Floquet control of the gain and loss in a \mathcal{P}\mathcal{T}-symmetric optical coupler

Abstract

Controlling the balanced gain and loss in a \mathcal{P}\mathcal{T}-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 \mathcal{P}\mathcal{T}-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 \mathcal{P}\mathcal{T} symmetry control schemes, our protocol can modulate the unbroken \mathcal{P}\mathcal{T}-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.

Keywords

\mathcal{P}\mathcal{T} symmetry / periodic modulation / optical coupler

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)

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

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

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

[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)

[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)

[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)

[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)

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

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

[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)

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

[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)

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

[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)

[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)

[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)

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

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

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

[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)

[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)

[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)

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

[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)

[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)

[28] 10.1103/PhysRevA.90.040101 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)

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

[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)

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

[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)

[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)

[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)

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

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

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

[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)

[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)

[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)

[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)

[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)

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