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Thin-film lithium niobate (TFLN) is a promising electro-optic (EO) photonics platform with high modulation bandwidth, low drive voltage, and low optical loss. However, EO modulation in TFLN is known to relax on long timescales. Instead, thermo-optic heaters are often used for stable biasing, but heaters incur challenges with cross-talk, high power, and low bandwidth. Here, we characterize the low-frequency (1 mHz to 1 MHz) EO response of TFLN modulators, investigate the root cause of EO relaxation and demonstrate methods to improve bias stability. We show that relaxation-related effects can enhance EO modulation across a frequency band spanning 1kHz to 20kHz in our devices – a counter-intuitive result that can confound measurement of half-wave voltage (V_π) in TFLN modulators. We also show that EO relaxation can be slowed by more than 10⁴-fold through control of the LN-metal interface and annealing, offering progress toward lifetime-stable EO biasing. Such robust EO biasing would enable applications for TFLN devices where cross-talk, power, and bias bandwidth are critical, such as quantum devices, high-density integrated photonics, and communications.

Mirrors are ubiquitous in optics and are used to control the propagation of optical signals in space. Here we propose and demonstrate frequency domain mirrors that provide reflections of the optical energy in a frequency synthetic dimension, using electro-optic modulation. First, we theoretically explore the concept of frequency mirrors with the investigation of propagation loss, and reflectivity in the frequency domain. Next, we explore the mirror formed through polarization mode-splitting in a thin-film lithium niobate micro-resonator. By exciting the Bloch waves of the synthetic frequency crystal with different wave vectors, we show various states formed by the interference between forward propagating and reflected waves. Finally, we expand on this idea, and generate tunable frequency mirrors as well as demonstrate trapped states formed by these mirrors using coupled lithium niobate micro-resonators. The ability to control the flow of light in the frequency domain could enable a wide range of applications, including the study of random walks, boson sampling, frequency comb sources, optical computation, and topological photonics. Furthermore, demonstration of optical elements such as cavities, lasers, and photonic crystals in the frequency domain, may be possible.