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Floquet control of the gain and loss in a PT-symmetric optical coupler

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Abstract

Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Further, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT symmetry control schemes, our protocol can modulate the unbroken PT-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.

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References

  1. S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, Nonlinear switching and solitons in PT-symmetric photonic systems, Laser Photonics Rev. 10(2), 177 (2016)

    Article  Google Scholar 

  2. V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in PT-symmetric systems, Rev. Mod. Phys. 88(3), 035002 (2016)

    Article  ADS  Google Scholar 

  3. N. Moiseyev, Non-Hermitian Quantum Mechanics, Cambridge: Cambridge University Press, 2011

    Book  MATH  Google Scholar 

  4. H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Parity-time symmetric microring lasers, Science 346(6212), 975 (2014)

    Article  ADS  Google Scholar 

  5. 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 (2014)

    Article  ADS  Google Scholar 

  6. 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(2), 108 (2012)

    Article  ADS  Google Scholar 

  7. B. Peng, S. K. Ozdemir, 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(5), 394 (2014)

    Article  Google Scholar 

  8. F. Nazari, N. Bender, H. Ramezani, M. K. Moravvej-Farshi, D. N. Christodoulides, and T. Kottos, Optical isolation via PT-symmetric nonlinear Fano resonances, Opt. Express 22(8), 9574 (2014)

    Article  ADS  Google Scholar 

  9. H. Xiong, L. Si, X. Yang, and Y. Wu, Asymmetric optical transmission in an optomechanical array, Appl. Phys. Lett. 107(9), 091116 (2015)

    Article  ADS  Google Scholar 

  10. S. Longhi and L. Feng, PT-symmetric microring laser absorber, Opt. Lett. 39(17), 5026 (2014)

    Article  ADS  Google Scholar 

  11. V. A. Vysloukh and Y. V. Kartashov, Resonant mode conversion in the waveguides with unbroken and broken PT symmetry, Opt. Lett. 39(20), 5933 (2014)

    Article  ADS  Google Scholar 

  12. J. Gan, H. Xiong, L. Si, X. Lü, and Y. Wu, Soliton in optomechanical arrays, Opt. Lett. 41(12), 2676 (2016)

    Article  ADS  Google Scholar 

  13. H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Parity-time-symmetric coupled microring lasers operating around an exceptional point, Opt. Lett. 40(21), 4955 (2015)

    Article  ADS  Google Scholar 

  14. X. Lü, H. Jing, J. Ma, and Y. Wu, PT-symmetrybreaking chaos in optomechanics, Phys. Rev. Lett. 114(25), 253601 (2015)

    Article  ADS  Google Scholar 

  15. H. Jing, S. K. Ozdemir, X. Lü, J. Zhang, L. Yang, and F. Nori, PT-symmetric phonon laser, Phys. Rev. Lett. 113(5), 053604 (2014)

    Article  ADS  Google Scholar 

  16. Y. V. Kartashov, V. A. Vysloukh, V. V. Konotop, and L. Torner, Diffraction control in PT-symmetric photonic lattices: From beam rectification to dynamic localization, Phys. Rev. A 93(1), 013841 (2016)

    Article  ADS  Google Scholar 

  17. J. Li, J. Li, Q. Xiao, and Y. Wu, Giant enhancement of optical high-order sideband generation and their control in a dimer of two cavities with gain and loss, Phys. Rev. A 93(6), 063814 (2016)

    Article  ADS  Google Scholar 

  18. H. Wang, Multi-peak solitons in PT-symmetric Bessel optical lattices with defects, Front. Phys. 11(5), 114204 (2016)

    Article  Google Scholar 

  19. C. M. Bender and S. Boettcher, Real spectra in Non- Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80(24), 5243 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. C. M. Bender, Making Sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70(6), 947 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  21. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Observation of parity-time symmetry in optics, Nat. Phys. 6(3), 192 (2010)

    Article  Google Scholar 

  22. 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(9), 093902 (2009)

    Article  ADS  Google Scholar 

  23. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Parity-time synthetic photonic lattices, Nature 488(7410), 167 (2012)

  24. S. Bittner, B. Dietz, U. Günther, H. L. Harney, M. Miski-Oglu, A. Richter, and F. Schäfer, PT symmetry and spontaneous symmetry breaking in a microwave billiard, Phys. Rev. Lett. 108(2), 024101 (2012)

