• Acta Optica Sinica
  • Vol. 44, Issue 17, 1732012 (2024)
Ruiqi Wang1,2, Chu Li1,2, and Yan Li1,2,3,*
Author Affiliations
  • 1State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
  • 2Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, China
  • 3Hefei National Laboratory, Hefei 230088, Anhui , China
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    DOI: 10.3788/AOS241040 Cite this Article Set citation alerts
    Ruiqi Wang, Chu Li, Yan Li. Three‐Dimensional Waveguide Topological Photonic Structures in Glass Fabricated by Femtosecond Laser Direct Writing (Invited)[J]. Acta Optica Sinica, 2024, 44(17): 1732012 Copy Citation Text show less
    Types of femtosecond laser direct writing waveguides[59]. (a) Type I waveguide; (b) type II waveguide; (c) depressed cladding waveguide
    Fig. 1. Types of femtosecond laser direct writing waveguides[59]. (a) Type I waveguide; (b) type II waveguide; (c) depressed cladding waveguide
    Topological optical waveguide systems breaking time reversal symmetry fabricated by FLDW. (a) Helical waveguides based Floquet topological insulator with honeycomb photonic lattice[73]; (b) one-dimensional auxiliary optical waveguide array and two-dimensional optical topological Anderson insulator[14]; (c)(d) four-step coupling structures of anomalous Floquet topological insulator[12-13]; (e) nonlinearity-induced photonic anomalous Floquet topological insulator[23]; (f) chain-driven honeycomb lattice[75]; (g) Sierpinski gasket fractal Floquet topological insulator[17]; (h) Sierpinski carpet fractal anomalous Floquet topological insulator and its edge modes[18]
    Fig. 2. Topological optical waveguide systems breaking time reversal symmetry fabricated by FLDW. (a) Helical waveguides based Floquet topological insulator with honeycomb photonic lattice[73]; (b) one-dimensional auxiliary optical waveguide array and two-dimensional optical topological Anderson insulator[14]; (c)(d) four-step coupling structures of anomalous Floquet topological insulator[12-13]; (e) nonlinearity-induced photonic anomalous Floquet topological insulator[23]; (f) chain-driven honeycomb lattice[75]; (g) Sierpinski gasket fractal Floquet topological insulator[17]; (h) Sierpinski carpet fractal anomalous Floquet topological insulator and its edge modes[18]
    AB cage lattices fabricated by FLDW. (a) Using curved waveguide array structure achieves linear gradient lattice energy, modulation of the waveguide propagation constant is realized by periodically varying the writing speed along the propagation direction, and AB cage is realized by introducing equivalent magnetic flux[77]; (b) introducing auxiliary optical waveguides with propagation constant detuning to achieve equivalent magnetic flux, constructing the AB cage[79]
    Fig. 3. AB cage lattices fabricated by FLDW. (a) Using curved waveguide array structure achieves linear gradient lattice energy, modulation of the waveguide propagation constant is realized by periodically varying the writing speed along the propagation direction, and AB cage is realized by introducing equivalent magnetic flux[77]; (b) introducing auxiliary optical waveguides with propagation constant detuning to achieve equivalent magnetic flux, constructing the AB cage[79]
    Chiral symmetric topological waveguide array fabricated by FLDW. (a) Observation of topological invariants by exciting 1D SSH arrays[81]; (b) quantitative measurement of topological phase transitions achieved by exciting boundary states in 1D SSH arrays[82]; (c) HOM interference achieved in 1D off-diagonal AAH arrays[87]; (d) evolution of quantum polarized entangled states in trivial and non-trivial topological structures[89]; (e) excitation of boundary states and bulk states in 1D off-diagonal AAH arrays, where boundary state excitation can preserve two-photon correlations[88]
    Fig. 4. Chiral symmetric topological waveguide array fabricated by FLDW. (a) Observation of topological invariants by exciting 1D SSH arrays[81]; (b) quantitative measurement of topological phase transitions achieved by exciting boundary states in 1D SSH arrays[82]; (c) HOM interference achieved in 1D off-diagonal AAH arrays[87]; (d) evolution of quantum polarized entangled states in trivial and non-trivial topological structures[89]; (e) excitation of boundary states and bulk states in 1D off-diagonal AAH arrays, where boundary state excitation can preserve two-photon correlations[88]
    Two-dimensional higher-order topological insulators fabricated by FLDW. (a) Realization of higher-order topological corner states in 2D photonic lattices with C6 symmetry[5]; (b) 2D photonic lattices with C3 symmetry and excitation of higher-order topological corner states[7]; (c) observation of continuum-bound states in two-dimensional photonic lattices with C4 symmetry[9]; (d) by introducing refractive index detuning to break chiral symmetry, the localization of corner states significantly deteriorates[9]
