1. Going beyond solving the E-H framework of Maxwell’s equations, as part of this project we developed the vector potential-scalar potential (A-Phi) framework of Maxwell’s equations and corresponding numerical techniques, which allows for simple, accurate, and seamless connections to quantum physics.
2. Going beyond the electric-dipole approximation, rotating-wave approximation, and no back-action approximation in the traditional quantum optics theory, we solved self-consistently and rigorously the coupled A-Phi equations for EM and optical Bloch equation for QM. The spatial and temporal multiscale issues were also overcome by newly proposed numerical schemes.
3. Going beyond the gauge invariance in EM theory, we numerically demonstrated the gauge invariance in arbitrary inhomogeneous EM environment.
4. Regarding the impact of the project, due to the research experience gained in the UK and research work on quantum EM, Dr. Sha has got the opportunity to become Associate Editor of IEEE Access journal (impact factor larger than 4), also secured a highly competitive National Science Foundation of China fund, and got an Assistant Professor position at Zhejiang University (one of top 5 universities in China). Also, the developed solver can be used by the academic community, enterprises, and institutions in Europe and worldwide, which will strengthen and advance Europe’s leading positions in nonlinear optics, low-dimensional materials, quantum physics, and related disciplines. The fellowship also opens up a new and exciting way to initiate collaborations between Dr Sha’s university/group and universities/groups in Europe, which contributed to his engagement visits and conference attendances.