Splitter engineering through optimizing topological adiababtic passage
Jia-Ning Zhang, Jin-Lei Wu, Cheng Lv, Jiabao Yao, Jie Song, Yong-Yuan Jiang
Splitter engineering through optimizing topological adiababtic passage
Topologically protected states are important in realizing robust optical behaviors that are quite insensitive to local defects or perturbations, which provide a promising solution for robust photonic integrations. Here, we propose to implement fast topological beam splitters and routers via the adiabatic passage of edge and interface states in the cross-linking configuration of Su–Schrieffer–Heeger (SSH) chains with interface defects. The channel state does not immerse into the band continuum during the adiabatic cycle, making the adiabatic restriction less stringent and the transport process more efficient. Based on the accelerated topological pumping, the beam splitters and routers exhibit improved robustness against losses of the system yet degraded resilience to fluctuation of coupling strengths and on-site energies compared with the conventional topological splitting and routing schemes. In addition, we confirm that the model demonstrates good scalability when the system size is varied. The simulation results of topological beam splitting in coupled waveguide arrays are in good consistency with theoretical analysis. This topological design provides a robust way to control photons, which may suggest further application of topological devices with unique properties and functionalities for integrated photonics.
topological effects in photonic systems / Su−Schrieffer−Heeger / topological photonics / waveguides
[1] |
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982)
CrossRef
ADS
Google scholar
|
[2] |
S. Rachel, Interacting topological insulators: A review, Rep. Prog. Phys. 81(11), 116501 (2018)
CrossRef
ADS
Google scholar
|
[3] |
C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)
CrossRef
ADS
Google scholar
|
[4] |
D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27(10), 6083 (1983)
CrossRef
ADS
Google scholar
|
[5] |
Q. Niu and D. J. Thouless, Quantised adiabatic charge transport in the presence of substrate disorder and many body interaction, J. Phys. Math. Gen. 17(12), 2453 (1984)
CrossRef
ADS
Google scholar
|
[6] |
Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Topological states and adiabatic pumping in quasicrystals, Phys. Rev. Lett. 109(10), 106402 (2012)
CrossRef
ADS
Google scholar
|
[7] |
M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, Topological pumping over a photonic Fibonacci quasicrystal, Phys. Rev. B 91(6), 064201 (2015)
CrossRef
ADS
Google scholar
|
[8] |
A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)
CrossRef
ADS
Google scholar
|
[9] |
P. Narang, C. A. C. Garcia, and C. Felser, The topology of electronic band structures, Nat. Mater. 20, 293 (2021)
CrossRef
ADS
Google scholar
|
[10] |
M. He, H. Sun, and Q. L. He, Topological insulator: Spintronics and quantum computations, Front. Phys. 14(4), 43401 (2019)
CrossRef
ADS
Google scholar
|
[11] |
O. Breunig and Y. Ando, Opportunities in topological insulator devices, Nat. Rev. Phys. 4(3), 184 (2021)
CrossRef
ADS
Google scholar
|
[12] |
F. Mei, G. Chen, L. Tian, S. L. Zhu, and S. Jia, Robust quantum state transfer via topological edge states in superconducting qubit chains, Phys. Rev. A 98(1), 012331 (2018)
