Abstract

Polarization beam splitters (PBSs) are central elements for polarization handling. Here, we present the design of an ultra-broadband, low-loss, and easy-to-fabricate PBS based on a silicon nitride asymmetrical directional coupler for polarization-sensitive optical coherence tomography systems. The phase difference between transverse electric and transverse magnetic modes is introduced by using straight waveguides with different widths and an offset between them. A bent waveguide is placed close to the end of the through port in order to increase the operating bandwidth (i.e., more than 220 nm with greater than 15 dB of extinction). The overall device length is only 400 µm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Polarization handling remains of great importance in many fields including optical telecommunication [1], data storage [2], quantum computing [3], signal processing [4], and medical imaging [5]. Polarization beam splitters (PBSs) are the central elements of polarization handling which split random polarization state of the input light into two orthogonal polarization states. This function is used for applications where a specific polarization state is needed to probe different properties (e.g. sensors, optical imaging etc.). For example, in optical imaging, the polarization state of the light gives tissue specific contrast to optical images, which is very important in differentiating different types of tissues. Polarization sensitive optical coherence tomography (PS-OCT) is a good example of such an optical imaging system, which provides quantitative information of tissues based on the fact that most tissues can alter the light’s polarization state and show therefore a tissue specific contrast in images [5,6] (see Fig. 1(a)). A PBS with high extinction ratio (ER), low loss, and large operational bandwidth is one of the core components of a PS-OCT system. Current PS-OCT systems use free-space PBSs, which are sensitive to mechanical motion in addition to being bulky. This limits the compatibility of such devices in clinical use.

 figure: Fig. 1

Fig. 1 (a) Schematic of a polarization-sensitive OCT system. Blue regions consist of polarization components. The size of the polarization delay unit (PDU) is approximately 20 cm x 20 cm. Modified from Ref [5]. with permission. (b) Schematic of the packaged integrated PBS with fiber connectors.

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Several integrated optics based PBS designs have been proposed in the literature, which use multi-mode interference couplers (MMIs) [7], asymmetrical Y-junction structures [8], Mach-Zehnder interferometers (MZIs) [9], symmetric and asymmetrical directional couplers [10–18] as the core splitting elements. The existing PBS devices are mainly designed for silicon photonics applications; therefore, silicon has been used as the guiding material in most of the designs. Some of these proposed structures require special fabrication procedures or exhibit a poor ER. MMIs usually have a large size since the total length should be integral multiples of the coupling lengths for both polarizations. Among these designs, asymmetrical directional coupler based PBSs show promising operational bandwidths, together with high ERs; however, these designs mostly require additional and non-standard fabrication steps. A simple PBS design based on two parallel silicon-on-insulator wire waveguides has been proposed by Liu et al.; however, only 12 dB of ER was achieved over 100 nm of bandwidth range [14]. Recently, Dai et al. demonstrated a simple and ultra-broadband PBS based on a bent directional coupler [15].

In this work, we propose a relatively simple, low-loss, and ultra-broadband PBS design based on a silicon nitride (Si3N4) asymmetrical directional coupler. From beam propagation method (BPM) simulations, the operational bandwidths of 250 nm, 150 nm, and 70 nm were obtained for the ER >10 dB, >15 dB, and >20 dB, respectively. The excess loss is less than −1 dB over the 1200-1450 nm wavelength range. With an additional waveguide placed close to the end of the through port, the operational bandwidth of the transverse magnetic (TM) mode was increased by 70 nm for ER> 15 dB. Upon the successful realization of the proposed PBS, it will be fiber coupled, and packaged as given in Fig. 1(b). With the external fiber couplers, it can be easily integrated into PS-OCT systems and can eliminate the bulky free space based polarization splitters while providing high performance. Additionally, these splitters would be one of the central components of on-chip OCT systems [19].

2. Device design

2.1 Waveguide geometry

The material system of the proposed PBS is 150-nm-thick LPCVD Si3N4 film on a thermally-oxidized silicon wafer. The oxide thickness is 8 μm with a refractive index value of 1.464. The refractive index of the Si3N4 layer is 2 at 1300 nm. A 4.0 μm-thick PECVD SiO2 (n = 1.44) is used as the top cladding. A channel waveguide geometry was chosen as it is being more tolerant to fabrication variations. Single mode channel waveguides with h = 0.15 μm of height and w = 1.5 μm of waveguide width were designed (Fig. 2(b)). The effective refractive index of the waveguide was calculated to be 1.54 and 1.48 for transverse electric (TE) and TM modes, respectively, by using BPM simulations. The minimum bending radius of the curved waveguides was calculated to be R = 150 μm with a bending loss of 0.1dB/cm.

 figure: Fig. 2

Fig. 2 Schematic of the (a) proposed PBS, showing the various design parameters. (Only Si3N4 guiding layer and the SiO2 bottom cladding are shown) and (b) waveguide geometry. (c) Effective refractive indices of the fundamental TE and TM modes for different waveguide widths. (d) Electric field distributions for the TE and TM polarizations at 1.3 µm wavelength.

