[1] Bloch, F. Über die quantenmechanik der elektronen in kristallgittern. Z. für. Phys. 52, 555-600 (1929). doi: 10.1007/BF01339455
[2] Zener, C. A theory of the electrical breakdown of solid dielectrics. Proc. Royal Soc. A 145, 523-529 (1934).
[3] Lenz, G., Talanina, I. & De Sterke, C. M. Bloch oscillations in an array of curved optical waveguides. Phys. Rev. Lett. 83, 963-966 (1999). doi: 10.1103/PhysRevLett.83.963
[4] Dreisow, F. et al. Bloch-Zener oscillations in binary superlattices. Phys. Rev. Lett. 102, 076802 (2009). doi: 10.1103/PhysRevLett.102.076802
[5] Corrielli, G. et al. Fractional Bloch oscillations in photonic lattices. Nat. Commun. 4, 1555 (2013). doi: 10.1038/ncomms2578
[6] Sanchis-Alepuz, H., Kosevich, Y. A. & Sánchez-Dehesa, J. Acoustic analogue of electronic bloch oscillations and resonant zener tunneling in ultrasonic superlattices. Phys. Rev. Lett. 98, 134301 (2007). doi: 10.1103/PhysRevLett.98.134301
[7] Lanzillotti-Kimura, N. D. et al. Bloch oscillations of THz acoustic phonons in coupled nanocavity structures. Phys. Rev. Lett. 104, 197402 (2010). doi: 10.1103/PhysRevLett.104.197402
[8] Dahan, M. B. et al. Bloch oscillations of atoms in an optical potential. Phys. Rev. Lett. 76, 4508-4511 (1996). doi: 10.1103/PhysRevLett.76.4508
[9] Geiger, Z. A. et al. Observation and uses of position-space bloch oscillations in an ultracold gas. Phys. Rev. Lett. 120, 213201 (2018). doi: 10.1103/PhysRevLett.120.213201
[10] Eisenberg, H. S. et al. Diffraction management. Phys. Rev. Lett. 85, 1863-1866 (2000). doi: 10.1103/PhysRevLett.85.1863
[11] Christodoulides, D. N., Lederer, F. & Silberberg, Y. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817-823 (2003). doi: 10.1038/nature01936
[12] Peschel, U., Pertsch, T. & Lederer, F. Optical Bloch oscillations in waveguide arrays. Opt. Lett. 23, 1701-1703 (1998). doi: 10.1364/OL.23.001701
[13] Pertsch, T. et al. Optical bloch oscillations in temperature tuned waveguide arrays. Phys. Rev. Lett. 83, 4752-4755 (1999). doi: 10.1103/PhysRevLett.83.4752
[14] Morandotti, R. et al. Experimental observation of linear and nonlinear optical bloch oscillations. Phys. Rev. Lett. 83, 4756-4759 (1999). doi: 10.1103/PhysRevLett.83.4756
[15] Regensburger, A. et al. Photon propagation in a discrete fiber network: an interplay of coherence and losses. Phys. Rev. Lett. 107, 233902 (2011). doi: 10.1103/PhysRevLett.107.233902
[16] Bersch, C., Onishchukov, G. & Peschel, U. Spectral and temporal Bloch oscillations in optical fibres. Appl. Phys. B 104, 495-501 (2011). doi: 10.1007/s00340-011-4627-8
[17] Bell, B. A. et al. Spectral photonic lattices with complex long-range coupling. Optica 4, 1433-1436 (2017). doi: 10.1364/OPTICA.4.001433
[18] Qin, C. Z. et al. Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials. Phys. Rev. Lett. 120, 133901 (2018). doi: 10.1103/PhysRevLett.120.133901
[19] Yuan, L. Q. et al. Synthetic dimension in photonics. Optica 5, 1396-1405 (2018). doi: 10.1364/OPTICA.5.001396
[20] Floß, J. et al. Observation of bloch oscillations in molecular rotation. Phys. Rev. Lett. 115, 203002 (2015). doi: 10.1103/PhysRevLett.115.203002
[21] Luo, X. W. et al. Synthetic-lattice enabled all-optical devices based on orbital angular momentum of light. Nat. Commun. 8, 16097 (2017). doi: 10.1038/ncomms16097
[22] Qin, C. Z. et al. Effective electric-field force for a photon in a synthetic frequency lattice created in a waveguide modulator. Phys. Rev. A 97, 063838 (2018). doi: 10.1103/PhysRevA.97.063838
[23] Bersch, C., Onishchukov, G. & Peschel, U. Experimental observation of spectral Bloch oscillations. Opt. Lett. 34, 2372-2374 (2009). doi: 10.1364/OL.34.002372
[24] Yuan, L. Q. & Fan, S. H. Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator. Optica 3, 1014-1018 (2016). doi: 10.1364/OPTICA.3.001014
[25] Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photonics 8, 821-829 (2014). doi: 10.1038/nphoton.2014.248
[26] Lin, Y. J. et al. A synthetic electric force acting on neutral atoms. Nat. Phys. 7, 531-534 (2011). doi: 10.1038/nphys1954
