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arxiv: 2604.20053 · v1 · submitted 2026-04-21 · ⚛️ physics.optics

Topological Polarization Beam Splitter with Polarization-Selective Edge States

Shirin Afzal , Amesh Kahloon , Shabir Barzanjeh This is my paper

Pith reviewed 2026-05-10 01:05 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords topological photonicspolarization beam splittermicroring latticeFloquet engineeringsilicon nitrideedge statesband gapson-chip optics
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0 comments X

The pith

A microring lattice splits TE and TM light by using complementary trivial and topological band gaps that switch with wavelength.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a lattice of coupled microrings can function as a polarization beam splitter where one polarization travels along a protected edge path while the orthogonal polarization is blocked by an ordinary gap. Tailoring the frequency dependence of the coupling between rings produces these opposite gap types for TE and TM modes, with the assignment reversing at shorter wavelengths. Because the separation relies on band topology rather than exact geometry, small fabrication variations do not destroy the splitting. This approach supplies a scalable route to robust polarization handling inside integrated photonic chips for both classical communication and quantum information tasks.

Core claim

By tailoring the dispersion of inter-ring coupling, the lattice supports complementary trivial and topological band gaps for orthogonal eigenpolarizations. At telecom wavelengths, TE modes propagate via a topological edge state while TM modes are suppressed by a trivial gap; this behavior reverses at shorter wavelengths. Measured extinction ratios reach 16-20 dB on the protected port, insertion loss is 2 dB at long wavelengths, and the device remains functional in the presence of defects because operation is governed by band topology.

What carries the argument

The Floquet-engineered microring lattice whose inter-ring coupling dispersion is adjusted to open complementary trivial and topological band gaps for the two eigenpolarizations.

If this is right

  • TE and TM modes exhibit reversed propagation at different wavelength bands due to the swapped trivial and topological gaps.
  • The topological edge transport persists in the presence of defects, providing intrinsic robustness to fabrication imperfections.
  • Spectral windows exist where both polarizations support nontrivial gaps, enabling polarization-independent edge transport.
  • Extinction ratios of 16-20 dB are obtained on the protected port with 2 dB insertion loss at telecom wavelengths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same coupling-dispersion principle could be applied to other waveguide platforms to shift the operating wavelengths or increase bandwidth.
  • Active tuning of the Floquet modulation might allow the device to switch between polarization-selective and polarization-independent routing on demand.
  • Polarization-tailored topological lattices may serve as building blocks for larger-scale photonic circuits that route quantum states encoded in polarization.

Load-bearing premise

The measured polarization-selective transmission and extinction ratios arise directly from the engineered trivial versus topological band gaps rather than from input coupling differences or scattering.

What would settle it

Fabricate the same lattice with controlled defects or altered input couplers and measure whether the wavelength-dependent polarization contrast in edge transmission remains unchanged.

Figures

Figures reproduced from arXiv: 2604.20053 by Amesh Kahloon, Shabir Barzanjeh, Shirin Afzal.

Figure 1
Figure 1. Figure 1: a shows the TPI microring lattice that im￾plements the PBS, a two-dimensional array of coupled square rings with one input port on the left and two out￾put ports on the right, labeled T (through/transmission) and R (reflection). For measurement convenience, the reflection path is re-routed so that both ports are col￾lected at the same chip facet. The unit cell (inset) com￾prises three evanescently coupled … view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Simulated results of nine PBS: one defect-free lat [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Simulated intensity distributions for the TE-protected topological PBS, illustrating the effect of defects on edge-state [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Experimental demonstration of robustness against a local defect in the proposed topological PBS lattice. The defect [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Suggested design for a high-performance TE [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