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2.2 Device layout and simulations

The schematic configuration of the PBS based on an asymmetrical directional coupler is shown in Fig. 2(a). It consists of two input ports, two output ports, two straight waveguide sections with length of L, and waveguide widths of w1 and w2, and four tapered waveguides with length of Ltaper. The curved waveguides are connected to the straight waveguides with different widths via tapered waveguides. The TE and TM modes enter the asymmetrical directional coupler from one of the input waveguides. Due to evanescent field coupling, the modes couple from one waveguide into the other. The coupling length differs for the TE and TM modes due to the different propagation constants of these modes. The difference between waveguide widths in the straight and the tapered sections introduces the necessary phase shift between the TE and TM modes in order to send them to different outputs. In this configuration, the TE mode remains in the same waveguide (i.e. through or bar) where the input light is sent in, and the TM mode couples to the other (i.e. cross) waveguide. Figure 2(c) shows the effective refractive indices (neff) of the fundamental TE mode (TE0), and the TM mode (TM0) of the channel waveguide. As they are different from each other, the complete coupling lengths are also different, thus there is a combination of aforementioned design parameters that the TM0 mode is almost coupled to the cross port while most TE0 mode is still in the through port. An offset was introduced between straight waveguide sections, which can be used as a parameter to increase the operating bandwidth of the proposed PBS by controlling the phase difference between PBS arms without increasing the device size. Figure 2(d) shows the simulated electric field distributions along the device for the TE and TM polarizations at 1.3 µm wavelength.

Some of the design parameters were preselected, e.g. w1 = 1.2 µm, and d = 1 μm, in order to reduce computation time as well as to be compliant with fabrication limitations. The length of the tapered sections was set to Ltaper = 50 μm for the adiabatic transition. In order to find the optimum values of the length of the straight sections, L, and the width of the wider straight waveguide, w2, we swept L from 90 μm to 150 μm, and w2 from 1.6 μm to 2.1 μm. For each combination of w2 and L, the transmission efficiency at 1300 nm of the two output ports for TE and TM polarizations were calculated. The simulation results are given in Fig. 3. From these results, it was concluded that the transmission is maximized for both polarizations when w2 = 1.8 µm, and L = 123 µm. An 1.5µm-wide and 160µm-long bent waveguide was placed close to the end of the through port (i.e. TE-port) in order to reduce the residual of the TM light in this port and thereby improve the ER. To ensure a wide operation wavelength range, an offset was induced between straight waveguide sections. For different offset values (both in positive (upward) and negative (downward) directions), the transmission efficiency over the wavelength range of 1200 nm-1450 nm of the two output ports for TE and TM polarizations were simulated. According to the results given in Fig. 4, for an offset value of 30 µm in the upward direction the transmission efficiency is maximized for both polarizations.

 figure: Fig. 3

Fig. 3 The calculated transmission efficiencies at1300 nm with different L and w2, (a) TE polarization input-through port output and (b) TM polarization input-cross port output.

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 figure: Fig. 4

Fig. 4 The calculated transmission efficiencies over the wavelength range from 1200 nm to 1450 nm for different offset values in the straight waveguide section. (a) TE polarization input-through port output and (b) TM polarization input-cross port output. Positive sign is for upward direction, and negative sign for downward direction.

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The performance of the final PBS design was simulated using the BPM and the results for both polarizations are given in Fig. 5(a). At 1300 nm, the ER value is 27.5 dB for both polarizations and the corresponding losses are about 0.2 dB and 0.3 dB, for TE and TM polarizations, respectively. The operational bandwidths for ER>10, >15, and >20 dB were obtained as 250 nm, 150 nm, and 70 nm, respectively. Loss values remained <1 dB over the 250 nm bandwidth range (i.e. 1200 nm −1450 nm). Using the additional bent waveguide in the through port, the bandwidth of the TM polarization for ER> 15 dB was increased more than 70 nm as given in Fig. 5(b). A very small increase in loss, i.e. ~0.1 dB, was observed for the TE polarization.

 figure: Fig. 5

Fig. 5 Simulated transmission values of the TE and TM polarizations for the (a) final PBS design, and (b) final PBS design with an additional bent waveguide in the end of the through part. The bandwidth with ER>15 was improved more than 70 nm for the TM polarization.

