Abstract

Designing a cavity with a high quality factor for omnidirectionally emitting laser (OEL) can extend its potential applications in optical communication and biomedical detection. We demonstrate a method including five steps to design a high-Q cavity for OEL using a one-dimensional topological photonic crystal heterostructure. A Si/SiO2 fiber cavity for OEL with solid gain medium Er-doped SiO2 is designed following our design steps. The designed fiber can axially transmit the pump energy at low confine loss and act as a cavity for the radial emission of the exited beam, simultaneously. The quality factor of this fiber cavity is on the order of magnitude of 108. Moreover, a method of further improving the Q-factor is proposed. The results in this paper are not restricted to the solid gain medium, and they also can be applied to designing a cavity for optofluidic OEL or quantum dot OEL. Our study may provide not only the reference for OEL manufacture, but also a route for improving the performance of OEL.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

2018 (7)

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018).
[Crossref] [PubMed]

W. Gao, X. Hu, C. Li, J. Yang, Z. Chai, J. Xie, and Q. Gong, “Fano-resonance in one-dimensional topological photonic crystal heterostructure,” Opt. Express 26(7), 8634–8644 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (1)

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

2014 (3)

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 21017 (2014).
[Crossref]

2012 (2)

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

2009 (1)

A. Kitagawa and J. Sakai, “Bloch theorem in cylindrical coordinates and its application to a Bragg fiber,” Phys. Rev. A 80(3), 033802 (2009).
[Crossref]

2006 (2)

2005 (2)

2003 (1)

2002 (2)

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Y. Xu, G. X. Ouyang, R. K. Lee, and A. Yariv, “Asymptotic Matrix Theory of Bragg Fibers,” J. Lightwave Technol. 20(3), 428–440 (2002).
[Crossref]

2000 (1)

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85(15), 3161–3164 (2000).
[Crossref] [PubMed]

1991 (2)

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

W. J. Miniscalco, “Erbium-Doped Glasses for Fiber Amplifiers at 1500 nm,” J. Lightwave Technol. 9(2), 234–250 (1991).
[Crossref]

1989 (1)

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref] [PubMed]

1984 (1)

M. V. Berry and M. Wilkinson, “Diabolical points in the spectra of triangles,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 15–43 (1984).
[Crossref]

1978 (1)

Abouraddy, A. F.

An, K.

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85(15), 3161–3164 (2000).
[Crossref] [PubMed]

Awasthi, S. K.

Benoit, G.

Berry, M. V.

M. V. Berry and M. Wilkinson, “Diabolical points in the spectra of triangles,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 15–43 (1984).
[Crossref]

Blaaderen, A. V.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Brewster, M. M.

Cai, X.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Chai, Z.

Chan, C. T.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 21017 (2014).
[Crossref]

Chen, Q.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

Cheng, X.

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Chough, Y. T.

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85(15), 3161–3164 (2000).
[Crossref] [PubMed]

Chua, S. L.

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Fan, X.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Fink, Y.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

O. Shapira, K. Kuriki, N. D. Orf, A. F. Abouraddy, G. Benoit, J. F. Viens, A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, Y. Fink, and M. M. Brewster, “Surface-emitting fiber lasers,” Opt. Express 14(9), 3929–3935 (2006).
[Crossref] [PubMed]

Gao, W.

Ge, L.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Genack, A. Z.

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Gong, C.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

Gong, C. Y.

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Gong, Q.

Gong, Y.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Guo, S.

Guobin, R.

Han, D.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Hang, Z. H.

He, H.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Hebbink, G. A.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Hofstraat, J. W.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Hu, P.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Hu, X.

Huang, B.

Huang, Y.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Ibanescu, M.

Joannopoulos, J. D.

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

O. Shapira, K. Kuriki, N. D. Orf, A. F. Abouraddy, G. Benoit, J. F. Viens, A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, Y. Fink, and M. M. Brewster, “Surface-emitting fiber lasers,” Opt. Express 14(9), 3929–3935 (2006).
[Crossref] [PubMed]

Kang, Y.