The realization of on-chip polarization beam splitters robust to fabrication imperfections remains a key challenge for polarization-sensitive photonic integration. We demonstrate a topologically protected polarization beam splitter based on a Floquet-engineered microring lattice implemented on a CMOS-compatible silicon nitride platform. By tailoring the dispersion of inter-ring coupling, the lattice supports complementary trivial and topological band gaps for orthogonal eigenpolarizations. At telecom wavelengths, TE modes propagate via a topological edge state while TM modes are suppressed by a trivial gap; this behavior reverses at shorter wavelengths. We measure extinction ratios of 16-20 dB for the protected port and 10-20 dB for the non-protected port, with insertion loss of 2 dB at long wavelengths. Reduced TM extinction at shorter wavelengths is attributed to suboptimal input coupling. We further identify spectral regions where both polarizations exhibit nontrivial band gaps, enabling polarization-independent edge transport and establishing a Floquet dual-polarization topological regime. Because operation is governed by band topology rather than geometric fine-tuning, the device shows intrinsic robustness to defects. These results establish polarization-tailored topological lattices as a scalable platform for robust beam splitting, routing, and interconnects in classical and quantum photonic systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper demonstrates a topologically protected polarization beam splitter realized via a Floquet-engineered microring lattice on a CMOS-compatible silicon nitride platform. By tailoring the dispersion of inter-ring coupling, the lattice is designed to support complementary trivial and topological band gaps for TE and TM eigenpolarizations. At telecom wavelengths, TE light propagates along a topological edge state while TM light is suppressed by a trivial gap; the roles reverse at shorter wavelengths. Measured performance includes extinction ratios of 16-20 dB (protected port) and 10-20 dB (non-protected port) with 2 dB insertion loss at long wavelengths. The work also identifies spectral regions of simultaneous nontrivial gaps for both polarizations, enabling polarization-independent edge transport, and claims intrinsic robustness to defects due to topological protection.

Significance. If the central claim is substantiated, this constitutes a meaningful experimental advance in topological photonics by extending Floquet engineering to polarization-selective routing in a scalable, CMOS-compatible platform. The demonstration of a dual-polarization topological regime and the claimed defect robustness could enable more reliable polarization handling in integrated photonic circuits for both classical and quantum applications. The approach avoids geometric fine-tuning, which is a practical strength for fabrication tolerance.

major comments (2)
  1. [Abstract / Experimental Results] Abstract and experimental results: The abstract states that reduced TM extinction at shorter wavelengths is 'attributed to suboptimal input coupling,' which directly indicates that polarization- and wavelength-dependent coupling efficiencies are non-negligible. The central claim requires that the reported extinction ratios arise from the engineered trivial/topological band gaps rather than from input/output interface effects or scattering. Without quantitative separation—such as full-wave simulations of the coupling region versus lattice propagation, or cut-back measurements isolating the lattice contribution—the data do not yet establish that band topology governs the selectivity.
  2. [Experimental Results] Experimental characterization: No error bars, raw spectra, or detailed device parameters (ring radii, gap sizes, modulation amplitudes) are provided in the abstract, and the soundness assessment notes the absence of simulation details or full parameters. This prevents independent verification that the observed 16-20 dB extinction is load-bearing evidence for the Floquet band structure rather than conventional polarization-dependent losses.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the lattice periodicity or modulation frequency used in the Floquet engineering to allow readers to assess the scale of the topological gaps.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comments point by point below, providing clarifications and proposing revisions to strengthen the evidence for the topological origin of the observed polarization selectivity.

read point-by-point responses

  1. Referee: [Abstract / Experimental Results] Abstract and experimental results: The abstract states that reduced TM extinction at shorter wavelengths is 'attributed to suboptimal input coupling,' which directly indicates that polarization- and wavelength-dependent coupling efficiencies are non-negligible. The central claim requires that the reported extinction ratios arise from the engineered trivial/topological band gaps rather than from input/output interface effects or scattering. Without quantitative separation—such as full-wave simulations of the coupling region versus lattice propagation, or cut-back measurements isolating the lattice contribution—the data do not yet establish that band topology governs the selectivity.

    Authors: We agree that the attribution in the abstract highlights a potential confounding factor and that clearer separation of contributions is needed to substantiate the central claim. The wavelength dependence of the extinction ratios closely tracks the predicted Floquet band gaps for each polarization (as calculated in the supplementary materials), which would not be expected from coupling effects alone. To address this rigorously, we will add full-wave simulations of the input coupling region in the revised manuscript, comparing the simulated coupling losses (approximately wavelength- and polarization-dependent but <3 dB) against the measured extinction. We did not perform cut-back measurements in the current fabrication run due to limited device yield, but the agreement between the lattice band-structure model and the observed spectral selectivity provides supporting evidence. The abstract will be revised to clarify this distinction. revision: yes

  2. Referee: [Experimental Results] Experimental characterization: No error bars, raw spectra, or detailed device parameters (ring radii, gap sizes, modulation amplitudes) are provided in the abstract, and the soundness assessment notes the absence of simulation details or full parameters. This prevents independent verification that the observed 16-20 dB extinction is load-bearing evidence for the Floquet band structure rather than conventional polarization-dependent losses.