CrossRef
ADS
Google scholar
|
[13] |
S. Longhi, Topological pumping of edge states via adiabatic passage, Phys. Rev. B 99(15), 155150 (2019)
CrossRef
ADS
Google scholar
|
[14] |
T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91(1), 015006 (2019)
CrossRef
ADS
Google scholar
|
[15] |
L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photonics 8(11), 821 (2014)
CrossRef
ADS
Google scholar
|
[16] |
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42(25), 1698 (1979)
CrossRef
ADS
Google scholar
|
[17] |
E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the Su–Schrieffer–Heeger model, Nat. Commun. 7(1), 13986 (2016)
CrossRef
ADS
Google scholar
|
[18] |
L. Qi, G. L. Wang, S. Liu, S. Zhang, and H. F. Wang, Engineering the topological state transfer and topological beam splitter in an even-sized Su–Schrieffer–Heeger chain, Phys. Rev. A 102(2), 022404 (2020)
CrossRef
ADS
Google scholar
|
[19] |
L. Qi, Y. Xing, X. D. Zhao, S. Liu, S. Zhang, S. Hu, and H. F. Wang, Topological beam splitter via defect-induced edge channel in the Rice‒Mele model, Phys. Rev. B 103(8), 085129 (2021)
CrossRef
ADS
Google scholar
|
[20] |
J. N. Zhang, J. X. Han, J. L. Wu, J. Song, and Y. Y. Jiang, Robust beam splitter with fast quantum state transfer through a topological interface, Front. Phys. 18(5), 51303 (2023)
CrossRef
ADS
Google scholar
|
[21] |
J. N. Zhang, J. L. Wu, J. X. Han, S. Tang, J. Song, and Y. Y. Jiang, Small admixture of nonadiabaticity facilitating topologically protected splitters and routers via optimizing coupling engineering, Phys. Rev. B 109(9), 094303 (2024)
CrossRef
ADS
Google scholar
|
[22] |
L. Qi, Y. Yan, Y. Xing, X. D. Zhao, S. Liu, W. X. Cui, X. Han, S. Zhang, and H. F. Wang, Topological router induced via long-range hopping in a Su–Schrieffer–Heeger chain, Phys. Rev. Res. 3(2), 023037 (2021)
CrossRef
ADS
Google scholar
|
[23] |
L. N. Zheng, X. Yi, and H. F. Wang, Engineering a phase-robust topological router in a dimerized superconducting-circuit lattice with long-range hopping and chiral symmetry, Phys. Rev. Appl. 18(5), 054037 (2022)
CrossRef
ADS
Google scholar
|
[24] |
L. N. Zheng, H. F. Wang, and X. Yi, Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain, New J. Phys. 25(11), 113003 (2023)
CrossRef
ADS
Google scholar
|
[25] |
H. Li, R. Yao, B. Zheng, S. An, M. Haerinia, J. Ding, C. S. Lee, H. Zhang, and W. Guo, Electrically tunable and reconfigurable topological edge state laser, Optics 3(2), 107 (2022)
CrossRef
ADS
Google scholar
|
[26] |
M. S. Wei, M. J. Liao, C. Wang, C. Zhu, Y. Yang, and J. Xu, Topological laser with higher-order corner states in the 2-dimensional Su–Schrieffer–Heeger model, Opt. Express 31(3), 3427 (2023)
CrossRef
ADS
Google scholar
|
[27] |
P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photonics 11, 651 (2017)
CrossRef
ADS
Google scholar
|
[28] |
M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Edgemode lasing in 1d topological active arrays, Phys. Rev. Lett. 120(11), 113901 (2018)
CrossRef
ADS
Google scholar
|
[29] |
G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science 359(6381), eaar4003 (2018)
CrossRef
ADS
Google scholar
|
[30] |