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2.3 Tolerance analysis

The fabrication tolerance of the proposed PBS design was further investigated by considering ± 1% deviation in waveguide height and ± 2% deviation in waveguide width. The simulation results are given in Fig. 6. A shift in the center of the operational bandwidth was observed in all cases. However, the PBS still has a >15dB ER over a very broad wavelength range (>100nm) for both polarizations. Figures 6(a) and 6(b) demonstrate that the overall performance of the PBS for both polarizations does not change obviously when waveguide thickness varies, indicating that the PBS has a good fabrication tolerance towards waveguide thickness. Figure 6(c) shows that this PBS is relatively sensitive to increase in waveguide width, though only the central position of the operation bandwidth shifts towards shorter wavelengths and no additional excess loss was observed. Decrease of waveguide width does not change the overall performance significantly. Usually, the central wavelength shift due to fabrication errors could be compensated by introducing a change of refractive index through thermo-optical or electro-optical effect.

 figure: Fig. 6

Fig. 6 Fabrication tolerance analysis of the proposed PBS design for (a) 1% increase in waveguide thickness, (b) 1% decrease in waveguide thickness, (c) 2% increase in waveguide width, and (d) 2% decrease in waveguide width.

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3. Conclusions

In summary, an ultra-broadband PBS design based on an asymmetrical directional coupler was proposed for PS-OCT systems. Si3N4 was chosen to be the guiding material; however, the proposed design can be implemented in any material system. The BPM simulation results showed that the ER is 27.5 dB and the excess loss is only 0.1 dB around the central wavelength of 1300 nm for both polarizations. For the ER >20, >15, and >10 dB, the corresponding bandwidths are 70, 150, and 250 nm, respectively. A fabrication tolerance of ± 1% for the waveguide height was also achieved. With an additional arm on the through port, the bandwidth of the TM polarization for ER> 15 dB was increased by more than 70 nm for the TM polarization. To summarize, our PBS design has the advantages of low loss, ultra-broadband wavelength range with high ER, ease of fabrication and relaxed fabrication tolerances. Therefore, it can be a robust and compact substitute for the bulky PBS configurations in PS-OCT systems. Additionally, it can be used in many other applications where polarization splitting has to be done by a compact and rugged device.

Funding

Technology Foundation STW, Innovational Research Incentives Scheme Veni (SH302031); Marie Curie Individual Fellowship (FOIPO 704364).

References

1. G. B. Xavier, G. Vilela de Faria, G. P. Temporão, and J. P. von der Weid, “Full polarization control for fiber optical quantum communication systems using polarization encoding,” Opt. Express 16(3), 1867–1873 (2008). [CrossRef]   [PubMed]  

2. X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018). [CrossRef]   [PubMed]  

3. B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014). [CrossRef]  

4. K. Kikuchi, “Electronic polarization-division demultiplexing based on digital signal processing in intensity-modulation direct-detection optical communication systems,” Opt. Express 22(2), 1971–1980 (2014). [CrossRef]   [PubMed]  

5. B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive OCT of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5(8), 2736–2758 (2014). [CrossRef]   [PubMed]  

6. J. F. de Boer, C. K. Hitzenberger, and Y. Yasuno, “Polarization sensitive optical coherence tomography - a review [Invited],” Biomed. Opt. Express 8(3), 1838–1873 (2017). [CrossRef]   [PubMed]  

7. Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013). [CrossRef]  

8. J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014). [CrossRef]   [PubMed]  

9. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012). [CrossRef]  

10. X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010). [CrossRef]  

11. B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017). [CrossRef]  

12. F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017). [CrossRef]  

13. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011). [CrossRef]   [PubMed]  

14. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011). [CrossRef]   [PubMed]  

15. D. Dai and J. E. Bowers, “Novel ultra-short and ultra-broadband polarization beam splitter based on a bent directional coupler,” Opt. Express 19(19), 18614–18620 (2011). [CrossRef]   [PubMed]  

16. H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017). [CrossRef]  

17. S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018). [CrossRef]  

18. J. Feng and R. Akimoto, “A three-dimensional silicon nitride polarizing beam splitter,” IEEE Photonics Technol. Lett. 26(7), 706–709 (2014). [CrossRef]  