    Authors: We acknowledge that the abstract is necessarily concise and omits these details, which limits immediate verification. The full manuscript and supplementary information contain the device parameters (ring radii, gap sizes, and modulation amplitudes) along with the Floquet band-structure simulations. In the revised version, we will move key parameters into the main text, include raw spectra and error bars (from repeated measurements on multiple devices) in the experimental figures, and expand the simulation details in the methods section to allow independent reproduction of the band gaps. These additions will directly link the measured extinction to the topological band structure rather than conventional losses. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration with independent validation

full rationale

The paper is an experimental demonstration of a fabricated device on a silicon nitride platform. Claims rest on measured extinction ratios (16-20 dB protected, 10-20 dB non-protected) and observed wavelength-dependent polarization selectivity, attributed to designed band gaps from inter-ring coupling dispersion. No equations reduce results to fitted parameters by construction, no self-citation chain supplies the central result, and no ansatz or uniqueness theorem is invoked to force outcomes. Validation is external via device measurements, making the work self-contained against benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The demonstration rests on standard photonic band theory and Floquet engineering without introducing new free parameters, axioms beyond domain assumptions, or invented entities.

axioms (1)
  • domain assumption Existence of topological and trivial band gaps in Floquet photonic lattices for orthogonal polarizations
    Invoked when stating that tailoring inter-ring coupling produces complementary gaps for TE and TM modes.

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discussion (0)

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Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Reviews of modern physics79, 135 (2007)

    work page 2007

  2. [2]

    J. Wang, F. Sciarrino, A. Laing, and M. G. Thompson, Integrated photonic quantum technologies, Nature Pho- tonics14, 273 (2020)

    work page 2020

  3. [3]

    T. Herr, M. L. Gorodetsky, and T. J. Kippenberg, Dissi- pative kerr solitons in optical microresonators, Nonlinear optical cavity dynamics: from microresonators to fiber lasers , 129 (2016)

    work page 2016

  4. [4]

    Chang, S

    L. Chang, S. Liu, and J. E. Bowers, Integrated optical frequency comb technologies, Nature Photonics16, 95 (2022)

    work page 2022

  5. [5]

    J. A. Dionne, L. A. Sweatlock, M. T. Sheldon, A. P. Alivisatos, and H. A. Atwater, Silicon-based plasmonics for on-chip photonics, IEEE Journal of Selected Topics in Quantum Electronics16, 295 (2010)

    work page 2010

  6. [6]

    V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, Toward integrated plasmonic circuits, MRS bulletin37, 728 (2012)

    work page 2012

  7. [7]

    A. H. Safavi-Naeini, D. Van Thourhout, R. Baets, and R. Van Laer, Controlling phonons and photons at the wavelength scale: integrated photonics meets integrated phononics, Optica6, 213 (2019)

    work page 2019

  8. [8]

    Barzanjeh, A

    S. Barzanjeh, A. Xuereb, S. Gr¨ oblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quan- tum technologies, Nature Physics18, 15 (2022)

    work page 2022

  9. [9]

    P´ erez-L´ opez and L

    D. P´ erez-L´ opez and L. Torrijos-Mor´ an, Large-scale pho- tonic processors and their applications, npj Nanophoton- 13 ics2, 32 (2025)

    work page 2025

  10. [10]

    M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science359, eaar4005 (2018)

    work page 2018

  11. [11]

    Nasari, G

    H. Nasari, G. G. Pyrialakos, D. N. Christodoulides, and M. Khajavikhan, Non-hermitian topological photonics, Optical Materials Express13, 870 (2023)

    work page 2023

  12. [12]

    Mittal, V

    S. Mittal, V. V. Orre, E. A. Goldschmidt, and M. Hafezi, Tunable quantum interference using a topological source of indistinguishable photon pairs, Nature Photonics15, 542 (2021)

    work page 2021

  13. [13]

    T. Dai, Y. Ao, J. Bao, J. Mao, Y. Chi, Z. Fu, Y. You, X. Chen, C. Zhai, B. Tang,et al., Topologically protected quantum entanglement emitters, Nature Photonics16, 248 (2022)

    work page 2022

  14. [14]

    Afzal, T

    S. Afzal, T. J. Zimmerling, M. Rizvandi, M. Taghavi, L. Esmaeilifar, T. Hrushevskyi, M. Kaur, V. Van, and S. Barzanjeh, Enhanced quantum emission from a topo- logical floquet resonance, PRX Quantum5, 040331 (2024)

    work page 2024

  15. [15]

    C. J. Flower, M. Jalali Mehrabad, L. Xu, G. Moille, D. G. Suarez-Forero, O. ¨Orsel, G. Bahl, Y. Chembo, K. Srini- vasan, S. Mittal,et al., Observation of topological fre- quency combs, Science384, 1356 (2024)

    work page 2024

  16. [16]

    L. Lu, J. D. Joannopoulos, and M. Soljaˇ ci´ c, Topologi- cal states in photonic systems, Nature Physics12, 626 (2016)

    work page 2016

  17. [17]

