Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states

Yun-Tuan Fang; Zhang-Xin Wang; Er-Pan Fan; Xiao-Xue Li; Hong-Jin Wang

doi:10.7498/aps.69.20200415

Journals >Acta Physica Sinica >Volume 69 >Issue 18 >Page 184101-1 > Article

Acta Physica Sinica
Vol. 69, Issue 18, 184101-1 (2020)

Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states

Yun-Tuan Fang^*, Zhang-Xin Wang, Er-Pan Fan, Xiao-Xue Li, and Hong-Jin Wang

Author Affiliations

School of Computer Science and Telecommunication Engineering, Jiangsu University, Zhenjiang 212013, China

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DOI: 10.7498/aps.69.20200415 Cite this Article

Yun-Tuan Fang, Zhang-Xin Wang, Er-Pan Fan, Xiao-Xue Li, Hong-Jin Wang. Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states[J]. Acta Physica Sinica, 2020, 69(18): 184101-1 Copy Citation Text

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Schematic of hexagonal honeycomb lattice (the hexagon is the unit cell, and a1 and a2 are the basic vectors of lattice): (a) The scatterer and matrix are air rods and dielectric, respectively; (b) the scatterer and matrix are dielectric rods and air, respectively; (c) the first Brillouin zone.

Fig. 1. Schematic of hexagonal honeycomb lattice (the hexagon is the unit cell, and a₁ and a₂ are the basic vectors of lattice): (a) The scatterer and matrix are air rods and dielectric, respectively; (b) the scatterer and matrix are dielectric rods and air, respectively; (c) the first Brillouin zone.

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Fig. 2. Band structures of the hexagonal honeycomb lattices, and the orbitals of p and d: (a) Type A; (b) type D.

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Fig. 3. Frequency positions of p and d orbits with the differences of

and

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Fig. 4. Band structures of the optimized lattices, and the orbitals of p and d: (a) Type A; (b) type D.

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Fig. 5. Construction and analysis of the edge states: (a) Supercell; (b) bands of the supercell; (c) mode analysis. The mode field E_z of the energy flow vectors of points A and B in (c) reveal the pseudo spins at the two edges of the middle non-trivial layer in (a). Because the energy flow vectors at the edge are much larger than those in the vortex, we move the vector plots to the non-trivial layer for a proper distance.

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Fig. 6. Edge state transmission of electromagnetic wave excited by pseudospin source (white hexagon star): (a) Frequency position at AB and counterclockwise spin; (b) frequency position at AB and clockwise spin; (c) frequency position at CD and counterclockwise spin; (d) frequency position at CD and clockwise spin.

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Fig. 7. Robust of the topological boundary states and the pseudo-spin source position represented by white hexagonal star: (a) The distribution of the E_z field amplitude with the obstacle (the black area in the illustration) permittivity 2.25; (b) the distribution of the E_z field amplitude with the obstacle permittivity 11.7; (c) the distribution of the E_z field from the edge state transmission along the z-type route (the inset shows a locally amplified Poynting vector distribution); (d) the distribution of the E_z field and the energy flow vectors from the edge state transmission along the z-type route with the source moved 3a to the right.

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	p orbit	d orbit
Type A	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {9.8962 \times { {10}^{ - 13} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {6.4143 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.01542\end{array}$	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {2.834 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {5.9366 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.04774\end{array}$
Type D	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {3.2652 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {9.2058 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.03574\end{array}$	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {3.603 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {8.5597 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.042\end{array}$

Table 1. Distribution of electric field energy density in two structures.

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