnref n="2" />, WINNIE N. YE<fnref n="4" />, LAURENT VIVIEN<fnref n="1" />, DELPHINE MARRIS-MORINI<fnref n="1" />, ERIC CASSAN<fnref n="1" />, CARLOS ALONSO-RAMOS<fnref n="1" />, DAN-XIA XU<fnref n="2" />, JIANHAO ZHANG<fnref n="2" />, MAZIYAR MILANIZADEH<fnref n="2" />, YURI GRINBERG<fnref n="3" />, PAVEL CHEBEN<fnref n="2" />, JENS H. SCHMID<fnref n="2" />, AND DANIELE MELATI<fnref n="1" />

Compiled April 17, 2025

Photonic integration in the silicon nitride (SiN) platform enables low propagation losses and a wide transparency range, making it ideal for quantum applications. However, polarization control in SiN is challenging because of its low birefringence. This work demonstrates polarization beam splitters using asymmetric directional couplers in SiN, designed for 950 nm and 1300 nm wavelengths. These devices exhibit low insertion losses (<1 dB) and high polarization extinction ratios (20-30 dB).

http://dx.doi.org/10.1364/ao.XX.XXXXXX

## 1. INTRODUCTION

Silicon nitride (SiN) has garnered significant attention due to the advantages it offers for photonic integration [1]. SiN waveguides can provide low propagation losses, reduced nonlinear effects, small birefringence, and a wide transparency window ranging from the visible to the mid-infrared spectrum (~500-3500 nm) [2]. These advantages are especially appealing for quantum applications [3, 4], which often require components with minimal insertion losses and operating at wavelengths shorter than those typically used in telecommunications (1300 nm - 1550 nm). For example, efficient sources of single photons have been demonstrated using InAsP quantum dots with an emission spectrum near 950 nm [5]. Quantum system integration, combining such sources with on-chip devices for photon manipulation, hence requires the development of SiN devices with sufficiently high performance in new wavelength ranges. In this context, polarization control devices are crucial. Orthogonal polarizations of a photon can be utilized as qubits to encode information [6]. As another example, the polarization extinction ratio limits the quantum bit error rate in quantum cryptography systems [7].

Despite the relatively low birefringence of SiN waveguides, particularly in comparison with the silicon-on-insulator platform,

the optical performance of devices still significantly depends on light polarization [8]. At the same time, the low birefringence of SiN waveguides makes designing devices particularly challenging, because the small difference in the transverse-electric (TE) and transverse-magnetic (TM) effective indices often leads to devices with a large footprint [9]. Polarization beam splitters (PBS) in the SiN platform have been demonstrated at $λ = 1550$ nm using multi-mode interferometers (MMIs) [10–12], Mach-Zehnder interferometers [13], and directional couplers [14]. MMI-based PBS often have a large footprint, exceeding several hundred micrometers, while Mach-Zehnder interferometers require accurate phase delay with active controllers to compensate for manufacturing imperfections [10]. Conversely, PBS based on directional couplers can achieve high performance with a comparatively compact footprint [14–16]. Despite the considerable interest in the large transparency range of SiN, only a few polarization control devices have been developed at wavelengths shorter than the optical communication C band. Polarization beam splitters have been demonstrated at wavelengths of 1300 nm [17] and 780 nm [18], but to the best of our knowledge, not yet at 950 nm.

In this paper, we present the design and experimental demonstration of polarization beam splitters with unprecedented performance based on asymmetric directional couplers in the SiN platform. The first device is designed for a central wavelength of 950 nm, covering the emission spectral range of InAsP quantum dots, and achieves a polarization extinction ratio (PER) of 24 dB and losses lower than 1 dB (limited by the experimental setup). The second device is designed for the datacom O-band at 1300 nm and serves as a benchmark for the 950 nm design, reaching a PER of 32 dB and record low losses of 0.1 dB. We also demonstrate a considerable improvement in the operational bandwidth of both devices by exploiting tapered directional couplers.