    Ozawa, H

    T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg,et al., Topological photonics, Reviews of Modern Physics91, 015006 (2019)

    work page 2019

  18. [18]

    J. Hu, Y. Wang, J. Niu, C. Wang, T. Liu, L. Shi, Y. Zhang, Y. Xia, and K. Chang, Observation of dual- polarization topological photonic states at optical fre- quencies, Laser & Photonics Reviews17, 2300515 (2023)

    work page 2023

  19. [19]

    Parappurath, F

    N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Ver- hagen, Direct observation of topological edge states in sil- icon photonic crystals: Spin, dispersion, and chiral rout- ing, Science advances6, eaaw4137 (2020)

    work page 2020

  20. [20]

    Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He,et al., Arbitrarily routed mode-division multiplexed photonic circuits for dense in- tegration, Nature communications10, 3263 (2019)

    work page 2019

  21. [21]

    A. Bag, M. Neugebauer, U. Mick, S. Christiansen, S. A. Schulz, and P. Banzer, Towards fully integrated photonic displacement sensors, Nature communications11, 2915 (2020)

    work page 2020

  22. [22]

    Tanzilli, W

    S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, A photonic quantum informa- tion interface, Nature437, 116 (2005)

    work page 2005

  23. [23]

    J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, S. Kim,et al., Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application, IEEE Photonics Technology Letters15, 72 (2003)

    work page 2003

  24. [24]

    X. Sun, J. S. Aitchison, and M. Mojahedi, Realization of an ultra-compact polarization beam splitter using asym- metric mmi based on silicon nitride/silicon-on-insulator platform, Optics Express25, 8296 (2017)

    work page 2017

  25. [25]

    J. Zhan, J. Brock, S. Veilleux, and M. Dagenais, Silicon nitride polarization beam splitter based on polarization- independent mmis and apodized bragg gratings, Optics Express29, 14476 (2021)

    work page 2021

  26. [26]

    Y. Shi, N. Shahid, M. Li, A. Berrier, S. He, and S. Anand, Experimental demonstration of an ultracompact polar- ization beamsplitter based on a multimode interference coupler with internal photonic crystals, Optical Engineer- ing49, 060503 (2010)

    work page 2010

  27. [27]

    L. Xu, Y. Wang, E. El-Fiky, D. Mao, A. Kumar, Z. Xing, M. G. Saber, M. Jacques, and D. V. Plant, Compact broadband polarization beam splitter based on multi- mode interference coupler with internal photonic crystal for the soi platform, Journal of Lightwave Technology37, 1231 (2019)

    work page 2019

  28. [28]

    L. Xu, D. Mao, J. Zhang, Y. Wang, Z. Xing, M. S. Alam, M. Jacques, Y. D’Mello, S. Bernal, and D. V. Plant, Broadband polarization beam splitters based on mmi couplers with internal photonic crystals fabricated using 193 nm photolithography, in2021 Optical Fiber Com- munications Conference and Exhibition (OFC)(IEEE,

    work page

  29. [29]

    Fukuda, K

    H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, Ultrasmall polarization splitter based on silicon wire waveguides, Optics Express 14, 12401 (2006)

    work page 2006

  30. [30]

    Li and D

    C. Li and D. Dai, Compact polarization beam splitter for silicon photonic integrated circuits with a 340-nm-thick silicon core layer, Optics Letters42, 4243 (2017)

    work page 2017

  31. [31]

    Y. Kim, M. H. Lee, Y. Kim, and K. H. Kim, High-extinction-ratio directional-coupler-type polariza- tion beam splitter with a bridged silicon wire waveguide, Optics Letters43, 3241 (2018)

    work page 2018

  32. [32]

    B. Shen, P. Wang, R. Polson, and R. Menon, An integrated-nanophotonics polarization beamsplitter with 2.4×2.4µm2 footprint, Nature Photonics9, 378 (2015)

    work page 2015

  33. [33]

    H. Xu, Y. Tian, Y. Li, D. Huang, and X. Zhang, In- verse design of highly-efficient and broadband polariza- tion beam splitter on soi platform, Optics Communica- tions572, 130986 (2024)

    work page 2024

  34. [34]

    Schonbrun, Q

    E. Schonbrun, Q. Wu, W. Park, T. Yamashita, and C. Summers, Polarization beam splitter based on a pho- tonic crystal heterostructure, Optics letters31, 3104 (2006)

    work page 2006

  35. [35]

