Synthetic photonic lattice with temporally controlled potentials is a versatile platform for realizing wave dynamics associated with physical areas of optics and quantum physics. Here, discrete optics in one-dimensionally synthetic photonic lattice is investigated systematically, in which the light behavior is highly similar to those in evanescently coupled one-dimensional discrete waveguides. Such a synthetic dimension is constructed with position-dependent periodic effective gauge fields based on Aharonov-Bohm effect arising from the phase accumulations of the fiber loops. By tuning the phase accumulations and coupling coefficient of the coupler, the band translation and gap property can be modulated which further results in the impulse and tailored Gaussian wave packet responses as well as Talbot recurrences. In addition, Bloch oscillations and Anderson localization can also be obtained when the phase accumulations are linearly changed and weakly modulated in random, respectively. The periodic effective gauge fields configuration in our protocol enables SPL to be a research platform for one-dimensional dynamically modulated elements or even non-Hermitian waveguides.
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