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Abstract 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. 

Lithium niobate (LN), an outstanding and versatile material, has influenced our daily life for decades—from enabling high-speed optical communications that form the backbone of the Internet to realizing radio-frequency filtering used in our cell phones. This half-century-old material is currently embracing a revolution in thin-film LN integrated photonics. The successes of manufacturing wafer-scale, high-quality thin films of LN-on-insulator (LNOI) and breakthroughs in nanofabrication techniques have made high-performance integrated nanophotonic components possible. With rapid development in the past few years, some of these thin-film LN devices, such as optical modulators and nonlinear wavelength converters, have already outperformed their legacy counterparts realized in bulk LN crystals. Furthermore, the nanophotonic integration has enabled ultra-low-loss resonators in LN, which has unlocked many novel applications such as optical frequency combs and quantum transducers. In this review, we cover—from basic principles to the state of the art—the diverse aspects of integrated thin-film LN photonics, including the materials, basic passive components, and various active devices based on electro-optics, all-optical nonlinearities, and acousto-optics. We also identify challenges that this platform is currently facing and point out future opportunities. The field of integrated LNOI photonics is advancing rapidly and poised to make critical impacts on a broad range of applications in communication, signal processing, and quantum information.