Abstract

Redirecting the flow of light on the basis of the absorption/gain properties of optical systems is of great interest in many research fields, ranging from optical routing to optical cloaking. In this paper we investigate the control of the direction of the light propagation through loss-induced absorption in passive linear coupled optical systems. The considered optical system consists of a mode-splitting resonant cavity formed by coupling a Fabry–Perot (FP) cavity with a ring resonator. The coalescence of the asymmetric resonances, generated through mode-splitting dynamics, is the spectral result of the parity time symmetry breaking at FP resonance wavelengths. For specific values of the FP overall loss, a predominant backward propagation in the FP ring resonator occurs. In fiber optics technology, this device shows an ability to invert the sense of propagation of the light, quantified through the contrast ratio, in the order of 20 dB. This value can be obtained by externally varying the FP loss coefficient for a fixed set of the other physical parameters of the FP ring resonator. Our results can open a new way toward novel high-performance optical modulation and routing schemes.

© 2018 Chinese Laser Press

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  1. C. E. Ruter, 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]
  2. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
    [Crossref]
  3. L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
    [Crossref]
  4. Y. Huang, G. Veronis, and C. Min, “Unidirectional reflectionless propagation in plasmonic waveguide-cavity systems at exceptional points,” Opt. Express 23, 29882–29895 (2015).
    [Crossref]
  5. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
    [Crossref]
  6. P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
    [Crossref]
  7. 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]
  8. B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
    [Crossref]
  9. C. E. Campanella, L. Mastronardi, F. De Leonardis, P. Malara, G. Gagliardi, and V. M. N. Passaro, “Investigation of fiber Bragg grating based mode-splitting resonant sensor,” Opt. Express 22, 25371–25384 (2014).
    [Crossref]
  10. H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
    [Crossref]
  11. W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. A 37, 2455–2464 (2004).
    [Crossref]
  12. W. D. Heiss, “Repulsion of resonance states and exceptional points,” Phys. Rev. E 61, 929–932 (2000).
    [Crossref]
  13. P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
    [Crossref]
  14. B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
    [Crossref]
  15. C. E. Campanella, P. Malara, C. M. Campanella, F. Giove, M. Dunai, G. Gagliardi, and V. M. N. Passaro, “Mode splitting cloning in birefringent fiber Bragg grating ring resonators,” Opt. Lett. 41, 2672–2675 (2016).
    [Crossref]
  16. M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
    [Crossref]
  17. B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
    [Crossref]

2017 (1)

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]

2016 (3)

P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
[Crossref]

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

C. E. Campanella, P. Malara, C. M. Campanella, F. Giove, M. Dunai, G. Gagliardi, and V. M. N. Passaro, “Mode splitting cloning in birefringent fiber Bragg grating ring resonators,” Opt. Lett. 41, 2672–2675 (2016).
[Crossref]

2015 (1)

2014 (4)

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

C. E. Campanella, L. Mastronardi, F. De Leonardis, P. Malara, G. Gagliardi, and V. M. N. Passaro, “Investigation of fiber Bragg grating based mode-splitting resonant sensor,” Opt. Express 22, 25371–25384 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

2013 (1)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

2012 (1)

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

2010 (2)

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
[Crossref]

C. E. Ruter, 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]

2009 (1)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

2007 (1)

P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
[Crossref]

2004 (1)

W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. A 37, 2455–2464 (2004).
[Crossref]

2000 (1)

W. D. Heiss, “Repulsion of resonance states and exceptional points,” Phys. Rev. E 61, 929–932 (2000).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Almeida, V. R.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Avino, S.

P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
[Crossref]

Bender, C.

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Campanella, C. E.

Campanella, C. M.

Cerjan, A.

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[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]

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Chen, Y.-F.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Christodoulides, D. N.

C. E. Ruter, 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]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

De Leonardis, F.

De Natale, P.

P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
[Crossref]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Dunai, M.

El-Ganainy, R.

C. E. Ruter, 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]

Fan, S.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Fegadolli, W. S.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Feng, L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Gagliardi, G.

Ge, L.

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Gianfreda, M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Giorgini, A.

P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
[Crossref]

Giove, F.

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Heiss, W. D.

W. D. Heiss, “Exceptional points of non-Hermitian operators,” J. Phys. A 37, 2455–2464 (2004).
[Crossref]

W. D. Heiss, “Repulsion of resonance states and exceptional points,” Phys. Rev. E 61, 929–932 (2000).
[Crossref]

Huang, Y.

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
[Crossref]

Kip, D.

C. E. Ruter, 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]

Kramer, J.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Lei, F.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Li, H.-K.

H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

Liertzer, M.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Long, G. L.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Longhi, S.

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
[Crossref]

Lu, M.-H.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Makris, K. G.

C. E. Ruter, 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]

Malara, P.

Mastronardi, L.

Min, C.

Monifi, F.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Nori, F.

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Odzemir, S. K.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Oliveira, J. E. B.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[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]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Passaro, V. M. N.

Peng, B.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Popovic, M. A.

P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
[Crossref]

Rakich, P. T.

P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
[Crossref]

Ramezani, H.

