[1] Lodahl P, Mahmoodian S, Stobbe S et al. Chiral quantum optics[J]. Nature, 541, 473-480(2017).

[2] Yang H, Qin G Q, Zhang H et al. Multimode interference induced optical routing in an optical microcavity[J]. Annalen der Physik, 533, 2000506(2021).

[3] Zhu Y, Zhao Y, Zhu L. Modal discrimination in parity-time-symmetric single microring lasers[J]. IEEE Photonics Journal, 9, 2700908(2017).

[4] Xia K, Lu G, Lin G et al. Reversible nonmagnetic single-photon isolation using unbalanced quantum coupling[J]. Physical Review A, 90, 043802(2014).

[5] Sayrin C, Junge C, Mitsch R et al. Nanophotonic optical isolator controlled by the internal state of cold atoms[J]. Physical Review X, 5, 041036(2015).

[6] Scheucher M, Hilico A, Will E et al. Quantum optical circulator controlled by a single chirally coupled atom[J]. Science, 354, 1577-1580(2016).

[7] Yang L, Zhang Y, Yan X B et al. Dynamically induced two-color nonreciprocity in a tripod system of a moving atomic lattice[J]. Physical Review A, 92, 053859(2015).

[8] Wang D W, Zhou H T, Guo M J et al. Optical diode made from a moving photonic crystal[J]. Physical Review Letters, 110, 093901(2013).

[9] Wu J H, Artoni M, La Rocca G C. Parity-time-antisymmetric atomic lattices without gain[J]. Physical Review A, 91, 033811(2015).

[10] Chaung Y L, Shamsi A, Abbas M et al. Coherent control of nonreciprocal reflections with spatial modulation coupling in parity-time symmetric atomic lattice[J]. Optics Express, 28, 1701-1713(2020).

[11] Xu X W, Li Y, Chen A X et al. Nonreciprocal conversion between microwave and optical photons in electro-optomechanical systems[J]. Physical Review A, 93, 023827(2016).

[12] Fang K, Luo J, Metelmann A et al. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering[J]. Nature Physics, 13, 465-471(2017).

[13] Li Y, Huang Y Y, Zhang X Z et al. Optical directional amplification in a three-mode optomechanical system[J]. Optics Express, 25, 18907-18916(2017).

[14] Jiang C, Song L N, Li Y. Directional amplifier in an optomechanical system with optical gain[J]. Physical Review A, 97, 053812(2018).

[15] Ruesink F, Miri M A, Alu A et al. Nonreciprocity and magnetic-free isolation based on optomechanical interactions[J]. Nature Communications, 7, 13662(2016).

[16] Yang P, Xia X, He H et al. Realization of nonlinear optical nonreciprocity on a few-photon level based on atoms strongly coupled to an asymmetric cavity[J]. Physical Review Letters, 123, 233604(2019).

[17] Wang J. Optical nonreciprocity in two-cavity optomechanical system[J]. Chinese Journal of Quantum Electronics, 37, 328-336(2020).

[18] Huang R, Miranowicz A, Liao J Q et al. Nonreciprocal photon blockade[J]. Physical Review Letters, 121, 153601(2018).

[19] Tang L, Tang J, Chen M et al. Quantum squeezing induced optical nonreciprocity[J]. Physical Review Letters, 128, 083604(2022).

[20] Zhang S, Hu Y, Lin G et al. Thermal-motion-induced non-reciprocal quantum optical system[J]. Nature Photonics, 12, 744-748(2018).

[21] Lin G, Zhang S, Hu Y et al. Nonreciprocal amplification with four-level hot atoms[J]. Physical Review Letters, 123, 033902(2019).

[22] Hu Y, Qi Y, You Y et al. Passive nonlinear optical isolators bypassing dynamic reciprocity[J]. Physical Review Applied, 16, 014046(2021).

[23] Jiang W, Ma Y, Yuan J et al. Deformable broadband metamaterial absorbers engineered with an analytical spatial Kramers‐Kronig permittivity profile[J]. Laser & Photonics Reviews, 11, 1600253(2017).

[24] Liu D, Huang Y, Hu H et al. Designing spatial Kramers-Kronig media using transformation optics[J]. IEEE Transactions on Antennas and Propagation, 68, 2945-2949(2019).

[25] Zhang Y, Wu J H, Artoni M et al. Controlled unidirectional reflection in cold atoms via the spatial Kramers-Kronig relation[J]. Optics Express, 29, 5890-5900(2021).

[26] Fan X, Pei X S, Geng Y et al. Dynamic manipulation of two-color non-reciprocal reflection based on spatial Kramers-Kronig relation[J]. Journal of Hainan Normal University (Natural Science Edition), 35, 275-281(2022).

[27] Artoni M, La Rocca G, Bassani F. Resonantly absorbing one-dimensional photonic crystals[J]. Physical Review E, 72, 046604(2005).

[28] Zhang Y, Xue Y, Wang G et al. Steady optical spectra and light propagation dynamics in cold atomic samples with homogeneous or inhomogeneous densities[J]. Optics Express, 19, 2111-2119(2011).

[29] Born M, Wolf E[M]. Principles of Optics(1999).