Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays

Zongyi Zhang; Yonggang Wu; Zihuan Xia; Jian Zhou; Xuefei Qin

doi:doi:10.3788/COL202018.063601

Chinese Optics Letters, 2020, 18 (6): 063601, Published Online: May. 14, 2020

Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays Download： 794次

Zongyi Zhang ^1,2,*Yonggang Wu ^1,2,**Zihuan Xia ^1,2,3Jian Zhou ^1,2Xuefei Qin ^1,2

Author Affiliations

¹ MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

² Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

³ School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Figures & Tables

Fig. 1. (a) 1BZ diagram of the tetragonal lattice; (b) the section of the elliptical nanowire array primitive cell model.

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Fig. 2. Comparison of the central elliptical nanowires (a) before and (b) after rotation.

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Fig. 3. TE and TM modes band structure calculated along the high symmetry lines (a) for $θ = 0 °$ and (b) for $θ = 90 °$ .

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Fig. 4. Stereograms of (a) band 1, (b) band 2, (c) band 3, and (d) band 4 that are calculated in the whole first BZ for the parallel elliptical nanowires array. The band values are projected to the plane of $k$ to form a contour map at the bottom.

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Fig. 5. Contour map of the four lowest TE mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°. (a1)–(g1) band 1, (a2)–(g2) band 2, (a3)–(g3) band 3, (a4)–(g4) band 4.

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Fig. 6. Contour map of the four lowest TM mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°.

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Fig. 7. First TE mode bandgap width of the arrays with the central element under different rotation angles.

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Fig. 8. (a) Contour map of the four lowest TE mode energy bands of the perpendicular elliptical nanowires arrays at different rotations. The first, second, and third rows are array diagrams and energy bands rotated with respect to the $θ = 90 °$ array in Fig. 5 by 15°, 30°, and 45°. (b) The first TE mode bandgap width of the perpendicular arrays under different rotation angles.

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Zongyi Zhang, Yonggang Wu, Zihuan Xia, Jian Zhou, Xuefei Qin. Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays[J]. Chinese Optics Letters, 2020, 18(6): 063601.

Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays Download： 794次

Fig. 1. (a) 1BZ diagram of the tetragonal lattice; (b) the section of the elliptical nanowire array primitive cell model.

Fig. 2. Comparison of the central elliptical nanowires (a) before and (b) after rotation.

Fig. 3. TE and TM modes band structure calculated along the high symmetry lines (a) for $θ = 0 °$ and (b) for $θ = 90 °$ .

Fig. 4. Stereograms of (a) band 1, (b) band 2, (c) band 3, and (d) band 4 that are calculated in the whole first BZ for the parallel elliptical nanowires array. The band values are projected to the plane of $k$ to form a contour map at the bottom.

Fig. 5. Contour map of the four lowest TE mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°. (a1)–(g1) band 1, (a2)–(g2) band 2, (a3)–(g3) band 3, (a4)–(g4) band 4.

Fig. 6. Contour map of the four lowest TM mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°.

Fig. 7. First TE mode bandgap width of the arrays with the central element under different rotation angles.

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Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays Download： 794次

Fig. 1. (a) 1BZ diagram of the tetragonal lattice; (b) the section of the elliptical nanowire array primitive cell model.

Fig. 2. Comparison of the central elliptical nanowires (a) before and (b) after rotation.

Fig. 3. TE and TM modes band structure calculated along the high symmetry lines (a) for θ=0° and (b) for θ=90°.

Fig. 4. Stereograms of (a) band 1, (b) band 2, (c) band 3, and (d) band 4 that are calculated in the whole first BZ for the parallel elliptical nanowires array. The band values are projected to the plane of k to form a contour map at the bottom.

Fig. 5. Contour map of the four lowest TE mode energy bands of the PC when θ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°. (a1)–(g1) band 1, (a2)–(g2) band 2, (a3)–(g3) band 3, (a4)–(g4) band 4.

Fig. 6. Contour map of the four lowest TM mode energy bands of the PC when θ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°.

Fig. 7. First TE mode bandgap width of the arrays with the central element under different rotation angles.

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Fig. 3. TE and TM modes band structure calculated along the high symmetry lines (a) for $θ = 0 °$ and (b) for $θ = 90 °$ .

Fig. 4. Stereograms of (a) band 1, (b) band 2, (c) band 3, and (d) band 4 that are calculated in the whole first BZ for the parallel elliptical nanowires array. The band values are projected to the plane of $k$ to form a contour map at the bottom.

Fig. 5. Contour map of the four lowest TE mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°. (a1)–(g1) band 1, (a2)–(g2) band 2, (a3)–(g3) band 3, (a4)–(g4) band 4.

Fig. 6. Contour map of the four lowest TM mode energy bands of the PC when $θ$ is 0°, 15°, 30°, 45°, 60°, 75°, and 90°.