Abstract

Optoelectronic oscillators (OEOs) are promising solutions for generating microwave signals with low phase noise and wideband tunability, and they can be applied to converging systems such as communications, radars, and electronic warfare systems. However, a significant challenge remains in ensuring a low phase noise, wideband tunability, and ultra-high side mode suppression ratio (SMSR) simultaneously. Parity-time (PT) symmetry breaking provides an excellent tool for single-mode oscillation by exploiting the interplay between the gain and loss. The oscillation mode was previously fixed because the breaking of the PT symmetry cannot be accurately manipulated. Herein, we propose an OEO with selective PT-symmetry breaking showing a wideband tunability and ultra-high SMSR. The tunability of the proposed OEO is attributed to the selection of different modes to break the PT symmetry using a widely tunable microwave photonic filter (MPF). The large roll-off of the MPF significantly enhances the gain difference between the selected and competing modes. Consequently, both the output power and SMSR of the OEO increase. During the experiment, the measured oscillation frequency is tuned from 2.6 to 40 GHz. The output power of the selected mode is enhanced by 12.9 dB, and the maximal SMSR reaches up to 71.4 dB. Further, the measured phase noise of the OEO at 17.74 GHz reaches 129dBc/Hz at a 10-kHz offset frequency. Exploration of the selective PT-symmetry breaking provides the possibility of developing classes of widely tunable OEOs with an ultra-high SMSR and excellent low phase noise simultaneously.

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

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2018 (3)

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4, eaar6782 (2018).
[Crossref]

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

H. Tang, Y. Yu, Z. Wang, and X. Zhang, “Wideband tunable optoelectronic oscillator based on a microwave photonic filter with an ultra-narrow passband,” Opt. Lett. 43, 2328–2331 (2018).
[Crossref]

2017 (2)

H. Tang, Y. Yu, C. Zhang, Z. Wang, L. Xu, and X. Zhang, “Analysis of performance optimization for a microwave photonic filter based on stimulated Brillouin scattering,” J. Lightwave Technol. 35, 4375–4383 (2017).
[Crossref]

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]

2016 (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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

2015 (1)

2014 (3)

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

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

2013 (2)

2012 (2)

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

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

2011 (3)

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5, 728–730 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

2010 (1)

T. Kottos, “Optical physics: Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[Crossref]

2009 (1)

2008 (1)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

2007 (3)

E. Salik and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

2006 (1)

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

2000 (1)

X. Steve Yao and L. Maleki, “Multiloop optoelectronic oscillator,” IEEE J. Quantum Electron. 36, 79–84 (2000).
[Crossref]

1998 (1)

C. M. Bender and S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

1996 (2)

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996).
[Crossref]

1966 (1)

D. B. Lesson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE 54, 329–330 (1966).
[Crossref]

Aditya, S.

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]

C. M. Bender and S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Böttcher, S.

C. M. Bender and S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Capmany, J.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Chen, Z.

Chou, C. W.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Christodoulides, D. N.

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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

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

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

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

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]

Diddams, S. A.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Eliyahu, D.

D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra low noise floor cross-correlation microwave photonic homodyne system,” in IEEE International Frequency Control Symposium (2008), pp. 811–814.

Ellis, F. M.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[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]

Feng, L.

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

Fortier, T. M.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (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]

Guo, P.

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]

Hao, T.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

Hartnett, J. G.

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

Hassan, A. U.

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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

Hati, A.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

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

Hodaei, H.

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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

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

Howe, D.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Ivanov, E. N.

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

Jiang, F.

Jiang, H.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Jiang, Y.

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

Khajavikhan, 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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

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

Kottos, T.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

T. Kottos, “Optical physics: Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[Crossref]

Lam, H. Q.

Lee, K. E. K.

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]

Lemke, N.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Lesson, D. B.

D. B. Lesson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE 54, 329–330 (1966).
[Crossref]

Li, A.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

Li, M.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

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]

Li, W.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

LiKamWa, P.

Lim, P. H.

Liu, W.

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]

W. Liu, M. Wang, and J. Yao, “Tunable microwave and sub-terahertz generation based on frequency quadrupling using a single polarization modulator,” J. Lightwave Technol. 31, 1636–1644 (2013).
[Crossref]

Liu, Y.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

Locke, C. R.

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[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]

Lu, M.

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]

Ludlow, A.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Ma, R.-M.

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

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Maleki, L.

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5, 728–730 (2011).
[Crossref]

E. Salik and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[Crossref]

X. Steve Yao and L. Maleki, “Multiloop optoelectronic oscillator,” IEEE J. Quantum Electron. 36, 79–84 (2000).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996).
[Crossref]

D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra low noise floor cross-correlation microwave photonic homodyne system,” in IEEE International Frequency Control Symposium (2008), pp. 811–814.

McNeilage, C.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

Miri, M. A.

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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

Miri, M.-A.

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

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

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]

Mossammaparast, M.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Nelson, C. W.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Norberg, E. 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).
[Crossref]

Nori, 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]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Oates, C. W.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Özdemir, S. K.

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]

Parker, J. 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]

Peng, B.

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]

Peng, H.

Quinlan, F.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Rosenband, T.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Salik, E.

E. Salik and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[Crossref]

Schindler, J.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

Searls, J. H.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

Seidel, D.

D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra low noise floor cross-correlation microwave photonic homodyne system,” in IEEE International Frequency Control Symposium (2008), pp. 811–814.

Shum, P. P.

Sidorowicz, R. S.

R. S. Sidorowicz, Design of Crystal and other Harmonic Oscillators (Wiley, 1983), pp. 20–30.

Stanwix, P. L.

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

Steve Yao, X.