    Zabelin, L

    V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdr´ e, M. Kotlyar, L. O’Faolain, and T. Krauss, Self-collimating photonic crystal polarization beam splitter, Optics letters 32, 530 (2007)

    work page 2007

  36. [36]

    Afzal and V

    S. Afzal and V. Van, Topological phases and the bulk- edge correspondence in 2d photonic microring resonator lattices, Optics express26, 14567 (2018)

    work page 2018

  37. [37]

    Afzal, T

    S. Afzal, T. J. Zimmerling, Y. Ren, D. Perron, and V. Van, Realization of anomalous floquet insulators in strongly coupled nanophotonic lattices, Physical Review Letters124, 253601 (2020)

    work page 2020

  38. [38]

    Kitagawa, E

    T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Topo- logical characterization of periodically driven quantum systems, Physical Review B—Condensed Matter and Ma- terials Physics82, 235114 (2010)

    work page 2010

  39. [39]

    L. J. Maczewsky, J. M. Zeuner, S. Nolte, and A. Szameit, Observation of photonic anomalous floquet topological insulators, Nature communications8, 13756 (2017)

    work page 2017

  40. [40]

    M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, Anomalous edge states and the bulk-edge correspondence for periodically¡? format?¿ driven two-dimensional sys- tems, Physical Review X3, 031005 (2013)

    work page 2013

  41. [41]

    Tsay and V

    A. Tsay and V. Van, Analytic theory of strongly-coupled 14 microring resonators, IEEE Journal of Quantum Elec- tronics47, 997 (2011)

    work page 2011

  42. [42]

    R. C. Gonzalez,Digital image processing(Pearson edu- cation india, 2009)

    work page 2009

  43. [43]

    Hafezi, E

    M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, Robust optical delay lines with topological protection, Nature physics7, 907 (2011)

    work page 2011

  44. [44]

    F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljaˇ ci´ c, H. Chen, L. Lu,et al., Prob- ing topological protection using a designer surface plas- mon structure, Nature communications7, 11619 (2016)

    work page 2016

  45. [45]

    Melati, A

    D. Melati, A. Melloni, and F. Morichetti, Real photonic waveguides: guiding light through imperfections, Ad- vances in Optics and Photonics6, 156 (2014)

    work page 2014

  46. [46]

    Ferrari, F

    C. Ferrari, F. Morichetti, and A. Melloni, Disorder in coupled-resonator optical waveguides, Journal of the Op- tical Society of America B26, 858 (2009)

    work page 2009

  47. [47]

    Ferrari, A

    C. Ferrari, A. Canciamilla, F. Morichetti, M. Sorel, and A. Melloni, Penalty-free transmission in a silicon coupled resonator optical waveguide over the full c-band, Optics letters36, 3948 (2011)

    work page 2011

  48. [48]

    Hafezi, S

    M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, Imaging topological edge states in silicon photonics, Na- ture Photonics7, 1001 (2013)

    work page 2013

  49. [49]

    Y. Su, M. Qin, M. Ouyang, L. Lei, L. He, T. Wang, and T. Yu, Compact topological polarization beam splitter based on all-dielectric fishnet photonic crystals, Optics Letters48, 3171 (2023)

    work page 2023

  50. [50]

    L. He, M. Ouyang, Y. Su, F. Peng, W. Deng, L. Wan, L. He, and T. Yu, Topological polarization beam splitter based on directional coupling between asymmetric val- ley photonic crystal waveguides, Optics Letters49, 5308 (2024)

    work page 2024

  51. [51]

    L. He, H. Zhang, W. Zhang, Y. Wang, and X. Zhang, Topologically protected vector edge states and polariza- tion beam splitter by all-dielectric valley photonic crystal slabs, New Journal of Physics23, 093026 (2021)

    work page 2021

  52. [52]

    He, C.-H

    X.-T. He, C.-H. Guo, G.-J. Tang, M.-Y. Li, X.-D. Chen, and J.-W. Dong, Topological polarization beam splitter in dual-polarization all-dielectric valley photonic crystals, Physical Review Applied18, 044080 (2022)

    work page 2022

  53. [53]

    Y. Li, Z. Kong, Y. Zhou, T. Sang, G. Yang, H. Zhou, D. Xu, and Y. Wang, T-shaped topological polarization beam splitter based on a synthetic dimension, Optics Let- ters50, 2334 (2025)

    work page 2025

  54. [54]

    Deng, Z.-X

    C.-S. Deng, Z.-X. Peng, and B.-X. Li, Ultrahigh extinc- tion ratio topological polarization beam splitter based on dual-polarization second-order topological photonic crys- tals, Advanced Quantum Technologies , 2400637 (2025)

    work page 2025