[27] Celi, A. et al. Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett. 112, 043001 (2014). doi: 10.1103/PhysRevLett.112.043001
[28] Goda, K. et al. Theory of amplified dispersive fourier transformation. Phys. Rev. A 80, 043821 (2009). doi: 10.1103/PhysRevA.80.043821
[29] Goda, K. & Jalali, B. Dispersive fourier transformation for fast continuous single-shot measurements. Nat. Photonics 7, 102-112 (2013). doi: 10.1038/nphoton.2012.359
[30] Mahjoubfar, A. et al. Time stretch and its applications. Nat. Photonics 11, 341-351 (2017). doi: 10.1038/nphoton.2017.76
[31] Liu, X. M., Yao, X. K. & Cui, Y. D. Real-time observation of the buildup of soliton molecules. Phys. Rev. Lett. 121, 023905 (2018). doi: 10.1103/PhysRevLett.121.023905
[32] Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555-559 (2011). doi: 10.1126/science.1193968
[33] Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator. Nature 568, 373-377 (2019). doi: 10.1038/s41586-019-1008-7
[34] Schliesser, A., Picqué, N. & Hänsch, T. W. Mid-infrared frequency combs. Nat. Photonics 6, 440-449 (2012). doi: 10.1038/nphoton.2012.142
[35] Lee, B. Review of the present status of optical fiber sensors. Opt. Fiber Technol. 9, 57-79 (2003). doi: 10.1016/S1068-5200(02)00527-8
[36] Peled, Y., Motil, A. & Tur, M. Fast Brillouin optical time domain analysis for dynamic sensing. Opt. Express 20, 8584-8591 (2012). doi: 10.1364/OE.20.008584
[37] Schliesser, A. et al. Frequency-comb infrared spectrometer for rapid, remote chemical sensing. Opt. Express 13, 9029-9038 (2005). doi: 10.1364/OPEX.13.009029
[38] Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photonics 11, 774-783 (2017). doi: 10.1038/s41566-017-0051-x
[39] Fang, K. J., Yu, Z. F. & Fan, S. H. Photonic aharonov-bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012). doi: 10.1103/PhysRevLett.108.153901
[40] Fang, K. J. et al. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys. 13, 465-471 (2017). doi: 10.1038/nphys4009
[41] Lin, Q. & Fan, S. H. Light guiding by effective gauge field for photons. Phys. Rev. X 4, 031031 (2014). doi: 10.1103/PhysRevX.4.031031
[42] Dutt, A. et al. Experimental band structure spectroscopy along a synthetic dimension. Nat. Commun. 10, 3122 (2019). doi: 10.1038/s41467-019-11117-9
[43] Agrawal, G. P. Nonlinear Fiber Optics 4th edn (Academic Press, 2007).
[44] Bersch, C., Onishchukov, G. & Peschel, U. Optical gap solitons and truncated nonlinear Bloch waves in temporal lattices. Phys. Rev. Lett. 109, 093903 (2012). doi: 10.1103/PhysRevLett.109.093903
[45] Haller, E. et al. Inducing transport in a dissipation-free lattice with super Bloch oscillations. Phys. Rev. Lett. 104, 200403 (2010). doi: 10.1103/PhysRevLett.104.200403
[46] Longhi, S. et al. Observation of dynamic localization in periodically curved waveguide arrays. Phys. Rev. Lett. 96, 243901 (2006). doi: 10.1103/PhysRevLett.96.243901
[47] Szameit, A. et al. Polychromatic dynamic localization in curved photonic lattices. Nat. Phys. 5, 271-275 (2009). doi: 10.1038/nphys1221
[48] Wang, K. et al. Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion. Light Sci. Appl. 9, 132 (2020). doi: 10.1038/s41377-020-0299-7
[49] Hu, Y. W. et al. Realization of high-dimensional frequency crystals in electro-optic microcombs. Optica 7, 1189-1194 (2020). doi: 10.1364/OPTICA.395114
[50] Li, Q., Davanço, M. & Srinivasan, K. Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics. Nat. Photonics 10, 406-414 (2016). doi: 10.1038/nphoton.2016.64
[51] Zaske, S. et al. Visible-to-telecom quantum frequency conversion of light from a single quantum emitter. Phys. Rev. Lett. 109, 147404 (2012). doi: 10.1103/PhysRevLett.109.147404
[52] Wimmer, M. et al. Observation of optical solitons in PT-symmetric lattices. Nat. Commun. 6, 7782 (2015). doi: 10.1038/ncomms8782
[53] Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167-171 (2012). doi: 10.1038/nature11298
[54] Weidemann, S. et al. Topological funneling of light. Science 368, 311-314 (2020). doi: 10.1126/science.aaz8727