## 2. DEVICE PRINCIPLE AND DESIGN

Our PBS incorporates two cascaded asymmetric directional couplers, as shown in Fig. 1. The device achieves polarization

<footnote n="1">¹Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 91120 Palaiseau, France</footnote>

<footnote n="2">²Quantum and Nanotechnologies Research Centre, National Research Council Canada, K1A 0R6 Ottawa, Canada</footnote>

<footnote n="3">³Digital Technologies Research Centre, National Research Council Canada, K1A 0R6 Ottawa, Canada</footnote>

<footnote n="4">⁴Department of Electronics, Carleton University, K1S 5B6 Ottawa, Canada</footnote>

<footnote>*zindine.mokeddem@cnrs.fr</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Schematic of the PBS and cross-sectional view of the directional coupler at the position (i) marked by the yellow dashed line.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Calculated effective refractive indices as a function of the waveguide width for the fundamental and first-order modes, for (a) 950 nm and (b) 1300 nm wavelengths. The black dashed line indicates the phase matching condition</figcaption></figure>

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splitting by coupling light propagating in the fundamental TM0 mode at the input port to the TM1 mode of the central waveguide through the first directional coupler (Fig. 1). The TM1 mode of the central waveguide is then coupled to the TM0 mode of the cross-port waveguide by a second coupler, identical to the first one. Efficient mode coupling is obtained by satisfying the phase-matching condition $n_{eff}^{TM0}(w_1) = n_{eff}^{TM1}(w_2)$, where $w_1$ is the width of the input and cross-port waveguides and $w_2$ is the width of the central waveguide (Fig. 1). This design also ensures that $n_{eff}^{TE0}(w_1) \neq n_{eff}^{TE1}(w_2)$. Therefore, light propagating in the fundamental TE0 mode of the input is not coupled to the central waveguide and propagates directly to the output through port.

We consider a silicon nitride platform with a waveguide core thickness of 400 nm, surrounded by 4.5 µm of SiO₂ buried oxide and 3 µm of SiO₂ upper cladding. The refractive index of the SiN material is 2.01 and 2.00 for wavelengths of 950 nm and 1300 nm, respectively. A finite-difference eigenmode solver was used to calculate the effective indices of the propagating modes for different waveguide widths. Simulation results are shown in Fig. 2(a) and (b) for $\lambda = 950$ nm and $\lambda = 1300$ nm, respectively. These calculations were used to determine the waveguide widths $w_1$ and $w_2$ for which the phase-matching condition is satisfied. For the device operating at 950 nm, $w_1 = 0.51$ µm and $w_2 = 1.28$ µm provide the required phase matching between the TM0 and TM1 modes, while ensuring the directional coupler is asynchronous for TE polarized modes. For $\lambda = 1300$ nm, the phase matching condition is found at $w_1 = 0.68$ µm and $w_2 = 1.79$ µm. In both cases, the value of $w_1$ was chosen to ensure that the waveguide remained single mode and that $n_{eff}^{TE0}(w_1) \neq n_{eff}^{TM0}(w_1)$ in order to avoid spurious polarization rotations.

The optimal coupling lengths (Lc) and gap widths ($w_{gap}$) were determined using an eigenmode expansion solver (EME)

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Simulated cross transmission from TM0 of the input waveguide to TM1 of the central waveguide for different fabrication biases $\delta w$ for (a) $\lambda = 950$ nm and (b) $\lambda = 1300$ nm.</figcaption></figure>

to calculate the conversion efficiency for the TM0 mode of the input (and cross-port) waveguide and the TM1 mode of the central waveguide. At a wavelength of 950 nm, a coupling length Lc = 55 µm with a gap width of $w_{gap} = 0.35$ µm provided the highest coupling efficiency. Likewise, the highest coupling was achieved at Lc = 62 µm and $w_{gap} = 0.55$ µm for $\lambda = 1300$ nm. In both cases, the calculated transmission from the input to the through and cross output ports were $T_{th}^{TE} = 94\%$ and $T_{x}^{TM} = 99\%$. The 94% transmission for TE is mainly due to residual coupling of TE0 to TE1 in the central waveguide.

In order to minimize losses, an S-bend was used to adiabatically vary the separation of the input and output cross and through ports from the central waveguide. A radius of 100 µm ensured a smooth transition without abrupt changes of the geometry and minimized spurious polarization rotations. Bent waveguides were however not included in the simulations due to difficulty of EME in handling steep angles.