H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

Rotter, S.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Ruter, C. E.

C. E. Ruter, 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]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Scherer, A.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Segev, M.

C. E. Ruter, 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]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Soljai, M.

P. T. Rakich, M. A. Popovic, M. Soljai, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1, 658–665 (2007).
[Crossref]

Stone, A.

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Türeci, H. E.

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Veronis, G.

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

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H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

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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).
[Crossref]

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
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[Crossref]

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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).
[Crossref]

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
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[Crossref]

Yilmaz, H.

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Yrlmaz, H.

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

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H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

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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. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
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Nature (1)

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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Opt. Express (2)

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S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
[Crossref]

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[Crossref]

Phys. Rev. Lett. (3)

H. Ramezani, H.-K. Li, Y. Wang, and X. Zhang, “Unidirectional spectral singularities,” Phys. Rev. Lett. 113, 263905 (2014).
[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

B. Peng, S. K. Odzemir, M. Liertzer, W. Chen, J. Kramer, H. Yrlmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

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P. Malara, C. E. Campanella, A. Giorgini, S. Avino, P. De Natale, and G. Gagliardi, “Super-resonant intra-cavity coherent absorption,” Sci. Rep. 6, 28947 (2016).
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Science (1)

B. Peng, S. K. Odzemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. (a) Physical system consisting of a Fabry–Perot (FP) cavity, made by two fiber Bragg gratings (FBGs) separated by a distance lFP enclosed in an optical fiber loop and excited by EiCW through coupler 1. ACW(0), ACCW(0) are the two counter-propagating modes at the input port (z=0), and ACW(lFP), ACCW(lFP) are the two counter-propagating modes at the output port (z=lFP). (b) Flux diagram of the physical system where two counter-propagating modes (CW and CCW) are excited.
Fig. 2.
Fig. 2. Mirror reflection coefficient r and FP attenuation coefficient a, satisfying the condition Asym=0 in the FP ring resonator.
Fig. 3.
Fig. 3. Contrast ratios with EiCW=1, with r equal to 0.4 (green curves) and 0.9 (yellow curves) and τ equal to 0.5 (dashed curves) and 0.7 (solid curves); contrast ratios with EiCW=1, with τ=0.2214 and r=0.98 (blue curve). Markers I, II are placed in CCW dominance region while markers III, IV are in the CW one. Marker V corresponds to CR=20  dB.
Fig. 4.
Fig. 4. (a) Spectral responses of CW exit, |EOCW|2 (dashed curves), and CCW exit, |EOCCW|2 (solid curves), with EiCW=1, with r=0.9, τ=0.7, a=0.65 (red curves) and a=0.95 (blue curves). (b) Spectral responses of CW exit, |EOCW|2 (dashed curves) and CCW exit, |EOCCW|2 (solid curves), with EiCW=1, with r=0.9, τ=0.5, a=0.65 (red curves) and a=0.95 (blue curves).

Equations (21)

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Tmirror=[tr2/tr/tr/t1/t],
[ACW(lFP)ACCW(lFP)]=Tmirror[  aejβlFP200aejβlFP2]Tmirror[ACW(0)ACCW(0)]=T[ACW(0)ACCW(0)],
Sc=1T22[det(T)T21T21det(T)]=[tFPrFPrFPtFP].
rFP=r(1e2jϕa)1r2e2jϕa,
tFP=(r21)ejϕa1r2e2jϕa,
[ACW(lFP)ACCW(0)]=Sc[ACW(0)ACCW(lFP)].
ACW(0)=jkeαIL/4ejβL/4EiCW+τ2eαILejβLACW(lFP),
ACCW(lFP)=τ2eαILejβLACCW(0),
[ACW(lFP)ACCW(0)]=Sc[jkeαIL/4ejβL/4EiCW0]+Sc[τ2eαILejβLACW(lFP)τ2eαILejβLACCW(0)],
M[ACW(lFP)ACCW(0)]=jkeαIL/4ejβL/4[tFPEiCWrFPEiCW],
M=[1tFPτ2eαILejβLrFPτ2eαILejβLrFPτ2eαILejβL1tFPτ2eαILejβL].
(1tFPτ2eαILejβL)2(rFPτ2eαILejβL)2=0.
βSym=(1L)·[2πq+2jln|tFP+rFP|2arg(tFP+rFP)+2jln(τaI)],βAsym=(1L)·[2πq+2jln|tFPrFP|2arg(tFPrFP)+2jln(τaI)],
βFP=(1lFP)[πm+2jln(ra)],
EOCW=jkeαIL/4ejβL/4ACW(lFP)=12Sym+12Asym,
EOCCW=jkeαIL/4ejβL/4ACCW(0)=12Sym12Asym,
Sym=k2aIejβL/2(tFP+rFP)1τ2aI2ejβL(tFP+rFP)EiCW,
Asym=k2aIejβL/2(tFPrFP)1τ2aI2ejβL(tFPrFP)EiCW.
ar2+(1a)ra=0.
Asym=0r=a1+(1a)24a2a.
CR=|EOCCWEOCW|2|EiCW=|SymAsymSym+Asym|2|EiCW.

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