19. B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, and M. Pollnau, “Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip,” Opt. Express 21(14), 16648–16656 (2013). [CrossRef]   [PubMed]  

References

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  1. G. B. Xavier, G. Vilela de Faria, G. P. Temporão, and J. P. von der Weid, “Full polarization control for fiber optical quantum communication systems using polarization encoding,” Opt. Express 16(3), 1867–1873 (2008).
    [Crossref] [PubMed]
  2. X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
    [Crossref] [PubMed]
  3. B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
    [Crossref]
  4. K. Kikuchi, “Electronic polarization-division demultiplexing based on digital signal processing in intensity-modulation direct-detection optical communication systems,” Opt. Express 22(2), 1971–1980 (2014).
    [Crossref] [PubMed]
  5. B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive OCT of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5(8), 2736–2758 (2014).
    [Crossref] [PubMed]
  6. J. F. de Boer, C. K. Hitzenberger, and Y. Yasuno, “Polarization sensitive optical coherence tomography - a review [Invited],” Biomed. Opt. Express 8(3), 1838–1873 (2017).
    [Crossref] [PubMed]
  7. Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
    [Crossref]
  8. J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014).
    [Crossref] [PubMed]
  9. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
    [Crossref]
  10. X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
    [Crossref]
  11. B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017).
    [Crossref]
  12. F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
    [Crossref]
  13. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011).
    [Crossref] [PubMed]
  14. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011).
    [Crossref] [PubMed]
  15. D. Dai and J. E. Bowers, “Novel ultra-short and ultra-broadband polarization beam splitter based on a bent directional coupler,” Opt. Express 19(19), 18614–18620 (2011).
    [Crossref] [PubMed]
  16. H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017).
    [Crossref]
  17. S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
    [Crossref]
  18. J. Feng and R. Akimoto, “A three-dimensional silicon nitride polarizing beam splitter,” IEEE Photonics Technol. Lett. 26(7), 706–709 (2014).
    [Crossref]
  19. B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, and M. Pollnau, “Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip,” Opt. Express 21(14), 16648–16656 (2013).
    [Crossref] [PubMed]

2018 (2)

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

2017 (4)

J. F. de Boer, C. K. Hitzenberger, and Y. Yasuno, “Polarization sensitive optical coherence tomography - a review [Invited],” Biomed. Opt. Express 8(3), 1838–1873 (2017).
[Crossref] [PubMed]

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017).
[Crossref]

H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017).
[Crossref]

2014 (5)

2013 (2)

B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, and M. Pollnau, “Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip,” Opt. Express 21(14), 16648–16656 (2013).
[Crossref] [PubMed]

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

2012 (1)

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
[Crossref]

2011 (3)

2010 (1)

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

2008 (1)

Akca, B. I.

Akimoto, R.

J. Feng and R. Akimoto, “A three-dimensional silicon nitride polarizing beam splitter,” IEEE Photonics Technol. Lett. 26(7), 706–709 (2014).
[Crossref]

Alex, A.

Alonso-Ramos, C.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Ang, S. S. N.

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

Baudot, C.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Benedikovic, D.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Boeuf, F.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Bowers, J. E.

Braaf, B.

Cassan, E.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Chen, C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Chen, M.-C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Chew, A. B.

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

Dai, D.

H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017).
[Crossref]

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
[Crossref]

D. Dai and J. E. Bowers, “Novel ultra-short and ultra-broadband polarization beam splitter based on a bent directional coupler,” Opt. Express 19(19), 18614–18620 (2011).
[Crossref] [PubMed]

D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011).
[Crossref] [PubMed]

de Boer, J. F.

de Groot, M.

de Ridder, R. M.

Ding, Y.

Drexler, W.

Duran-Valdeiglesias, E.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Fang, Y.-Q.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Feng, J.

J. Feng and R. Akimoto, “A three-dimensional silicon nitride polarizing beam splitter,” IEEE Photonics Technol. Lett. 26(7), 706–709 (2014).
[Crossref]

Gan, F.

Guerber, S.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Hitzenberger, C. K.

Hu, W.

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Huang, H.-L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Huang, J. Z.

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Huang, Y.

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Hvam, J. M.

Jiang, X.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Kikuchi, K.

Le Roux, X.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Li, L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Li, W.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014).
[Crossref] [PubMed]

Li, Y.

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Li, Z.

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Liu, C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Liu, F.

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Liu, L.

Liu, N.-L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Lu, C.-Y.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Luo, Y.-H.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Marris-Morini, D.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Mei, T.