The performance of the PBS relies strongly on satisfying the phase-matching condition. The impact of fabrication imperfections needs to be considered, as manufactured waveguide widths can deviate from the nominal values. To assess the impact of fabrication, we used EME simulations to compute the coupling efficiency between the TM0 mode of the input and cross-port waveguides and the TM1 mode of the central waveguide, varying the waveguide width by $\delta w \pm 10$ nm. The calculated results are shown in Fig. 3. Deviations in waveguide widths result in a decrease of the maximum conversion efficiency and a shift in the central wavelength. Fabrication errors have a more pronounced impact on the device operating at 950 nm compared to 1300 nm. For $\delta w = +10$ nm at $\lambda = 950$ nm, the conversion efficiency decreases from 99.3 % to 95.3 %, and the central wavelength is blue-shifted by 7 nm. Although the 4 % drop in conversion efficiency is comparatively small, the device re-converts the TM1 mode of the central waveguide to the TM0 mode of the output waveguide, yielding a full transmission $T_{x}^{TM} = 90.8\%$, i.e., a 7 % penalty compared to the nominal value. At 1300 nm, the conversion from TM0 to TM1 decreases only slightly from 99.5 % to 98.8 %, with a central wavelength shift of 6 nm. The higher robustness of the 1300 nm design is primarily due to the derivative of the mode effective refractive index with respect to waveguide width that is larger at 950 nm than at 1300 nm (see Fig. 2).

To mitigate the impact of waveguide width deviations and increase the operational bandwidth, we incorporated linear tapers in the access and central waveguides of the two directional couplers as shown in Fig. 4 [18]. In this tapered design, the width of the input waveguide varies from $w_1 + \Delta w$ to $w_1 - \Delta w$ while
<figure><img src="image_5.png" /><figcaption>Fig. 4. Schematic of the tapered PBS design.</figcaption></figure>

the central waveguide is tapered from $w_2 - \Delta w$ to $w_2 + \Delta w$, i.e., the gap width remains invariant. For the nominal design (no fabrication bias), the phase-matching condition is fulfilled at the center of the tapers. Unlike for the design without tapers (Fig. 1), even in the presence of fabrication imperfections, the two waveguide widths $w_1$ and $w_2$ required for phase matching are still located within the taper region, thereby improving fabrication robustness.

The optimal taper length ($L_t$) and width variation ($\Delta w$) were determined by calculating the coupling between TM0 and TM1 modes using EME simulations. The maximum coupling efficiency was achieved for $\Delta w = 0.05$ µm and $\Delta w = 0.03$ µm for the 1300 nm and 950 nm designs, respectively. The required coupling length was almost twice larger for tapered design compared to that without tapers, i.e., $L_t = 145$ µm and $L_t = 121$ µm for 1300 nm and 950 nm, respectively. This is because without tapers, the phase-matching condition is achieved all along the directional coupler, hence making coupling more efficient. The maximum transmissions are $T_{th}^{TE} = 84\%$ and $T_x^{TM} = 98\%$ at $\lambda = 950$ nm, and $T_{th}^{TE} = 91\%$ and $T_x^{TM} = 99\%$ at $\lambda = 1300$ nm.

Device performance was further evaluated by investigating the polarization extinction ratio (PER) and the insertion loss (IL), defined for TE input as $PER_{TE} = 10 \cdot \log_{10} T_{th}/T_x$ and $IL_{TE} = -10 \cdot \log_{10} T_{th}$ and for TM input $PER_{TM} = 10 \cdot \log_{10} T_x/T_{th}$ and $IL_{TM} = -10 \cdot \log_{10} T_x$. For devices without tapers, simulations predict $PER_{TE/TM} = 26$ dB / 21 dB at 950 nm and $PER_{TE/TM} = 27$ dB / 23 dB at 1300 nm. For devices with tapers, $PER_{TE/TM} = 16$ dB / 19 dB at 950 nm and $PER_{TE/TM} = 22$ dB / 24 dB at 1300 nm. Figure 5 shows the dependence of $PER_{TM}$ on wavelength for different manufacturing bias, for devices with and without tapers. For devices operating at 950 nm, for $\delta w = +10$ nm, $PER_{TM}$ increases from 12 dB (no taper) to 18 dB (with taper), i.e., an ER increase of 6 dB. Furthermore, the wavelength shift is reduced from 7 nm (no taper) to 2 nm (with taper). For the 1300 nm device, the use of tapers is also effective in improving the device robustness, resulting in $PER_{TM}$ above 23 dB for a fabrication bias of $\pm 10$ nm. The wavelength shift is also reduced, from 6 nm (no taper) to less than 0.5 nm (with taper).

