• Chinese Optics Letters
  • Vol. 18, Issue 5, 051301 (2020)
Tianying Lin1、2, Ze Chen1、2, Xiaopei Zhang1、2, He Li1、2, Xiaoping Liu1、2、*, and Haibin Lü1、2、**
Author Affiliations
  • 1National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
  • 2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • show less
    DOI: 10.3788/COL202018.051301 Cite this Article Set citation alerts
    Tianying Lin, Ze Chen, Xiaopei Zhang, He Li, Xiaoping Liu, Haibin Lü. Experimental observation of topologically protected defect states in silicon waveguide arrays[J]. Chinese Optics Letters, 2020, 18(5): 051301 Copy Citation Text show less

    Abstract

    Photonic waveguide arrays provide a simple and versatile platform for simulating conventional topological systems. Here, we investigate a novel one-dimensional (1D) topological band structure, a dimer chain, consisting of silicon waveguides with alternating self-coupling and inter-coupling. Coupled mode theory is used to study topological features of such a model. It is found that topological invariants of our proposed model are described by the global Berry phase instead of the Berry phase of the upper or lower energy band, which is commonly used in the 1D topological models such as the Su–Schrieffer–Heeger model. Next, we design an array configuration composed of two dimer patterns with different global Berry phases to realize the topologically protected waveguiding. The topologically protected propagation feature is simulated based on the finite-difference time-domain method and then observed in the experiment. Our results provide an in-depth understanding of the dynamics of the topological defect state in a 1D silicon waveguide array, and may provide different routes for on-chip lightwave shaping and routing.
    idan(z)dz=βaan(z)+c2bn1(z)+c1bn(z),(1)

    View in Article

    idbn(z)dz=βbbn(z)+c2an+1(z)+c1an(z),(2)

    View in Article

    H(q)=[βav*(q)v(q)βb],(3)

    View in Article

    λ±=βaη±vq2+η2,(4)

    View in Article

    λ+|=[eiθqcosφ2sinφ2],(5)

    View in Article

    λ|=[eiθqsinφ2cosφ2],(6)

    View in Article

    ψB±=iλ±|q|λ±dq=12(1±cosφ)dθq.(7)

    View in Article

    ψBg=12(ψB++ψB)=12dθq={0,c1/c2>1π,c1/c2<1.(8)

    View in Article

    idA(z)dz=HA(z),(9)

    View in Article

    H=[c1000c1βbc2000c2βac2000c2βbc1000c1]61×61,(10)

    View in Article

    d˜1n=d1+W2ξn,(11)

    View in Article

    d˜2n=d2+W2ξn,(12)

    View in Article

    Tianying Lin, Ze Chen, Xiaopei Zhang, He Li, Xiaoping Liu, Haibin Lü. Experimental observation of topologically protected defect states in silicon waveguide arrays[J]. Chinese Optics Letters, 2020, 18(5): 051301
    Download Citation