Deep-learning-empowered synthetic dimension dynamics: morphing of light into topological modes

Shiqi Xia; Sihong Lei; Daohong Song; Luigi Di Lauro; Imtiaz Alamgir; Liqin Tang; Jingjun Xu; Roberto Morandotti; Hrvoje Buljan; Zhigang Chen

doi:10.1117/1.AP.6.2.026005

[1] T. Ozawa, H. M. Price. Topological quantum matter in synthetic dimensions. Nat. Rev. Phys., 6, 349-357(2019).

[2] E. Lustig, M. Segev. Topological photonics in synthetic dimensions. Adv. Opt. Photonics, 13, 426-461(2021).

[3] O. Boada et al. Quantum simulation of an extra dimension. Phys. Rev. Lett., 108, 133001(2012).

[4] A. Celi et al. Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett., 112, 043001(2014).

[5] T. Ozawa et al. Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics. Phys. Rev. A, 93, 043827(2016).

[6] B. Lian, S.-C. Zhang. Weyl semimetal and topological phase transition in five dimensions. Phys. Rev. B, 95, 235106(2017).

[7] S.-C. Zhang, J. Hu. A four-dimensional generalization of the quantum Hall effect. Science, 294, 823-828(2001).

[8] D. Jukić, H. Buljan. Four-dimensional photonic lattices and discrete tesseract solitons. Phys. Rev. A, 87, 013814(2013).

[9] K. Wang et al. Generating arbitrary topological windings of a non-Hermitian band. Science, 371, 1240-1245(2021).

[10] K. Wang et al. Topological complex-energy braiding of non-Hermitian bands. Nature, 598, 59-64(2021).

[11] S. Weidemann et al. Topological funneling of light. Science, 368, 311-314(2020).

[12] A. Regensburger et al. Parity–time synthetic photonic lattices. Nature, 488, 167-171(2012).

[13] A. L. M. Muniz et al. 2D Solitons in PT-symmetric photonic lattices. Phys. Rev. Lett., 123, 253903(2019).

[14] S. Weidemann et al. Topological triple phase transition in non-Hermitian Floquet quasicrystals. Nature, 601, 354-359(2022).

[15] C. Leefmans et al. Topological dissipation in a time-multiplexed photonic resonator network. Nat. Phys., 18, 442-449(2022).

[16] A. Dutt et al. A single photonic cavity with two independent physical synthetic dimensions. Science, 367, 59-64(2020).

[17] A. Dutt et al. Experimental band structure spectroscopy along a synthetic dimension. Nat. Commun., 10, 3122(2019).

[18] G. Li et al. Direct extraction of topological Zak phase with the synthetic dimension. Light Sci. Appl., 12, 81(2023).

[19] E. Lustig et al. Photonic topological insulator induced by a dislocation in three dimensions. Nature, 609, 931-935(2022).

[20] E. Lustig et al. Photonic topological insulator in synthetic dimensions. Nature, 567, 356-360(2019).

[21] M. Yang et al. Topological band structure via twisted photons in a degenerate cavity. Nat. Commun., 13, 2040(2022).

[22] M. Yang et al. Realization of exceptional points along a synthetic orbital angular momentum dimension. Sci. Adv., 9, eabp8943(2023).

[23] L. Yuan et al. Synthetic dimension in photonics. Optica, 5, 1396-1405(2018).

[24] Z. Yang et al. Mode-locked topological insulator laser utilizing synthetic dimensions. Phys. Rev. X, 10, 011059(2020).

[25] H. Buljan, D. Jukić, Z. Chen. Loss leads the way to utopia. Nat. Phys., 18, 371-372(2022).

[26] N. K. Efremidis, D. N. Christodoulides. Revivals in engineered waveguide arrays. Opt. Commun., 246, 345-356(2005).

[27] C. Li, D. Liu, D. Dai. Multimode silicon photonics. Nanophotonics, 8, 227-247(2019).

[28] C. Li et al. Subwavelength silicon photonics for on-chip mode-manipulation. PhotoniX, 2, 11(2021).

[29] M. P. Hokmabadi et al. Supersymmetric laser arrays. Science, 363, 623-626(2019).

[30] F. O. Wu, A. U. Hassan, D. N. Christodoulides. Thermodynamic theory of highly multimoded nonlinear optical systems. Nat. Photonics, 13, 776-782(2019).

[31] H. Pourbeyram et al. Direct observations of thermalization to a Rayleigh–Jeans distribution in multimode optical fibres. Nat. Phys., 18, 685-690(2022).

[32] W. P. Su, J. R. Schrieffer, A. J. Heeger. Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979).

[33] J. Yim et al. Broadband continuous supersymmetric transformation: a new paradigm for transformation optics. eLight, 2, 16(2022).

[34] Y. LeCun, Y. Bengio, G. Hinton. Deep learning. Nature, 521, 436-444(2015).

[35] G. Carleo et al. Machine learning and the physical sciences. Rev. Mod. Phys., 91, 045002(2019).

[36] G. Wetzstein et al. Inference in artificial intelligence with deep optics and photonics. Nature, 588, 39-47(2020).

[37] Z. Chen, M. Segev. Highlighting photonics: looking into the next decade. eLight, 6, 2(2021).

[38] W. Ma et al. Deep learning for the design of photonic structures. Nat. Photonics, 15, 77-90(2021).

[39] P. R. Wiecha et al. Deep learning in nano-photonics: inverse design and beyond. Photonics Res., 9, B182-B200(2021).

[40] Y. Shen et al. Deep learning with coherent nanophotonic circuits. Nat. Photonics, 11, 441-446(2017).

[41] S. Pai et al. Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science, 380, 398-404(2023).

[42] L. M. Narducci, M. Orszag. Eigenvalues and eigenvectors of angular momentum operator J_x without the theory of rotations. Am. J. Phys., 40, 1811-1814(1972).

[43] Y. E. Kraus et al. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett., 109, 106402(2012).

[44] O. Zilberberg et al. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Nature, 553, 59-62(2018).

[45] S. Xia et al. Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology. Light Sci. Appl., 9, 147(2020).

[46] T. Kreis. Digital holographic interference-phase measurement using the Fourier-transform method. J. Opt. Soc. Am. A, 3, 847-855(1986).

[47] N. Malkova et al. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett., 34, 1633-1635(2009).

[48] S. Xia et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science, 372, 72-76(2021).

[49] J. Wang et al. Topologically tuned terahertz confinement in a nonlinear photonic chip. Light Sci. Appl., 11, 152(2022).

[50] A. Dutt et al. Higher-order topological insulators in synthetic dimensions. Light Sci. Appl., 9, 131(2020).

[51] Y. Xiong, R. B. Priti, O. Liboiron-Ladouceur. High-speed two-mode switch for mode-division multiplexing optical networks. Optica, 4, 1098-1102(2017).

[52] K. Chen et al. Broadband optical switch for multiple spatial modes based on a silicon densely packed waveguide array. Opt. Lett., 44, 907-910(2019).

[53] L.-T. Feng et al. On-chip coherent conversion of photonic quantum entanglement between different degrees of freedom. Nat. Commun., 7, 11985(2016).

[54] A. Mohanty et al. Quantum interference between transverse spatial waveguide modes. Nat. Commun., 8, 14010(2017).

[55] H. Jia et al. WDM-compatible multimode optical switching system-on-chip. Nanophotonics, 8, 889-898(2019).

[56] A. Balčytis et al. Synthetic dimension band structures on a Si CMOS photonic platform. Sci. Adv., 8, eabk0468(2022).