F. M. D’Angelis, F. A. Pinheiro, D. Guery-Odelin, S. Longhi, and F. Impens, Fast and robust quantum state transfer in a topological Su–Schrieffer–Heeger chain with next-to-nearest-neighbor interactions, Phys. Rev. Res. 2(3), 033475 (2020)
CrossRef
ADS
Google scholar
|
[31] |
I. Brouzos, I. Kiorpelidis, F. K. Diakonos, and G. Theocharis, Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain, Phys. Rev. B 102(17), 174312 (2020)
CrossRef
ADS
Google scholar
|
[32] |
N. E. Palaiodimopoulos, I. Brouzos, F. K. Diakonos, and G. Theocharis, Fast and robust quantum state transfer via a topological chain, Phys. Rev. A 103(5), 052409 (2021)
CrossRef
ADS
Google scholar
|
[33] |
C. Wu, W. Liu, Y. Jia, G. Chen, and F. Chen, Observation of topological pumping of a defect state in a Fock photonic lattice, Phys. Rev. A 107(3), 033501 (2023)
CrossRef
ADS
Google scholar
|
[34] |
J. Yuan, C. Xu, H. Cai, and D. W. Wang, Gap-protected transfer of topological defect states in photonic lattices, APL Photonics 6(3), 030803 (2021)
CrossRef
ADS
Google scholar
|
[35] |
M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, Robust interferometer for the routing of light beams carrying orbital angular momentum, New J. Phys. 13(9), 093014 (2011)
CrossRef
ADS
Google scholar
|
[36] |
W. Bogaerts, D. Pérez, J. Capmany, D. A. B. Miller, J. Poon, D. Englund, F. Morichetti, and A. Melloni, Programmable photonic circuits, Nature 586(7828), 207 (2020)
CrossRef
ADS
Google scholar
|
[37] |
H. Oukraou, V. Coda, A. A. Rangelov, and G. Montemezzani, Broadband photonic transport between waveguides by adiabatic elimination, Phys. Rev. A 97(2), 023811 (2018)
CrossRef
ADS
Google scholar
|
[38] |
T. Lunghi, F. Doutre, A. P. Rambu, M. Bellec, M. P. De Micheli, A. M. Apetrei, O. Alibart, N. Belabas, S. Tascu, and S. Tanzilli, Broadband integrated beam splitter using spatial adiabatic passage, Opt. Express 26(21), 27058 (2018)
CrossRef
ADS
Google scholar
|
[39] |
A. K. Taras, A. Tuniz, M. A. Bajwa, V. Ng, J. M. Dawes, C. G. Poulton, and C. M. De Sterke, Shortcuts to adiabaticity in waveguide couplers – theory and implementation, Adv. Phys. X 6, 1894978 (2021)
CrossRef
ADS
Google scholar
|
[40] |
Y. X. Lin, M. Younesi, H. P. Chung, H. K. Chiu, R. Geiss, Q. H. Tseng, F. Setzpfandt, T. Pertsch, and Y. H. Chen, Ultra-compact, broadband adiabatic passage optical couplers in thin-film lithium niobate on insulator waveguides, Opt. Express 29(17), 27362 (2021)
CrossRef
ADS
Google scholar
|
[41] |
A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, Topological optical waveguiding in silicon and the transition between topological and trivial defect states, Phys. Rev. Lett. 116(16), 163901 (2016)
CrossRef
ADS
Google scholar
|
[42] |
X.T. HeE. T. LiangJ.J. YuanH.Y. QiuX.D. Chen F.L. ZhaoJ. W. Dong, A silicon-on-insulator slab for topological valley transport, Nat. Commun. 10(1), 872 (2019)
|
[43] |
M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, Robust topologically protected transport in photonic crystals at telecommunication wavelengths, Nat. Nanotechnol. 14(1), 31 (2019)
CrossRef
ADS
Google scholar
|
[44] |
B. Sun, F. Morozko, P. S. Salter, S. Moser, Z. Pong, R. B. Patel, I. A. Walmsley, M. Wang, A. Hazan, N. Barré, A. Jesacher, J. Fells, C. He, A. Katiyi, Z. N. Tian, A. Karabchevsky, and M. J. Booth, On-chip beam rotators, adiabatic mode converters, and waveplates through low-loss waveguides with variable crosssections, Light Sci. Appl. 11(1), 214 (2022)
