Phase fields in momentum space of photonic crystal slabs
Optical phase modulation is of great significant importance in fields such as optical communication, information processing, and precision measurement. Compared with real-space modulation, momentum-space phase modulation has distinct advantages: it is free from structural center constraints, supports unlimited mode capacity, and possesses intrinsic topological protection. This inherent flexibility and scalability allow practical applications systems to operate without stringent optical alignment while providing a large number of independent control channels, thereby advancing the development of high-performance, highly integrated optical systems. Photonic crystal slabs, with their open boundary periodicity and capabilities for momentum-space optical field manipulation, have become a crucial platform for research on momentum-space phase fields. Based on polarization orthogonal decomposition and the scattering matrix within temporal coupled-mode theory, this paper systematically elucidates the generation mechanisms of both two-dimensional momentum-space phase fields, including phase vortices, phase gradients, and phase difference, and multidimensional synthetic momentum-space phase fields in photonic crystal slabs, and reviews recent research and application progress in this area. Finally, the development status, advantages, and possible breakthroughs in the field of momentum-space phase fields are summarized and prospects for future work are discussed.