    Article  ADS  Google Scholar 

  25. N. Moiseyev, Crossing rule for a PT-symmetric two-level time-periodic system, Phys. Rev. A 83(5), 052125 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  26. X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Y. S. Kivshar, and C. Lee, Pseudo-parity-time symmetry in optical systems, Phys. Rev. Lett. 110(24), 243902 (2013)

    Article  ADS  Google Scholar 

  27. X. Lian, H. Zhong, Q. Xie, X. Zhou, Y. Wu, and W. Liao, PT-symmetry-breaking induced suppression of tunneling in a driven non-Hermitian two-level system, Eur. Phys. J. D 68(7), 189 (2014)

    Article  ADS  Google Scholar 

  28. Y. N. Joglekar, R. Marathe, P. Durganandini, and R. K. Pathak, PT spectroscopy of the Rabi problem, Phys. Rev. A 90(4), 040101(R) (2014)

    Article  ADS  Google Scholar 

  29. J. Gong and Q. H. Wang, Stabilizing non-Hermitian systems by periodic driving, Phys. Rev. A 91(4), 042135 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  30. Z. Zhou, B. Zhu, and L. Zhang, Analytical study on propagation dynamics of optical beam in parity-time symmetric optical couplers, Commum. Theor. Phys. 63(4), 406 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. S. Longhi, PT phase control in circular multi-core fibers, Opt. Lett. 41(9), 1897 (2016)

    Article  ADS  Google Scholar 

  32. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Theory of coupled optical PT symmetric structures, Opt. Lett. 32(17), 2632 (2007)

    Article  ADS  MATH  Google Scholar 

  33. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Beam dynamics in PT symmetric optical lattices, Phys. Rev. Lett. 100(10), 103904 (2008)

    Article  ADS  Google Scholar 

  34. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Optical solitons in PT periodic potentials, Phys. Rev. Lett. 100(3), 030402 (2008)

    Article  ADS  MATH  Google Scholar 

  35. A. Yariv, Optical Electronics in Modern Communications, Oxford: Oxford University Press, 1997

    Google Scholar 

  36. P. Yeh, Introduction to Photorefractive Nonlinear Optics, Wiley Series in Pure and Applied Optics, New York: Wiley, 2001

    Google Scholar 

  37. S. Longhi, Quantum-optical analogies using photonic structures, Laser Photonics Rev. 3(3), 243 (2009)

    Article  MathSciNet  Google Scholar 

  38. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Light propagation and localization in modulated photonic lattices and waveguides, Phys. Rep. 518(1–2), 1 (2012)

    Article  ADS  Google Scholar 

  39. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Inhibition of light tunneling in waveguide arrays, Phys. Rev. Lett. 102(15), 153901 (2009)

    Article  ADS  Google Scholar 

  40. A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Nonlinearity-induced broadening of resonances in dynamically modulated couplers, Opt. Lett. 34(18), 2700 (2009)

    Article  ADS  Google Scholar 

  41. G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Visualization of coherent destruction of tunneling in an optical double well system, Phys. Rev. Lett. 98(26), 263601 (2007)

    Article  ADS  Google Scholar 

  42. J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, Optical analogues for massless Dirac particles and conical diffraction in one dimension, Phys. Rev. Lett. 109(2), 023602 (2012)

    Article  ADS  Google Scholar 

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Acknowledgments

We acknowledge helpful discussion with Chaohong Lee. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11465008, 11574405, and 11426223), the Hunan Provincial Natural Science Foundation (Grant Nos. 2015JJ2114, 2015JJ4020, and 14JJ3114), and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 14A118).

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Authors and Affiliations

  1. Department of Physics, Engineering University of CAPF, Xi’an, 710086, China

    Yi Wu

  2. School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai, 519082, China

    Bo Zhu

  3. Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, 410004, China

    Shu-Fang Hu & Hong-Hua Zhong

  4. Department of Physics, Hunan Institute of Technology, Hengyang, 421002, China

    Zheng Zhou

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  1. Yi Wu
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  5. Hong-Hua Zhong
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Correspondence to Hong-Hua Zhong.

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arXiv: 1612.04628.

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Wu, Y., Zhu, B., Hu, SF. et al. Floquet control of the gain and loss in a PT-symmetric optical coupler. Front. Phys. 12, 121102 (2017). https://doi.org/10.1007/s11467-016-0642-x

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