CrossRef
ADS
Google scholar
|
[45] |
T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Anomalous refraction and diffraction in discrete optical systems, Phys. Rev. Lett. 88(9), 093901 (2002)
CrossRef
ADS
Google scholar
|
[46] |
M. J. Ablowitz and J. T. Cole, Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators, Physica D 440, 133440 (2022)
CrossRef
ADS
Google scholar
|
[47] |
Y. Zhao, Y. Chen, Z. S. Hou, B. Han, H. Fan, L. H. Lin, X. F. Ren, and H. B. Sun, Polarization-dependent Bloch oscillations in optical waveguides, Opt. Lett. 47(3), 617 (2022)
CrossRef
ADS
Google scholar
|
[48] |
W. F. Zhang, X. Zhang, Y. V. Kartashov, X. Chen, and F. Ye, Bloch oscillations in arrays of helical waveguides, Phys. Rev. A 97(6), 063845 (2018)
CrossRef
ADS
Google scholar
|
[49] |
W. Li, C. Qin, T. Han, H. Chen, B. Wang, and P. Lu, Bloch oscillations in photonic spectral lattices through phase-mismatched four-wave mixing, Opt. Lett. 44(22), 5430 (2019)
CrossRef
ADS
Google scholar
|
[50] |
T. L. Silva, W. B. Cardoso, A. T. Avelar, and J. M. C. Malbouisson, Nonclassical properties and Anderson localization of quantum states in coupled waveguides, Phys. Rev. A 105(2), 023710 (2022)
CrossRef
ADS
Google scholar
|
[51] |
Y. Yang, R. J. Chapman, B. Haylock, F. Lenzini, Y. N. Joglekar, M. Lobino, and A. Peruzzo, Programmable high-dimensional Hamiltonian in a photonic waveguide array, Nat. Commun. 15(1), 50 (2024)
CrossRef
ADS
Google scholar
|
[52] |
K. Jin, Y. Li, F. Li, M. R. Belic, Y. Zhang, and Y. Zhang, Rabi oscillations of azimuthons in weakly nonlinear waveguides, Adv. Photonics 2(4), 046002 (2020)
CrossRef
ADS
Google scholar
|
[53] |
J. Beierlein, E. Rozas, O. A. Egorov, M. Klaas, A. Yulin, H. Suchomel, T. H. Harder, M. Emmerling, M. D. Martın, I. A. Shelykh, C. Schneider, U. Peschel, L. Vina, S. Hofling, and S. Klembt, Propagative oscillations in co-directional polariton waveguide couplers, Phys. Rev. Lett. 126(7), 075302 (2021)
CrossRef
ADS
Google scholar
|
[54] |
C. Jorg, G. Queralto, M. Kremer, G. Pelegrı, J. Schulz, A. Szameit, G. von Freymann, J. Mompart, and V. Ahufinger, Artificial gauge field switching using orbital angular momentum modes in optical waveguides, Light Sci. Appl. 9(1), 150 (2020)
CrossRef
ADS
Google scholar
|
[55] |
Y. Lumer, M. A. Bandres, M. Heinrich, L. J. Maczewsky, H. Herzig-Sheinfux, A. Szameit, and M. Segev, Light guiding by artificial gauge fields, Nat. Photonics 13(5), 339 (2019)
CrossRef
ADS
Google scholar
|
[56] |
K. Xu, F. Chen, H. Chen, M. Fang, Z. Huang, and Y. Yang, Waveguide channel splitting induced by artificial gauge fields, ACS Photonics 10(3), 632 (2023)
CrossRef
ADS
Google scholar
|
[57] |
W. Song, T. Li, S. Wu, Z. Wang, C. Chen, Y. Chen, C. Huang, K. Qiu, S. Zhu, Y. Zou, and T. Li, Dispersionless coupling among optical waveguides by artificial gauge field, Phys. Rev. Lett. 129(5), 053901 (2022)
CrossRef
ADS
Google scholar
|
[58] |
P. Zhou, T. Li, Y. Lin, L. Xia, L. Shen, X. Xu, T. Li, and Y. Zou, Artificial gauge field enabled low-crosstalk, broadband, half-wavelength pitched waveguide arrays, Laser Photonics Rev. 17(6), 2200944 (2023)
CrossRef
ADS
Google scholar
|
[59] |