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Ke, M.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Khanikaev, A. B.

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Kitagawa, A.

A. Kitagawa and J. Sakai, “Bloch theorem in cylindrical coordinates and its application to a Bragg fiber,” Phys. Rev. A 80(3), 033802 (2009).
[Crossref]

Klink, S. I.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Kuriki, K.

Lee, R. K.

Li, .-L.

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Li, C.

Li, J.

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Li, K.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Li, X.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Li, Z.-L.

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

Lindner, N. H.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Liu, B.

Liu, C.

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Liu, H.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Liu, Y.-G.

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Liu, Z.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Lumer, Y.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Luo, Y.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

Malaviya, U.

Marom, E.

Meng, Y.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
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Miniscalco, W. J.

W. J. Miniscalco, “Erbium-Doped Glasses for Fiber Amplifiers at 1500 nm,” J. Lightwave Technol. 9(2), 234–250 (1991).
[Crossref]

Moon, H. J.

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85(15), 3161–3164 (2000).
[Crossref] [PubMed]

Ni, X.

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Ojha, S. P.

Olszewski, J.

Orf, N. D.

Ouyang, G. X.

Peng, G. D.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Plotnik, Y.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Qiu, C.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Rao, Y. J.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Rechtsman, M. C.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
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Reinhoudt, D. N.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Rodriguez, A.

Sakai, J.

A. Kitagawa and J. Sakai, “Bloch theorem in cylindrical coordinates and its application to a Bragg fiber,” Phys. Rev. A 80(3), 033802 (2009).
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J. Sakai, “Hybrid modes in a Bragg fiber: general properties and formulas under the quarter-wave stack condition,” J. Opt. Soc. Am. B 22(11), 2319–2330 (2005).
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Segev, M.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Shapira, O.

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
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O. Shapira, K. Kuriki, N. D. Orf, A. F. Abouraddy, G. Benoit, J. F. Viens, A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, Y. Fink, and M. M. Brewster, “Surface-emitting fiber lasers,” Opt. Express 14(9), 3929–3935 (2006).
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Shum, P. P.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Shuqin, L.

Slooff, L. H.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Sorin, F.

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

Stolyarov, A. M.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

Stützer, S.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

Su, S.

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Sun, J.

Sun, X. W.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Szameit, A.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
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Szpulak, M.

Tian, J.-G.

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Titum, P.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
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Urbanczyk, W.

Veggel, F. C. J. M. V.

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

Viens, J. F.

Wang, D.

Wang, S.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Wang, Y.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Wei, L.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

Weijun, L.

Wen, W.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
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M. V. Berry and M. Wilkinson, “Diabolical points in the spectra of triangles,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 15–43 (1984).
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Wu, X.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Wu, Y.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Xiang, H.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Xiao, M.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 21017 (2014).
[Crossref]

Xie, J.

Xu, Y.

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
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Yan, M.

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Yang, H.

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Yang, J.

Yang, Y.

Yariv, A.

Ye, L.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Ye, Q.

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Yeh, P.

Ying, C.-F.

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

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J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref] [PubMed]

Zhang, F.

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

Zhang, H.

Zhang, N.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Zhang, R.-Y.

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Zhang, T.

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Zhang, W. L.

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Zhang, Z. Q.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 21017 (2014).
[Crossref]

Zhi, W.

Zhou, W.-Y.

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

ACS Photonics (1)

N. Zhang, H. Liu, A. M. Stolyarov, T. Zhang, K. Li, P. P. Shum, Y. Fink, X. W. Sun, and L. Wei, “Azimuthally Polarized Radial Emission from a Quantum Dot Fiber Laser,” ACS Photonics 3(12), 2275–2279 (2016).
[Crossref]

Appl. Phys. Lett. (1)

Z.-L. Li, Y.-G. Liu, M. Yan, W.-Y. Zhou, C.-F. Ying, Q. Ye, and J.-G. Tian, “A simplified hollow-core microstructured optical fibre laser with microring resonators and strong radial emission,” Appl. Phys. Lett. 105(7), 71902 (2014).
[Crossref]

Appl. Phys. Rev. (1)

L. H. Slooff, A. V. Blaaderen, G. A. Hebbink, S. I. Klink, F. C. J. M. V. Veggel, D. N. Reinhoudt, and J. W. Hofstraat, “Rare-earth doped polymers for planar optical amplifiers,” Appl. Phys. Rev. 91(7), 3954–3980 (2002).