### 3. FABRICATION AND CHARACTERIZATION

The PBS was fabricated using a fabrication process based on electron beam lithography. Edge couplers based on inverse tapers were used for light coupling at each port. The taper tip width was selected as 0.13 µm for the 950 nm design and 0.18 µm for the 1300 nm design. EME simulations of the inverse taper at 950 nm yielded insertion losses of 0.8 dB for TE and 2.3 dB for TM, respectively. Similarly, at 1300 nm, the simulations predicted insertion losses of 1.1 dB for TE and 1.4 dB for TM. In both cases, no polarization rotation occurred within the inverse taper. The polarization of the light injected at the input port during the characterization was controlled with a half-wave plate and a

<figure><img src="image_6.png" /><figcaption>Fig. 5. Simulation of $PER_{TM}$ as a function of wavelength for various fabrication manufacturing imperfection ($\delta w$). (a) Design without taper and (c) with taper at 950 nm; (b) design without taper and (d) with taper at 1300 nm.</figcaption></figure>

polarizer. The light was then injected into the chip and collected from the chip by using micro-objectives (see Supplementary).

Figures 6 (a-d) show the measured transmission spectra $T_x$ and $T_{th}$ at the cross and through ports (blue and red solid lines, respectively) for the PBS operating at 950 nm wavelength. Results are shown for TE and TM input modes and for the PBS with and without tapers. Transmission is normalized to that of a straight reference waveguide without a PBS for each polarization independently. Simulated transmissions spectra obtained with the EME solver (dashed lines) are shown for comparison. The device without tapers achieves $PER_{TE} = 29$ dB and $PER_{TM} = 24$ dB at 930 nm. For the PBS with tapers, the maximum TE polarization extinction is $PER_{TE} = 26$ dB ($\lambda = 915$ nm), and is reduced for the TM mode to $PER_{TM} = 17$ dB ($\lambda = 980$ nm). Improved performance in terms of PER variation with wavelength is observed with the tapered device; $PER_{TM}$ remains above 10 dB over the 930 to 980 nm wavelength range, while for the devices without tapers PER drop from over 20 dB to less than 10 dB over the same range. $PER_{TM}$ is the limiting parameter in both cases, while $PER_{TE}$ exceeds 15 dB over the entire measured band. This is expected because the TM mode couples through the two directional couplers (see Fig. 1), while the TE mode propagates directly from the input to the through port. For the tapered device, we notice that the $PER_{TE}$ decreases at higher wavelengths. This is because the taper favors phase-matching for TE at these wavelengths. For both PBS designs, the TE and TM insertion losses are below 1 dB over the 915 nm - 945 nm wavelength range, while $IL_{TM}$ increases to $\sim 3$ dB for the device without taper beyond 970 nm.

The experimental results for the PBS devices operating at $\lambda = 1300$ nm are shown in Fig. 6 (e-h) alongside simulated transmission spectra. In this case, the device without tapers achieves $PER_{TE/TM} = 32$ dB at 1310 nm. For a precise characterization of insertion losses by means of a cut-back method, test structures with multiple cascaded devices were fabricated for this design. This approach yielded an exceptional low value of 0.1 dB for both TE and TM modes. To the best of our knowledge, this PBS exhibits the lowest reported insertion loss on the SiN platform (see Supplementary). This is primarily achieved by optimizing the transition between the input waveguide and the first coupler while minimizing abrupt geometric changes. Incorporating tapers in the directional couplers has a similar impact on performance to that observed for the device operating at 950 nm. $PER_{TE}$ is affected by the coupler at longer wavelength, while
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Simulated (dashed lines) and measured (solid lines) transmission spectra at the through and cross ports of the four PBS designs. (a,c) TE mode input for the PBS without and with tapers near 950 nm. (b,d) TM mode input for the same devices. (e-h) Results for the devices operating in the 1300 nm wavelength band.</figcaption></figure>

$PER_{TM}$ is reduced to 17 dB at 1310 nm. The PBS with tapers shows a larger operational bandwidth. $PER_{TM}$ remains above 10 dB across the wavelength range of 1250 nm - 1350 nm. For the device without a taper, $PER_{TM}$ is above 10 dB only in the wavelength range of 1280 nm - 1340 nm. $PER_{TE}$ does not show a significant wavelength dependence and remains above 25 dB over the entire bandwidth. The insertion losses for the device with tapers, $IL_{TE}$ and $IL_{TM}$, remain below 1 dB over the entire wavelength band.

