Abstract

The synergetic use of gain and loss in parity-time symmetric coupled resonators has been shown to lead to single-mode lasing operation. However, at the corresponding resonance frequency, an ideal ring resonator tends to support two degenerate eigenmodes, traveling along the cavity in opposite directions. Here, we show a unidirectional single-moded parity-time symmetric laser by incorporating active S-bend structures with opposite chirality in the respective ring resonators. Such chiral elements break the rotation symmetry of the ring cavities by providing an asymmetric coupling between the clockwise (CW) and the counterclockwise (CCW) traveling modes, hence creating a new type of exceptional point. This property, consequently, leads to the suppression of one of the counter-propagating modes. In this paper, we first measure the extinction ratio between the CW and CCW modes in a single ring resonator in the presence of an S-bend waveguide. We then experimentally investigate the unidirectional emission in PT-symmetric systems below and above the exceptional point. Finally, unidirectional emission will be shown in systems of two S-bend ring resonators coupled through a link structure.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  26. H. Benisty, A. Lupu, and A. Degiron, “Transverse periodic P T symmetry for modal demultiplexing in optical waveguides,” Phys. Rev. A 91(5), 053825 (2015).
    [Crossref]
  27. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2018 (2)

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(1), 11–19 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref] [PubMed]

2017 (5)

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
[Crossref] [PubMed]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref] [PubMed]

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

S. Longhi and L. Feng, “Unidirectional lasing in semiconductor microring lasers at an exceptional point,” Photon. Res. 5(6), B1–B6 (2017).
[Crossref]

2016 (4)

H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
[Crossref]

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113(25), 6845–6850 (2016).
[Crossref] [PubMed]

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016).
[Crossref] [PubMed]

2015 (5)

S. Kharitonov and C. S. Bres, “Isolator-free unidirectional thulium-doped fiber laser,” Light Sci. Appl. 4(10), e340 (2015).
[Crossref]

H. Benisty, A. Lupu, and A. Degiron, “Transverse periodic P T symmetry for modal demultiplexing in optical waveguides,” Phys. Rev. A 91(5), 053825 (2015).
[Crossref]

S. Kharitonov and C.-S. Bres, “Isolator-Free Unidirectional Thulium-Doped Fiber Laser,” Light Sci. Appl. 4(10), e340 (2015).
[Crossref]

W. D. Sacher, M. L. Davenport, M. J. Heck, J. C. Mikkelsen, J. K. Poon, and J. E. Bowers, “Unidirectional hybrid silicon ring laser with an intracavity S-bend,” Opt. Express 23(20), 26369–26376 (2015).
[Crossref] [PubMed]

S. S. Sui, M. Y. Tang, Y. D. Yang, J. L. Xiao, Y. Du, and Y. Z. Huang, “Hybrid spiral-ring microlaser vertically coupled to silicon waveguide for stable and unidirectional output,” Opt. Lett. 40(21), 4995–4998 (2015).
[Crossref] [PubMed]

2014 (3)

M. Kim, K. Kwon, J. Shim, Y. Jung, and K. Yu, “Partially directional microdisk laser with two Rayleigh scatterers,” Opt. Lett. 39(8), 2423–2426 (2014).
[Crossref] [PubMed]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

2012 (1)

2011 (1)

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84(6), 063828 (2011).
[Crossref]

2010 (1)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

2006 (1)

M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically Integrated Twin Ring Diode Lasers for Rotation Sensing Applications,” J. Cryst. Growth 288(1), 144–147 (2006).
[Crossref]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

1993 (1)

J. P. Hohimer, G. A. Vawter, and D. C. Craft, “Unidirectional operation in a semiconductor ring diode laser,” Appl. Phys. Lett. 62(11), 1185–1187 (1993).
[Crossref]

Bandres, M. A.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref] [PubMed]

Benisty, H.

H. Benisty, A. Lupu, and A. Degiron, “Transverse periodic P T symmetry for modal demultiplexing in optical waveguides,” Phys. Rev. A 91(5), 053825 (2015).
[Crossref]

Bowers, J. E.

Bres, C. S.

S. Kharitonov and C. S. Bres, “Isolator-free unidirectional thulium-doped fiber laser,” Light Sci. Appl. 4(10), e340 (2015).
[Crossref]

Bres, C.-S.

S. Kharitonov and C.-S. Bres, “Isolator-Free Unidirectional Thulium-Doped Fiber Laser,” Light Sci. Appl. 4(10), e340 (2015).
[Crossref]

Cao, H.

M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically Integrated Twin Ring Diode Lasers for Rotation Sensing Applications,” J. Cryst. Growth 288(1), 144–147 (2006).
[Crossref]

Capasso, F.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Chen, W.

W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
[Crossref] [PubMed]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113(25), 6845–6850 (2016).
[Crossref] [PubMed]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Chow, W.

Christodoulides, D.

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(1), 11–19 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
[Crossref]

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

M. A. Miri, P. LiKamWa, and D. N. Christodoulides, “Large area single-mode parity-time-symmetric laser amplifiers,” Opt. Lett. 37(5), 764–766 (2012).
[Crossref] [PubMed]

J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

Coldren, L. A.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref] [PubMed]

Craft, D. C.

J. P. Hohimer, G. A. Vawter, and D. C. Craft, “Unidirectional operation in a semiconductor ring diode laser,” Appl. Phys. Lett. 62(11), 1185–1187 (1993).
[Crossref]

Davenport, M. L.