E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M. A. Bandres, A. Szameit, and M. Segev, Photonic topological insulator in synthetic dimensions, Nature 567(7748), 356 (2019)
CrossRef
ADS
Google scholar
|
[60] |
M. J. Ablowitz and J. T. Cole, Topological insulators in longitudinally driven waveguides: Lieb and kagome lattices, Phys. Rev. A 99(3), 033821 (2019)
CrossRef
ADS
Google scholar
|
[61] |
T. Biesenthal, L. J. Maczewsky, Z. Yang, M. Kremer, M. Segev, A. Szameit, and M. Heinrich, Fractal photonic topological insulators, Science 376(6597), 1114 (2022)
CrossRef
ADS
Google scholar
|
[62] |
S. Shen, Y. V. Kartashov, Y. Li, and Y. Zhang, Floquet edge solitons in modulated trimer waveguide arrays, Phys. Rev. Appl. 20(1), 014012 (2023)
CrossRef
ADS
Google scholar
|
[63] |
S. K. Ivanov, Y. V. Kartashov, and V. V. Konotop, Floquet defect solitons, Opt. Lett. 46(21), 5364 (2021)
CrossRef
ADS
Google scholar
|
[64] |
S. Mukherjee and M. C. Rechtsman, Observation of floquet solitons in a topological bandgap, Science 368(6493), 856 (2020)
CrossRef
ADS
Google scholar
|
[65] |
J. Zurita, C. E. Creffield, and G. Platero, Fast quantum transfer mediated by topological domain walls, Quantum 7, 1043 (2023)
CrossRef
ADS
Google scholar
|
[66] |
N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89(1), 015006 (2017)
CrossRef
ADS
Google scholar
|
[67] |
S. Tang, J. L. Wu, C. Lu, J. Song, and Y. Jiang, Functional acoustic metamaterial using shortcut to adiabatic passage in acoustic waveguide couplers, Phys. Rev. Appl. 18(1), 014038 (2022)
CrossRef
ADS
Google scholar
|
[68] |
S. Tang, J. L. Wu, C. Lu, X. Wang, J. Song, and Y. Jiang, Acoustic wavelength selected metamaterials designed by reversed fractional stimulated Raman adiabatic passage, Phys. Rev. B 105(10), 104107 (2022)
CrossRef
ADS
Google scholar
|
[69] |
S. Tang, J. L. Wu, C. Lu, J. Yao, Y. Pei, and Y. Jiang, Unidirectional beam splitting in acoustic metamaterial governed by double fractional stimulated Raman adiabatic passage, Appl. Phys. Lett. 122(21), 212201 (2023)
CrossRef
ADS
Google scholar
|
[70] |
S. Tang, J. L. Wu, C. Lu, J. Yao, X. Wang, J. Song, and Y. Jiang, One-way acoustic beam splitting in spatial four-waveguide couplers designed by adiabatic passage, New J. Phys. 25(3), 033032 (2023)
CrossRef
ADS
Google scholar
|
[71] |
J. L. Wu, S. Tang, Y. Wang, X. S. Wang, J. X. Han, C. Lu, J. Song, S. L. Su, Y. Xia, and Y. Y. Jiang, Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations, Sci. China Phys. Mech. Astron. 65(2), 220311 (2022)
CrossRef
ADS
Google scholar
|
[72] |
W. P. Huang, Coupled-mode theory for optical waveguides: An overview, J. Opt. Soc. Am. A 11(3), 963 (1994)
CrossRef
ADS
Google scholar
|
[73] |
H. A. Haus and W. Huang, Coupled-mode theory, Proc. IEEE 79(10), 1505 (1991)
CrossRef
ADS
Google scholar
|
[74] |
W. Liu, C. Wu, Y. Jia, S. Jia, G. Chen, and F. Chen, Observation of edge-to-edge topological transport in a photonic lattice, Phys. Rev. A 105(6), L061502 (2022)
CrossRef
ADS
Google scholar
|
[75] |
L. Huang, Z. Tan, H. Zhong, and B. Zhu, Fast and robust quantum state transfer assisted by zero energy interface states in a splicing Su–Schrieffer–Heeger chain, Phys. Rev. A 106(2), 022419 (2022)
CrossRef
ADS
Google scholar
|
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〈 | 〉 |