    Fig. 5. Two-dimensional higher-order topological insulators fabricated by FLDW. (a) Realization of higher-order topological corner states in 2D photonic lattices with C6 symmetry[5]; (b) 2D photonic lattices with C3 symmetry and excitation of higher-order topological corner states[7]; (c) observation of continuum-bound states in two-dimensional photonic lattices with C4 symmetry[9]; (d) by introducing refractive index detuning to break chiral symmetry, the localization of corner states significantly deteriorates[9]
    Topological protection of 2D higher-order topological insulators fabricated by FLDW for quantum information processing. (a) Schematic illustration of the evolution test results of single-photon superposition states in higher-order topological photonic insulators[10]; (b) HOM interference visibility of the two-photon path entangled state before the injection of nontrivial lattices is approximately 93.6%, while the HOM interference visibility of the entangled two-photon corner state excited by lattice diagonal injection is approximately 91%[11]
    Fig. 6. Topological protection of 2D higher-order topological insulators fabricated by FLDW for quantum information processing. (a) Schematic illustration of the evolution test results of single-photon superposition states in higher-order topological photonic insulators[10]; (b) HOM interference visibility of the two-photon path entangled state before the injection of nontrivial lattices is approximately 93.6%, while the HOM interference visibility of the entangled two-photon corner state excited by lattice diagonal injection is approximately 91%[11]
    Non-Hermitian topological photonic structures fabricated by FLDW. (a) 2D diagonal non-Hermitian SSH array structure and its corner states’ distribution[100]; (b) PT-symmetric non-Hermitian SSH arrays and their PT-symmetric topological interface states[20]; (c) non-Hermitian helical optical waveguide array structure, and the observation of Weyl point and Weyl exceptional ring[101]
    Fig. 7. Non-Hermitian topological photonic structures fabricated by FLDW. (a) 2D diagonal non-Hermitian SSH array structure and its corner states’ distribution[100]; (b) PT-symmetric non-Hermitian SSH arrays and their PT-symmetric topological interface states[20]; (c) non-Hermitian helical optical waveguide array structure, and the observation of Weyl point and Weyl exceptional ring[101]
    Non-Hermitian topological photonic structures fabricated by FLDW. (a) PT-symmetric photonic topological insulators and their counter-propagating topological edge states[102]; (b) demonstrations of 1D non-Hermitian skin effect and 2D non-Hermitian skin-topological effect[107]
    Fig. 8. Non-Hermitian topological photonic structures fabricated by FLDW. (a) PT-symmetric photonic topological insulators and their counter-propagating topological edge states[102]; (b) demonstrations of 1D non-Hermitian skin effect and 2D non-Hermitian skin-topological effect[107]
    Schematic diagrams of eigenvalue and eigenstate evolutions in EEP process[108]. (a) Schematic diagram of closed loop in parameter space under EEP; (b) evolution of system eigenvalues under EEP, with eigenvalues exchanged; (c) evolution of system eigenstates under EEP, with one eigenstate dominating the output; (d)-(f) closed loop, eigenvalue and eigenstate evolutions in the non-EEP case
    Fig. 9. Schematic diagrams of eigenvalue and eigenstate evolutions in EEP process[108]. (a) Schematic diagram of closed loop in parameter space under EEP; (b) evolution of system eigenvalues under EEP, with eigenvalues exchanged; (c) evolution of system eigenstates under EEP, with one eigenstate dominating the output; (d)-(f) closed loop, eigenvalue and eigenstate evolutions in the non-EEP case
    Dynamic enveloping EEP structures fabricated by FLDW. (a) Periodic dual-waveguide coupling PT symmetric EEP system[109]; (b) anti-PT symmetric EEP system[110]; (c) implementation of robust all-optical logical XOR/OR gates based on 3D auxiliary waveguide overpassing dual waveguide PT symmetric EEP system[111]
    Fig. 10. Dynamic enveloping EEP structures fabricated by FLDW. (a) Periodic dual-waveguide coupling PT symmetric EEP system[109]; (b) anti-PT symmetric EEP system[110]; (c) implementation of robust all-optical logical XOR/OR gates based on 3D auxiliary waveguide overpassing dual waveguide PT symmetric EEP system[111]
    Ruiqi Wang, Chu Li, Yan Li. Three‐Dimensional Waveguide Topological Photonic Structures in Glass Fabricated by Femtosecond Laser Direct Writing (Invited)[J]. Acta Optica Sinica, 2024, 44(17): 1732012
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