Abstract

Open waveguides are widely used in modern photonic devices, such as microstructured fiber filters and sensors. Their absorption and transmission spectra are the most important properties in determining the overall performance of the photonic devices. The imaginary parts of their eigenvalues have been commonly used to calculate the absorption and consequently the transmission spectra. Here we show that this formulism is generally incorrect and not consistent with the simulation results obtained by the beam propagation method. We revisit the fundamental theory for the absorption of open waveguides and present a general formulism. We found that parity-time-symmetry transitions, which have been conventionally ignored, play a critical role in the properties of the coupled waveguide. The absorption and transmission are highly dependent on the physical length of the system. On the basis of our findings, optimization criteria for designing photonic sensors and filters are presented.

© 2018 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (2)

C. Liu, W. Su, Q. Liu, X. Lu, F. Wang, T. Sun, and P. K. Chu, “Symmetrical dual D-shape photonic crystal fibers for surface plasmon resonance sensing,” Opt. Express 26, 9039–9042 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

2017 (6)

L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11, 752–762 (2017).
[Crossref]

T. Wu, Y. Shao, Y. Wang, S. Cao, W. Cao, F. Zhang, C. Liao, J. He, Y. Huang, M. Hou, and Y. Wang, “Surface plasmon resonance biosensor based on gold-coated side-polished hexagonal structure photonic crystal fiber,” Opt. Express 25, 20313–20322 (2017).
[Crossref]

C. Liu, L. Yang, X. Lu, Q. Liu, F. Wang, J. Lv, T. Sun, H. Mu, and P. K. Chu, “Mid-infrared surface plasmon resonance sensor based on photonic crystal fibers,” Opt. Express 25, 14227–14237 (2017).
[Crossref]

A. K. Jahromi, A. U. Hassan, D. N. Christodoulides, and A. F. Abouraddy, “Statistical parity-time-symmetric lasing in an optical fibre network,” Nat. Commun. 8, 1359 (2017).
[Crossref]

L. Pilozzi and C. Conti, “Topological cascade laser for frequency comb generation in PT-symmetric structure,” Opt. Lett. 42, 5174–5177 (2017).
[Crossref]

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

2015 (1)

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

2014 (3)

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
[Crossref]

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

2013 (3)

2012 (1)

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

2010 (2)

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Ablowitz, M. J.

M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, 2nd ed., Cambridge Texts in Applied Mathematics (Cambridge University, 2003).

Abouraddy, A. F.

A. K. Jahromi, A. U. Hassan, D. N. Christodoulides, and A. F. Abouraddy, “Statistical parity-time-symmetric lasing in an optical fibre network,” Nat. Commun. 8, 1359 (2017).
[Crossref]

Bai, Z.-Y.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

Biancalana, F.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Brody, D. C.

D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
[Crossref]

Cao, S.

Cao, W.

Chen, L.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Chen, W.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

Christodoulides, D. N.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

A. K. Jahromi, A. U. Hassan, D. N. Christodoulides, and A. F. Abouraddy, “Statistical parity-time-symmetric lasing in an optical fibre network,” Nat. Commun. 8, 1359 (2017).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Chu, P. K.

Chua, S.-L.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Conti, C.

L. Pilozzi and C. Conti, “Topological cascade laser for frequency comb generation in PT-symmetric structure,” Opt. Lett. 42, 5174–5177 (2017).
[Crossref]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Doppler, J.

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

El-Ganainy, R.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11, 752–762 (2017).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Feng, L.

L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11, 752–762 (2017).
[Crossref]

Fokas, A. S.

M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, 2nd ed., Cambridge Texts in Applied Mathematics (Cambridge University, 2003).

Ge, L.

L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11, 752–762 (2017).
[Crossref]

Gong, Q.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Hassan, A. U.

A. K. Jahromi, A. U. Hassan, D. N. Christodoulides, and A. F. Abouraddy, “Statistical parity-time-symmetric lasing in an optical fibre network,” Nat. Commun. 8, 1359 (2017).
[Crossref]

He, J.

Holmes, C. A.

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

Hou, M.

Hsu, C. W.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Huang, Y.

Jahromi, A. K.