For devices without tapers, simulations show slightly worse performance than indicated by the experimental results. This is due to the fact that EME simulations used to calculate the conversion from mode TM0 to TM1 did not include S-bent waveguides. The central waveguide was introduced abruptly in the simulation, resulting in extra losses due to the transition. These additional losses are not considered when calculating the residual

TM transmission to the through port as $T_{th}^{TM} = 1 - T_{TM0/TM1}$ (with $T_{TM0/TM1}$ the result of the EME simulation), which is hence overestimated. These losses are minimized in the fabricated device with the introduction of the S bends that allow to gradually bring the two waveguides together

## 4. CONCLUSION

We have experimentally demonstrated polarization splitters in the SiN platform operating at 950 and 1300 nm wavelengths. Fabricated devices consistently show low insertion loss below 1 dB. For the PBS without taper operating at the 1300 nm wavelength, dedicated test structures enabled a precise quantification of losses, revealing exceptionally low values of 0.1 dB for both TE and TM modes. Devices operating at 950 nm and utilizing straight cascaded directional couplers have a maximum PER of 24 dB, while employing tapered directional couplers yields a large operational bandwidth of 70 nm with a PER exceeding 10 dB. Devices designed for 1300 nm have a maximum PER of 32 dB without the use of tapered couplers, while an operational bandwidth of 100 nm with a PER larger than 10 dB is achieved by using tapered coupled waveguides. Even higher PERs could be obtained by cascading multiple PBSs or using on-chip polarization filters. We believe that these results represent significant advancements in polarization management for SiN-based photonic integrated circuits operating at 950 nm and 1300 nm wavelengths.

**Acknowledgment.** This work has been supported by an Ideation Fund-Small Teams Initiative by the National Research Council Canada.

**Disclosures.** The authors declare no conflicts of interest.

**Supplemental document.** See Supplement 1 for supporting content

## REFERENCES

1. D. J. Blumenthal, R. Heideman, D. Geuzebroek, A. Leinse, C. Roelofszen, IEEE **106** (2018).

2. P. Muñoz, G. Micó, L. A. Bru, D. Pastor, D. Pérez, J. D. Doménech, J. Fernández, R. Baños, B. Gargallo, R. Alemany, A. M. Sánchez, J. M. Cirera, R. Mas, and C. Domínguez, Sensor **17** (2017).

3. D. J. Blumenthal, APL Photonics **5** (2020).

4. J. G. Rarity, P. R. Tapster, P. M. Gorman and P. Knight, New J. Phys. **4** (2002).

5. D. Dalacu, K. Mnaymneh, J. Lapointe, X. Wu, P. J. Poole, G. Bulgarini, V. Zwiller, and M. E. Reimer, Nano Lett. **12**, 5919 (2012).

6. W. Tittel, G. Weihs, Quantum Inf. Comput. **1**, 3 (2001).

7. P. Wang, Q. Zhang, H. Xie and B. Guo, Electronics **12**, 1859 (2023).

8. D. Dai, L. Liu, S. Gao, D. Xu, S. He, Laser Photonics Rev **7**, 303 (2013).

9. S. Gao, Y. Wang, K. Wang and E. Skafidas, IEEE Photonics Technology Lett. **28** (2016).

10. M. Tosi, A. Fasciszewki, L. A. B. Rossini, P. A. Costanzo Caso, IET Optoelectron. **14**, 120 (2019).

11. J. Zhan, J. Brock, S. Veilleux and M. Dagenais, Opt. Express **29**, 14476 (2021).

12. R. Kudalippalliyalil, T. Murphy and K. Grutter, Opt. Express **28**, 34111 (2020).

13. J. Feng and R. Akimoto, Jpn. J. Appl. Phys. **54** (2015).

14. B. Bhandari, C. Im, O. R. Sapkota, S. Lee, Opt. Lett **45**, 5974 (2020).

15. C. Li, M. Zhang, J. Bowers and D. Dai, Opt. Lett. **45**, 2259 (2020).

16. D. Wang, Y. Hu, W. Yue, Y. Zeng, Z. Tu, Y. Cai, W. Wang, Q. Fang and M. Yu, Appl. Opt. **58**, 8221 (2019).

17. S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Durán-Valdeiglesias, X. Le Roux, N. Vulliet, E. Cassan, D. Marris-Morini, C. Baudot, F. Boeuf and L. Vivien, IEEE Photonics Technol. Lett. **30**, 19 (2018).

