[1] Bender C M, Boettcher S. Real spectra in non-Hermitian Hamiltonians having PT symmetry[J]. Physical Review Letters, 80, 5243-5246(1998).

[2] Bender C M. Making sense of non-Hermitian Hamiltonians[J]. Reports on Progress in Physics, 70, 947-1018(2007).

[3] El-Ganainy R, Makris K G, Christodoulides D N et al. Theory of coupled optical PT-symmetric structures[J]. Optics Letters, 32, 2632-2634(2007).

[4] Rüter C E, Makris K G, El-Ganainy R et al. Observation of parity-time symmetry in optics[J]. Nature Physics, 6, 192-195(2010).

[5] Guo A, Salamo G J, Duchesne D et al. Observation of PT-symmetry breaking in complex optical potentials[J]. Physical Review Letters, 103, 093902(2009).

[6] Wang Y Y, Xia J, Fang Y T. Unique non-reciprocal mode with a parity-time symmetric structure under magneto-optic effects[J]. Chinese Journal of Lasers, 45, 1213001(2018).

[7] Lin Z, Ramezani H, Eichelkraut T et al. Unidirectional invisibility induced by PT-symmetric periodic structures[J]. Physical Review Letters, 106, 213901(2011).

[8] Longhi S. Invisibility in PT-symmetric complex crystals[J]. Journal of Physics A: Mathematical and Theoretical, 44, 485302(2011).

[9] Longhi S. PT-symmetric laser absorber[J]. Physical Review A, 82, 031801(2010).

[10] Chong Y D, Ge L, Cao H et al. Coherent perfect absorbers: time-reversed lasers[J]. Physical Review Letters, 105, 053901(2010).

[11] Sun Y, Tan W, Li H Q et al. Experimental demonstration of a coherent perfect absorber with PT phase transition[J]. Physical Review Letters, 112, 143903(2014).

[12] Nazari F, Nazari M. Moravvej-Farshi M K. A 2×2 spatial optical switch based on PT-symmetry[J]. Optics Letters, 36, 4368-4370(2011).

[13] Feng L, Xu Y L, Fegadolli W S et al. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies[J]. Nature Materials, 12, 108-113(2013).

[14] Chang L, Jiang X S, Hua S Y et al. Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators[J]. Nature Photonics, 8, 524-529(2014).

[15] Musslimani Z H, Makris K G, El-Ganainy R et al. Optical solitons in PT periodic potentials[J]. Physical Review Letters, 100, 030402(2008).

[16] Zhang C H, Xu S L. Multipole solitons in two dimensions PT-symmetric optical potentials[J]. Acta Optica Sinica, 36, 0219001(2016).

[17] Li Y L, Qin Y L, Mao S Y et al. Propagation characteristics of optical solitons in parity-time symmetric potentials with longitudinal barriers[J]. Laser & Optoelectronics Progress, 54, 081901(2017).

[18] Makris K G, El-Ganainy R, Christodoulides D N et al. PT-symmetric optical lattices[J]. Physical Review A, 81, 063807(2010).

[19] Nixon S, Ge L J, Yang J K. Stability analysis for solitons in PT-symmetric optical lattices[J]. Physical Review A, 85, 023822(2012).

[20] Abdullaev F K, Kartashov Y V, Konotop V V et al. Solitons in PT-symmetric nonlinear lattices[J]. Physical Review A, 83, 041805(2011).

[21] Miri M A, Aceves A B, Kottos T et al. Bragg solitons in nonlinear PT-symmetric periodic potentials[J]. Physical Review A, 86, 033801(2012).

[22] He Y J, Zhu X, Mihalache D et al. Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices[J]. Physical Review A, 85, 013831(2012).

[23] Shi Z, Jiang X, Zhu X et al. Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials[J]. Physical Review A, 84, 053855(2011).

[24] Khare A. Al-Marzoug S M, Bahlouli H. Solitons in PT-symmetric potential with competing nonlinearity[J]. Physics Letters A, 376, 2880-2886(2012).

[25] Midya B, Roychoudhury R. Nonlinear localized modes in PT-symmetric optical media with competing gain and loss[J]. Annals of Physics, 341, 12-20(2014).

[26] Al Khawaja U. Al-Marzoug S M, Bahlouli H, et al. Unidirectional soliton flows in PT-symmetric potentials[J]. Physical Review A, 88, 023830(2013).

[27] Xu Y J, Dai C Q. Nonlinear tunnelling of spatial solitons in PT-symmetric potential[J]. Optics Communications, 318, 112-119(2014).

[28] Hu S M, Ma X K, Lu D Q et al. Solitons supported by complex PT-symmetric Gaussian potentials[J]. Physical Review A, 84, 043818(2011).

[29] Dang T T, Wang J F, An Y D et al. Transmission and control of bright solitons in parity-time symmetric waveguide[J]. Acta Physica Sinica, 64, 064211(2015).

[30] Chen Y X, Dai C Q, Wang X G. Two-dimensional nonautonomous solitons in parity-time symmetric optical media[J]. Optics Communications, 324, 10-17(2014).

[31] Ahmed Z. Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential[J]. Physics Letters A, 282, 343-348(2001).