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

Miao, X. S.

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Ni, B.

B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017).
[Crossref]

Ni, R. W.

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Niu, B.

Pan, J.-W.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Peters, J.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
[Crossref]

Pollnau, M.

Považay, B.

Qi, M.

Ren, G.

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Sheng, Z.

Su, Z.-E.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Temporão, G. P.

Teng, J.

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

Tu, X.

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

Tu, Z.

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Vermeer, K. A.

Vienola, K. V.

Vilela de Faria, G.

Vivien, L.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

von der Weid, J. P.

Vulliet, N.

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

Wang, J.

Wang, X.

Wang, X.-L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Wang, Z.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
[Crossref]

D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011).
[Crossref] [PubMed]

Wörhoff, K.

Wu, A.

Wu, H.

H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017).
[Crossref]

Xavier, G. B.

Xiao, J.

B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017).
[Crossref]

Yasuno, Y.

Ye, S.

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Yi, H.

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Yvind, K.

Zeng, B. J.

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Zhang, J.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Zhang, K.

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Zou, S.

Biomed. Opt. Express (2)

IEEE J. Quantum Electron. (1)

B. Ni and J. Xiao, “Ultracompact and broadband silicon-based polarization beam splitter using an asymmetrical directional coupler,” IEEE J. Quantum Electron. 53(4), 1–8 (2017).
[Crossref]

IEEE Photonics J. (1)

F. Liu, S. Ye, K. Zhang, and G. Ren, “Controllable Unidirectional Emission With Double-Resonant Plasmonic Antenna,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (5)

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder interferometer based on silicon-on-insulator waveguides,” IEEE Photonics Technol. Lett. 24(8), 673 (2012).
[Crossref]

X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photonics Technol. Lett. 22(17), 1324–1326 (2010).
[Crossref]

H. Wu and D. Dai, “High-performance polarizing beam splitters based on cascaded bent directional couplers,” IEEE Photonics Technol. Lett. 29(5), 474–477 (2017).
[Crossref]

S. Guerber, C. Alonso-Ramos, D. Benedikovic, E. Duran-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), 1679–1682 (2018).
[Crossref]

J. Feng and R. Akimoto, “A three-dimensional silicon nitride polarizing beam splitter,” IEEE Photonics Technol. Lett. 26(7), 706–709 (2014).
[Crossref]

J. Opt. (1)

B. J. Zeng, R. W. Ni, J. Z. Huang, Z. Li, and X. S. Miao, “Polarization-based multiple-bit optical data storage,” J. Opt. 16(12), 125402 (2014).
[Crossref]

Opt. Commun. (1)

Y. Huang, Z. Tu, H. Yi, Y. Li, X. Wang, and W. Hu, “High extinction ratio polarization beam splitter with multimode interference coupler on SOI,” Opt. Commun. 307, 46–49 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-Qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of a polarization-sensitive OCT system. Blue regions consist of polarization components. The size of the polarization delay unit (PDU) is approximately 20 cm x 20 cm. Modified from Ref [5]. with permission. (b) Schematic of the packaged integrated PBS with fiber connectors.
Fig. 2
Fig. 2 Schematic of the (a) proposed PBS, showing the various design parameters. (Only Si3N4 guiding layer and the SiO2 bottom cladding are shown) and (b) waveguide geometry. (c) Effective refractive indices of the fundamental TE and TM modes for different waveguide widths. (d) Electric field distributions for the TE and TM polarizations at 1.3 µm wavelength.
Fig. 3
Fig. 3 The calculated transmission efficiencies at1300 nm with different L and w2, (a) TE polarization input-through port output and (b) TM polarization input-cross port output.
Fig. 4
Fig. 4 The calculated transmission efficiencies over the wavelength range from 1200 nm to 1450 nm for different offset values in the straight waveguide section. (a) TE polarization input-through port output and (b) TM polarization input-cross port output. Positive sign is for upward direction, and negative sign for downward direction.
Fig. 5
Fig. 5 Simulated transmission values of the TE and TM polarizations for the (a) final PBS design, and (b) final PBS design with an additional bent waveguide in the end of the through part. The bandwidth with ER>15 was improved more than 70 nm for the TM polarization.
Fig. 6
Fig. 6 Fabrication tolerance analysis of the proposed PBS design for (a) 1% increase in waveguide thickness, (b) 1% decrease in waveguide thickness, (c) 2% increase in waveguide width, and (d) 2% decrease in waveguide width.

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