IEEE J. Sel. Top. Quantum Electron. (2)

C. Y. Gong, Y. Gong, W. L. Zhang, Y. Wu, Y. J. Rao, G. D. Peng, and X. Fan, “Fiber Optofluidic Microlaser With Lateral Single Mode Emission,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–6 (2018).
[Crossref]

Y. Xu, C. Gong, Q. Chen, Y. Luo, Y. Wu, Y. Wang, G. D. Peng, Y. J. Rao, X. Fan, and Y. Gong, “Highly Reproducible, Isotropic Optofluidic Laser Based on Hollow Optical Fiber,” IEEE J. Sel. Top. Quantum Electron. 25(1), 1–6 (2019).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, and A. Z. Genack, “Pseudo-spin-valley coupled edge states in a photonic topological insulator,” Nat. Commun. 9(1), 3029 (2018).
[Crossref] [PubMed]

Nat. Photonics (1)

A. M. Stolyarov, L. Wei, O. Shapira, F. Sorin, S. L. Chua, J. D. Joannopoulos, and Y. Fink, “Microfluidic directional emission control of anazimuthally polarized radial fibre laser,” Nat. Photonics 6(4), 229–233 (2012).
[Crossref]

Nature (2)

H. He, C. Qiu, L. Ye, X. Cai, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Topological negative refraction of surface acoustic waves in a Weyl phononic crystal,” Nature 560(7716), 61–64 (2018).
[Crossref] [PubMed]

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref] [PubMed]

New J. Phys. (1)

Y. Meng, X. Wu, R.-Y. Zhang, X. Li, P. Hu, L. Ge, Y. Huang, H. Xiang, D. Han, S. Wang, and W. Wen, “Designing topological interface states in phononic crystals based on the full phase diagrams,” New J. Phys. 20(7), 073032 (2018).
[Crossref]

Opt. Express (5)

Optik (Stuttg.) (1)

H. Yang, C. Liu, Y. Wang, S. Su, and J. Li, “Simulation design for the structures of Bragg fibers,” Optik (Stuttg.) 123(1), 63–66 (2012).
[Crossref]

Phys. Rev. A (1)

A. Kitagawa and J. Sakai, “Bloch theorem in cylindrical coordinates and its application to a Bragg fiber,” Phys. Rev. A 80(3), 033802 (2009).
[Crossref]

Phys. Rev. Lett. (2)

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref] [PubMed]

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85(15), 3161–3164 (2000).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 21017 (2014).
[Crossref]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

M. V. Berry and M. Wilkinson, “Diabolical points in the spectra of triangles,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 15–43 (1984).
[Crossref]

SPIE Proc. (1)