X. Steve Yao and L. Maleki, “Multiloop optoelectronic oscillator,” IEEE J. Quantum Electron. 36, 79–84 (2000).
[Crossref]

Stockwell, A.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

Suddaby, M. E.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

Sun, T.

Tang, H.

Taylor, J.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Tobar, M. E.

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

Wang, M.

Wang, Y.

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

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

Wang, Z.

Wong, J. H.

Wong, Z. J.

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

Xie, X.

Xu, L.

Yang, E.

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

Yang, 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]

Yao, J.

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4, eaar6782 (2018).
[Crossref]

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]

W. Liu, M. Wang, and J. Yao, “Tunable microwave and sub-terahertz generation based on frequency quadrupling using a single polarization modulator,” J. Lightwave Technol. 31, 1636–1644 (2013).
[Crossref]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27, 314–335 (2009).
[Crossref]

Yao, X. S.

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996).
[Crossref]

Yu, J.

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

Yu, Y.

Zelenka, J.

J. Zelenka, Piezoelectric Resonators and their Applications (Elsevier Science, 1986), pp. 10–15.

Zhang, C.

Zhang, J.

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4, eaar6782 (2018).
[Crossref]

Zhang, L.

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

Zhang, X.

Zheng, M. C.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

Zhou, J.

Zhu, N.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

Zhu, X.

Appl. Phys. Lett. (2)

J. G. Hartnett, C. R. Locke, E. N. Ivanov, M. E. Tobar, and P. L. Stanwix, “Cryogenic sapphire oscillator with exceptionally high long-term frequency stability,” Appl. Phys. Lett. 89, 203513 (2006).
[Crossref]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, and S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

IEEE J. Quantum Electron. (2)

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996).
[Crossref]

X. Steve Yao and L. Maleki, “Multiloop optoelectronic oscillator,” IEEE J. Quantum Electron. 36, 79–84 (2000).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Y. Jiang, J. Yu, Y. Wang, L. Zhang, and E. Yang, “An optical domain combined dual-loop optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 807–809 (2007).
[Crossref]

E. Salik and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (1)

Laser Photon. 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 Photon. Rev. 10, 494–499 (2016).
[Crossref]

Light Sci. Appl. (1)

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7, 38–47 (2018).
[Crossref]

Nat. Commun. (1)

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]

Nat. Photonics (2)

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5, 728–730 (2011).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Nat. Phys. (2)

T. Kottos, “Optical physics: Broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010).
[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]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011).
[Crossref]

Phys. Rev. Lett. (2)

C. M. Bender and S. Böttcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Proc. IEEE (1)

D. B. Lesson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE 54, 329–330 (1966).
[Crossref]

Sci. Adv. (1)

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4, eaar6782 (2018).
[Crossref]

Science (2)

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

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

Other (7)

D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra low noise floor cross-correlation microwave photonic homodyne system,” in IEEE International Frequency Control Symposium (2008), pp. 811–814.

M. Mossammaparast, C. McNeilage, A. Stockwell, J. H. Searls, and M. E. Suddaby, “Low phase noise division from X-band to 640  MHz,” in IEEE Frequency Control Symposium and PDA Exhibition (2002), pp. 685–689.

J. Zelenka, Piezoelectric Resonators and their Applications (Elsevier Science, 1986), pp. 10–15.

R. S. Sidorowicz, Design of Crystal and other Harmonic Oscillators (Wiley, 1983), pp. 20–30.

http://literature.cdn.keysight.com/litweb/pdf/5988-7454EN.pdf .

http://literature.cdn.keysight.com/litweb/pdf/N9030-90017.pdf .

https://oewaves.com/hi-q-oeo .

Supplementary Material (1)

NameDescription
» Visualization 1       A stable 17.74-GHz microwave signal generated by the OEO with selective PT-symmetry breaking.

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Figures (9)

Fig. 1.
Fig. 1. Experimental setup. LD, laser diode; PC, polarization controller; PM, phase modulator; HNLF, high nonlinear fiber; TLD, tunable laser diode; PBS, polarization beam splitter; OTDL, optical tunable delay line; BPD, balanced photodetector; EA, electrical amplifier; ESA, electrical spectrum analyzer.
Fig. 2.
Fig. 2. Mode selectivity principle of the selective PT-symmetry breaking.
Fig. 3.
Fig. 3. Measured microwave signal at 17.74 GHz generated by the OEO: (a) spectra of the generated microwave signal based only on the SBS-MPF with RBW=20kHz, (b) single-mode oscillation with PT symmetry with RBW=50kHz, (c) zoomed-in view of the spectrum in (b) with RBW=1kHz, and (d) single-mode oscillation with SMSR of 71.4 dB with RBW=3kHz. (Visualization 1)
Fig. 4.
Fig. 4. (a) Measured electrical spectra of the OEO for a 10-min period when the oscillating frequency is 17.42 GHz and (b) the frequency jitter of the proposed OEO.
Fig. 5.
Fig. 5. Frequency tunability of the proposed OEO scheme.
Fig. 6.
Fig. 6. Phase noises of different frequencies.
Fig. 7.
Fig. 7. Measured spectra at the central frequency at 17.74 GHz of the OEO with a 2-km loop length, span = 300 kHz, and RBW=1kHz.
Fig. 8.
Fig. 8. Simulated SMSR of OEO with different loop lengths.
Fig. 9.
Fig. 9. Measured phase noises of the OEO with different loop lengths and a commercial Agilent microwave source.

Equations (5)

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

ddt[GnAn]=[jωn+gjκjκjωnα][GnAn],
ωn(g,α)=ωn+jgα2±κ2(g+α2)2.
ωn(g,α)=ωn±κ2g2.
Δg=gmaxgsub_max,
ΔgPT_max=gmax2gsub_max2=Δg·gmax+gsub_maxgmaxgsub_max.

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