Objective Ultrashort pulses, with a pulse duration of tens of picoseconds (10-12 ps) or less, are timing tools with the highest precision available currently. Their narrow pulse width and high peak power characteristics have considerably advanced the development of nonlinear optics. However, ultrashort pulse lasers unavoidably suffer from the dispersion introduced by various optical elements during their operation, resulting in pulse deformation and power attenuation, which adversely affect the performance of ultrashort pulses. Therefore, extensive research has been conducted on pulse width regulation. The current solution is primarily based on the utilization of dispersion- compensation devices, which suffer from low integration characteristics and nonactive regulation. Recently, the optical Moire structure has become a widely discussed topic due to its high potential in the modulation of light field by changing Moire angles. However, most published works introduce physical twisted angles, and optical Moire structures combined with the concept of synthetic dimensions have rarely been reported. Therefore, we propose an optical Moire lattice with artificially synthesized Moire angles to achieve ultrashort pulse width modulation. Methods A method of constructing optical Moire lattices with artificially synthesized Moire angles (nonphysical twisted angles) is proposed herein. Moire lattices comprise two simple photonic lattices with different periods, and the ratio of the arctangents of their periods represents the Moire angle of the optical Moire lattice. Three optical Moire lattices with gradually increasing Moire angles are theoretically designed, and the band structure of the optical Moire lattices is determined by the transfer matrix method; we observe that the increase in Moire angles leads to the flattening of the band structure. The band dispersion is further analyzed, following which the group velocity and pulse width changes introduced by an ultrashort pulse through the Moire lattices are computed. The theoretical calculations demonstrate the effect of Moire lattices on the width of ultrashort pulses. Subsequently, an optical path based on an autocorrelator is built to experimentally verify the theoretical results. Further, we define the variation rate of pulse width to effectively illustrate the modulation of ultrashort pulses. Results and Discussions First, the effects of artificially synthesized Moire angles on the band structure are analyzed: the increase in the Moire angles results in higher band compression coefficients ( Fig. 2), which indicates a decrease in the bandwidth (Fig. 3). Meanwhile, a narrow band leads to a decreased group velocity ( Fig. 4) and considerable second- and third-order group velocity dispersion (Fig. 5). We demonstrate a theoretical model to explain the effect of group velocity dispersion on the width of ultrashort pulses (Equations 3- 8). The equations imply that Moire lattices with high group velocity dispersion lead to intense pulse broadening and pulse compression of ultrashort pulses. The results of pulse width measurements before and after passing through the three Moire lattices were obtained using the autocorrelator (Table 1). As seen from Table 1, the variation in pulse width increases with the increase in the Moire angle. The accurate modulation of the ultrashort pulse width by the optical Moire lattice is confirmed by the comparison of the theoretical and experimental values of the pulse width ratio (Fig. 7). Conclusions The construction method for the optical Moire lattices in the synthetic space proposed herein can effectively realize the analogy of traditional optical Moire lattices with physical twisted angles. The regularity of the artificially synthesized Moire angles affecting band structures has been clearly confirmed. Theoretical calculations show the following: a larger artificially synthesized Moire angle leads to lower group velocity and more considerable second- and third-order group velocity dispersion, which results in larger variations in pulse widths. Moreover, the accurate modulation achieved by the optical Moire lattice indicates that the lattices can be predesigned to satisfy universal requirements such as a wide range of pulse width adjustments. In theory, we can design a series of Moire lattices with different artificially synthesized Moire angles, resulting in rich and more predictable pulse width variations. In summary, first, we state that the optical Moire lattice in the synthetic dimension considerably simplifies the complexity of structural processing: traditional optical Moire lattices require precise control of the physical twisted angles of the two sublattices, while the optical Moire lattice in the synthetic space depends on strategic parameter definitions. The one-dimensional structure in the geometric space renders its processing highly convenient. Second, the optical Moire lattice provides a new degree of light field modulation, which means that a flattened band structure can be obtained by changing the Moire angle. Finally, the overall thickness of our optical Moire lattice is at the micrometer level, which has the advantage of high integration. Our structure can become the key component in the manufacturing of laser pulse width compressors.