Z.-L. Li, W.-Y. Zhou, Y.-G. Liu, M. Yan, and J.-G. Tian, “Simplified Hollow-core microstructural optical fiber laser with intense output and polarized radial emission,” SPIE Proc. 8960, 89600K (2014).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic drawing of the omnidirectionally emitting laser. (b) Schematic drawing of the designed fiber cavity. The cladding of the fiber is composed of three types of PhC. (c) Detail of the layers of the fiber cavity. The function of PhC1 is to confine the pump light. PhC2 and PhC3 form a topological photonic crystal heterostructure to improve the Q-factor of the cavity.
Fig. 2
Fig. 2 (a,b) Band structures of PhC2 and PhC3. The magenta strip indicates the gap with positive topological property, and the cyan trip indicates gap with negative topological property. Here, λ = 1550 nm and Λ = 375 nm. (c) Transmission spectra of the whole multilayer structure (PhC2 + PhC3). The numbers of period of PhC2 and PhC3 are both 5. (d) Zoom-in of the transmission peak of the photonic topological edge state in (c).
Fig. 3
Fig. 3 (a) Field distribution of the fundamental mode. The cladding comprises PhC1(10 periods), PhC2(5 periods) and PhC2(5 periods). The radius is 1 μm. (b) Confinement loss as a function of wavelength in vacuum for different numbers of period of PhC2 and PhC3. N2 and N3 are the numbers of period of PhC2 and PhC3, respectively.
Fig. 4
Fig. 4 (a) Normalized field distribution at 1546.7 nm in x-y plane. (b) Summation of the power outflow at the boundary in (a) as a function of wavelength. (c) Normalized angular emission pattern measured around the fiber in x-y cross section. (d) Normalized field distribution at 1546.7 nm in x-z plane. (e) Summation of the power outflow at the upmost boundary in (d) as a function of wavelength (f) Far field distribution of the light with wavelength of 1546.6 nm, 1546.7 nm and 1546.8 nm. The far field distribution is measured at the upmost boundary in (d).
Fig. 5
Fig. 5 (a-f) Band structures of PhC2 + PhC3 calculated on the basis of supercell method. From (a) to (f), the numbers of period of PhC2 and PhC3 changes from 4 to 9. (g) Zoom-in of the crossed bands in (a,b). (h) Zoom-in of the lower band of the two appeared in the gap in (c-f). Λi is the period of the supercell comprising i periods of PhC2 and PhC3.
Fig. 6
Fig. 6 (a) Transmission spectrum for different numbers of period of PhC2 and PhC3 based on Bragg reflection theory. (b) Sum of the power outflow for different numbers of period of PhC2 and PhC3. The power out flow is measured at the outmost boundary of the models in x-y cross section (e.g. Fig. 4(b)). Power outflows are normalized by the maximum power outflows measured in each case with different N2 and N3. N2 and N3 are the numbers of period of PhC2 and PhC3, respectively. (c) Quality factor calculated with the help of FEM and Bragg reflection theory.
Fig. 7
Fig. 7 Schematic drawing of the supercell chosen for calculating the band structure with N2 = N3 = 5.
Fig. 8
Fig. 8 Transmission spectra of multilayer structure composed of 50 periods of supercells with different N2 and N3: (a) N2 = N3 = 5; (b) N2 = N3 = 6; (c) N2 = N3 = 7; (d) N2 = N3 = 8.
Fig. 9
Fig. 9 (a) Normalized field distribution at 1544.9 nm in x-y plane. (b) Summation of the power outflow at the boundary in (a) as a function of wavelength. (c) Normalized angular emission pattern measured around the fiber in x-y cross section. (d) Normalized field distribution at 1544.4 nm in x-z plane. (e) Summation of the power outflow at the upmost boundary in (d) as a function of wavelength (f) Far field distribution of the light with wavelength of 1544.3 nm, 1544.4 nm and 1544.5 nm. The far field distribution is measured at the upmost boundary in (d).
Fig. 10
Fig. 10 Quality factor calculated with the help of FEM and Bragg reflection theory. The results obtained by FEM result from two types of light source.

Equations (6)

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n 1 l 1 λ 1 = n 2 l 2 λ 2 = 1 4
N TE 23.9In( Δn+ n 2 ) In[ ( Δn+ n 2 ) ]In[ n 2 2 1 ]
N TM 23.9+In( Δn+ n 2 ) 2[ In( Δn+ n 2 )In( n 2 ) ]
sgn( ϕ n )= ( 1 ) n ( 1 ) l exp( i m=1 n1 θ m Zak )χ
θ m Zak = π/Λ π/Λ [ i unit cell dzε( z ) u m,q * ( z ) q u m,q ( z ) ]dq
CL= 20 In( 10 ) Im( β )

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