Fig. 1. Discrete non-reciprocal optical devices based on the Faraday effect. (a) Structure and working principle of a magneto-optic isolator based on the Faraday effect; (b) commercial free-space magneto-optic isolator; (c) commercial in-line fiber magneto-optic circulator

Fig. 2. Principle of non-reciprocal mode coupling in magneto-optic waveguides. (a) Schematic diagram of the structure and working principle of an integrated NRMC optical isolator; (b) dependence of polarization evolution on Q value within an NRMC waveguide

Fig. 3. NRMC type nonreciprocal photonic devices. (a) Faraday rotators and isolators with birefringence control^[19]; (b) integrated Faraday rotators and isolators with quasi-phase matching^[16]

Fig. 4. Schematics of NRPS-type integrated non-reciprocal photonic devices. (a) Waveguide structures and mode field distributions of non-reciprocal phase-shift waveguides; (b) schematics of integrated magneto-optic isolators/circulators based on NRPS

Fig. 5. NRPS type non-reciprocal photonic devices fabricated by wafer bonding. (a) Magneto-optic isolators fabricated by direct bonding^[48]; (b) magneto-optic isolators fabricated by adhesive bonding^[34]; (c) MRR-type magneto-optic modulator fabricated by direct bonding^[46]; (d) polarimetric independent magneto-optic circulator fabricated by adhesive bonding^[39]

Fig. 6. NRPS-type non-reciprocal photonic devices fabricated by direct deposition. (a) Schematic diagram of the direct deposition process, including the distribution characteristics of the magneto-optic thin film on silicon wafer and the distribution of the magneto-optic effect across the wafer; (b) SOI-based integrated MZI-type magneto-optic isolators^[22]; (c) microring-type magneto-optic isolator on silicon based on GeSbSe waveguides^[52]; (d) ultra-broadband magneto-optic isolators and circulators integrated on SiN waveguides^[53-54]

Fig. 7. Principle of non-reciprocal photonic effect in nonlinear optical materials and asymmetric optical waveguide structures^[63]

Fig. 8. Non-reciprocal photonic devices based on nonlinear effects. (a) Micro-ring type optical isolators based-on dynamic non-reciprocal effect^[71]; (b) non-reciprocal photonic devices based on parametric amplification^[74]; (c) periodically poled lithium niobate waveguide optical isolators based on non-reciprocal four-wave mixing^[75]; (d) integrated optical isolator based on exceptional points in PT-symmetric systems^[78]

Fig. 9. Schematic diagrams of the working principle of spatio-temporal modulation non-reciprocal photonic devices. (a) Waveguide band structure, with arrows representing interband transition induced by index modulation; (b) forward phase match with high transmission efficiency; (c) reverse phase match with low transmission efficiency

Fig. 10. Integrated non-reciprocal photonic devices based on spatio-temporal modulation. (a) TFLN integrated optical isolators based on electro-optic modulation^[88]; (b) silicon nitride integrated optical isolators based on acousto-optic modulation^[93]; (c) cavity optomechanical non-reciprocal photonic memory^[101]