Degiron, A.

H. Benisty, A. Lupu, and A. Degiron, “Transverse periodic P T symmetry for modal demultiplexing in optical waveguides,” Phys. Rev. A 91(5), 053825 (2015).
[Crossref]

Diehl, L.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Du, Y.

Edamura, T.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

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(1), 11–19 (2018).
[Crossref]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Eliseev, P. G.

M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically Integrated Twin Ring Diode Lasers for Rotation Sensing Applications,” J. Cryst. Growth 288(1), 144–147 (2006).
[Crossref]

Feng, L.

S. Longhi and L. Feng, “Unidirectional lasing in semiconductor microring lasers at an exceptional point,” Photon. Res. 5(6), B1–B6 (2017).
[Crossref]

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016).
[Crossref] [PubMed]

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

Garcia-Gracia, H.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Guzzon, R. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref] [PubMed]

Harari, G.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref] [PubMed]

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

Hassan, A. U.

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
[Crossref]

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Hayenga, W. E.

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
[Crossref]

J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

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Heinrich, M.

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
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H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
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J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
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H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
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H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
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J. P. Hohimer, G. A. Vawter, and D. C. Craft, “Unidirectional operation in a semiconductor ring diode laser,” Appl. Phys. Lett. 62(11), 1185–1187 (1993).
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G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
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H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
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J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

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Litchinitser, N. M.

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016).
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M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically Integrated Twin Ring Diode Lasers for Rotation Sensing Applications,” J. Cryst. Growth 288(1), 144–147 (2006).
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W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
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W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
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M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
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J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

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B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113(25), 6845–6850 (2016).
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Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
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H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
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J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

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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(1), 11–19 (2018).
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Soltani, M.

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G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
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Sun, J.

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Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
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P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016).
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Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
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W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
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B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113(25), 6845–6850 (2016).
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M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
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J. Ren, W. E. Hayenga, M. Parto, F. Wu, D. N. Christodoulides, and M. Khajavikhan, “Tunable orbital angular momentum microring laser,” 2018 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2018), pp. 5-6.

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Yamanishi, M.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
[Crossref] [PubMed]

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Yao, J.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
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B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113(25), 6845–6850 (2016).
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Yu, K.

Yu, N.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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Zhang, X.

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
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Zhang, Z.

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016).
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Zhao, G.

W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
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Appl. Phys. Lett. (2)

J. P. Hohimer, G. A. Vawter, and D. C. Craft, “Unidirectional operation in a semiconductor ring diode laser,” Appl. Phys. Lett. 62(11), 1185–1187 (1993).
[Crossref]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M. A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry,” IEEE J. Sel. Top. Quantum Electron. 22(5), 1–7 (2016).
[Crossref]

J. Cryst. Growth (1)

M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically Integrated Twin Ring Diode Lasers for Rotation Sensing Applications,” J. Cryst. Growth 288(1), 144–147 (2006).
[Crossref]

Laser Photonics Rev. (1)

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
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Figures (6)

Fig. 1
Fig. 1 Schematic of a ring laser with an S-bend inside. CW and CCW field amplitudes are labeled with their respective directions of propagation. A bus waveguide with a second-order grating is placed beside the ring to monitor the output power from the two counter-propagating directions.
Fig. 2
Fig. 2 (a)Time evolution of the electrical field and mode analysis in an S-bend microring resonator. (b) Field distribution in an individual S-element as obtained from FDTD-simulations. (c) Normalized intensity of the electrical field in the ring with an S-bend obtained using FEM.
Fig. 3
Fig. 3 Lasing emission without/with S-bend. (a) Cross section of the microring cavity. (b) Normalized electric field magnitude of the TE polarized mode of the waveguide. (c, d) Schematic of microring resonators without and with an S-bend. (e, f) Intensity profiles of the resonators and the outcoupling gratings. (g, h) Emission Spectra, demonstrating a 28 dB extinction ratio of the clockwise mode with respect to the counter-clockwise mode when incorporating the S-bend.
Fig. 4
Fig. 4 Design of unidirectional PT-symmetric lasers. (a) SEM image of coupled microresonators incorporated with an S-bend inside the cavities. (b) Schematic of unidirectional light emission in a PT-symmetric microring system.
Fig. 5
Fig. 5 Unidirectional PT-symmetric microring lasers. (a, b) Camera images from the coupled microcavities and outcoupling gratings. (c, d) Corresponding spectra (log scale) below and above the PT-symmetric breaking point.
Fig. 6
Fig. 6 Chiral emission behavior in more complex systems. (a) Schematic of resonators comprised of two rings coupled through an intermediate link cavity (S-bends are imbedded only in the ring resonators). (b) Intensity profile of the resonators and outcoupling gratings (radii: 10 μm).

Equations (4)

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 { d E CW dt =( gγ ) E CW d E CCW dt =( gγ ) E CCW +iκ E CW
{ E n+1,ccw = σ 3 g r e i ϕ r E n,ccw +κσ g s e i ϕ s (σ g r 3 4 e i3 ϕ r 4 E a + g r 1 4 e i ϕ r 4 E b ) E n+1,cw = σ 3 e i ϕ r g r E n,cw
σ 3 g r e i ϕ r =1
U= | E out,ccw E out,cw | 2 = | 2 κ 2 σ 2 g r g s e i ϕ s e i ϕ r 1 σ 3 g r e i ϕ r | 2

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