18. K. Gallacher, P. F. Griffin, E. Riis, M. Sorel, D. J. Paul, APL Photonics **7** (2022).
FULL REFERENCES

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

1. D. J. Blumenthal, R. Heideman, D. Geuzebroek, A. Leinse, C. Roelof-fzen, "Silicon Nitride in Silicon Photonics," IEEE 106 (2018).

2. P. Muñoz, G. Micó, L. A. Bru, D. Pastor, D. Pérez, J. D. Doménech, J. Fernández, R. Baños, B. Gargallo, R. Alemany, A. M. Sánchez, J. M. Cirera, R. Mas, and C. Domínguez, "Silicon Nitride Photonic Integration Platforms for Visible, Near-Infrared and Mid-Infrared Applications," Sensor 17 (2017).

3. D. J. Blumenthal, "Photonic integration for UV to IR applications," APL Photonics 5 (2020).

4. J. G. Rarity, P. R. Tapster, P. M. Gorman and P. Knight, "Ground to satellite secure key exchange using quantum cryptography," New J. Phys. 4 (2002).

5. D. Dalacu, K. Mnaymneh, J. Lapointe, X. Wu, P. J. Poole, G. Bulgarini, V. Zwiller, and M. E. Reimer, "Ultraclean Emission from InAsP Quantum Dots in Defect-Free Wurtzite InP Nanowires," Nano Lett. 12, 5919-5923 (2012).

6. W. Tittel, G. Weihs, "Photonic entanglement for fundamental tests and quantum communications," Quantum Inf. Comput. 1, 3-56 (2001).

7. P. Wang, Q. Zhang, H. Xie and B. Guo, "Optimized Polarization Encoder with High Extinction Ratio for Quantum Key Distribution System," Electronics 12, 1859 (2023).

8. D. Dai, L. Liu, S. Gao, D. Xu, S He, "Polarization management for silicon photonic integrated circuits," Laser Photonics Rev 7, 303-328 (2013).

9. S. Gao, Y. Wang, K. Wang and E. Skafidas, "Low-Loss and Broadband 2 × 2 Polarization Beam Splitter Based on Silicon Nitride Platform," IEEE Photonics Thechnology Lett. 28 (2016).

10. M. Tosi, A. Fasciszewki, L. A. B. Rossini, P. A. Costanzo Caso, "Silicon nitride polarisation beam splitters: a review," IET Optoelectron. 14, 120-124 (2019).

11. J. Zhan, J. Brock, S. Veilleux and M. Dagenais, "Silicon nitride polarization beam splitter based on polarization-independent MMIs and apodized Bragg gratings," Opt. Express 29, 14476-14485 (2021).

12. R. Kudalippalliyalil, T. Murphy and K. Grutter, "Low-loss and ultra-broadband silicon nitride angled MMI polarization splitter/combiner," Opt. Express 28, 34111-34122 (2020).

13. J. Feng and R. Akimoto, "Silicon nitride polarizing beam splitter with potential application for intersubband-transition-based all-optical gate device," Jpn. J. Appl. Phys. 54 (2015).

14. B. Bhandari, C. Im, O. R. Sapkota, S. Lee, "Highly efficient broadband silicon nitride polarization beam splitter incorporating serially cascaded asymmetric directional couplers," Opt Lett 45, 5974-5977 (2020).

15. C. Li, M. Zhang, J. Bowers and D. Dai, "Ultra-broadband polarization beam splitter with silicon subwavelength-grating waveguides," Opt. Lett. 45, 2259-2262 (2020).

16. D. Wang, Y. Hu, W. Yue, Y. Zeng, Z. Tu, Y. Cai, W. Wang, Q. Fang and M. Yu, "Broadband and compact polarization beam splitter based on an asymmetrical directional coupler with extra optimizing designs," Appl. Opt. 58, 8221-8226 (2019).

17. S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Durán-Valdeiglesias, X. Le Roux, N. Vulliet, E. Cassan, D. Marris-Morini, C. Baudot, F. Boeuf and L. Vivien, "Broadband Polarization Beam Splitter on a Silicon Nitride Platform for O-Band Operation," IEEE Photonics Technol. Lett. 30, 19 (2018).

18. K. Gallacher, P. F. Griffin, E. Riis, M Sorel, D. J. Paul, "Silicon nitride waveguide polarization rotator and polarization beam splitter for chip-scale atomic systems," APL Photonics 7 (2022).