A. K. Jahromi, A. U. Hassan, D. N. Christodoulides, and A. F. Abouraddy, “Statistical parity-time-symmetric lasing in an optical fibre network,” Nat. Commun. 8, 1359 (2017).
[Crossref]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Kang, M. S.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Khajavikhan, M.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Lee, H. W.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Li, M.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Li, P.

Li, S.

Li, Y.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Liao, C.

Liu, C.

Liu, Q.

Liu, Y.

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Liu, Y.-C.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Lu, X.

Lv, J.

Makris, K. G.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Milburn, T. J.

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

Mu, H.

Musslimani, Z. H.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

Özdemir, S. K.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

Pilozzi, L.

Portolan, S.

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

Qin, W.

Rabl, P.

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

Rotter, S.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, “General description of quasiadiabatic dynamical phenomena near exceptional points,” Phys. Rev. A 92, 052124 (2015).
[Crossref]

Russell, P. St. J.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Shao, Y.

Sieg, J.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Soljacic, M.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Su, W.

Sun, T.

Sun, X.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Wang, B.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Wang, F.

Wang, L.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Wang, Y.

Weiss, T.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Wiersig, J.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

Wong, G. K. L.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref]

Wu, T.

Xiao, Y.

Xiao, Y.-F.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. Appl. 82, 065804 (2010).
[Crossref]

Xin, X.

Xue, J.

Yan, T.

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

Yan, T.-Y.

L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

Yang, L.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

C. Liu, L. Yang, X. Lu, Q. Liu, F. Wang, J. Lv, T. Sun, H. Mu, and P. K. Chu, “Mid-infrared surface plasmon resonance sensor based on photonic crystal fibers,” Opt. Express 25, 14227–14237 (2017).
[Crossref]

Zhang, F.

Zhang, L.

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
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L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
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Zhang, W.

L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
[Crossref]

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L. Chen, W.-G. Zhang, L. Wang, Z.-Y. Bai, S.-S. Zhang, B. Wang, T.-Y. Yan, and J. Sieg, “Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length,” Chin. Phys. B 23, 104220 (2014).
[Crossref]

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L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
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W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
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L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
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L. Chen, W. Zhang, Z. Zhang, Y. Liu, J. Sieg, L. Zhang, Q. Zhou, L. Wang, B. Wang, and T. Yan, “Design for a single-polarization photonic crystal fiber wavelength splitter based on hybrid-surface plasmon resonance,” IEEE Photon. J. 6, 2200909 (2014).
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C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
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C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

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G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
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Figures (7)

Fig. 1.
Fig. 1. (a) Representative PCF structure and (b) its dominant core and cladding eigenmodes. (c) Equivalent two-core fiber and (d) its eigenmodes.
Fig. 2.
Fig. 2. (a) Real and (b) imaginary parts of n+ and n as functions of Im(nd)/|G| obtained from the theory (solid lines) and the FEM simulation (dashed lines).
Fig. 3.
Fig. 3. Eigenvalues of the coupled system n+ (blue) and n (red) as functions of the wavelength (λ) with Im(nd)/|G| of (a) 0.25 (dashed) and 0.25 (solid), (b) 1 (dashed) and 1 (solid), and (c) 1.5 (dashed) and 1.5 (solid), respectively.
Fig. 4.
Fig. 4. Transmission spectra obtained by (a), (d) the conventional formulism, (b), (e) the quantum formulism, and (c), (f) the BPM simulation with Im(nd)/|G| of (a)–(c) 0.25 and (d)–(f) 0. Color map scales are independent.
Fig. 5.
Fig. 5. Transmission spectrum as a function of the propagation length with Im(nd)/|G| of (a) −0.25 and (d) 0.25, (b) 1 and (e) 1, and (c) 1.5 and (f) 1.5, respectively.
Fig. 6.
Fig. 6. Eigenmode overlap factor at the phase matching point (1.55 μm).
Fig. 7.
Fig. 7. Phase diagram in a λ versus Im(nd)/|G| plot. The blue region indicates a PT-symmetry phase, and the orange region indicates a PT-symmetry-breaking phase.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

H^=ωn1aa+ωn2bb+g(ab+ba),
[a˙b˙]=iωM[ab],
M=[n1G12G21n2],
M=PΛP1,
[a(t)b(t)]=K[a(0)b(0)],
Ia=aaandIb=bb.
α=20ln(10)×2πλ×Im(n±).

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