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Electron-positron pair production in spatial inhomogeneous electric fields with sinusoidal phase modu lation is studied within the Dirac-Heisenberg-Wigner formalism. The focus is on discussing the effects of the modulation parameters on the momentum spectrum and the reduced particle number at various spatial scales. For the momentum spectrum, the interference effect becomes more and more remarkable with the increase of modulated amplitude or frequency, while the symmetry is severely destroyed with modulated amplitude. For the reduced particle number, it is greatly enhanced at about a few times and evenly one order of magnitude when modulation parameters are applied. Moreover, the effect of spatial scales on the reduced particle number are carefully examined and found that it increases rapidly at small spatial scales, while it tends to be a constant at large spatial scales. Importantly, two interesting results are revealed for the reduced particle number. One is for the more reduced pair number production which can be achieved at small spatial scales. The other is for the optimal pair production that can be achieved through different modulations. These results can provide a possibility for realizing the optimal pair production by combining the advantages of field spatial inhomogeneity with different choice of phase modulation.

Vortices in multiphoton pair production are revisited by two counter-rotating fields with time delay for different cycles in pulse. Novel findings include that for subcycle fields, the remarkable vortex structure in the momentum spectrum can be still caused by a large time delay compared to the previous study for supercycle case where it is easier to be generated by a small time delay. And also there exist a range of critical polarization values for the vortices appearance corresponding to the different cycle number. The relative phase difference between two fields causes not only severe symmetry breaking of the momentum spectra pattern and vortex, but also a significant change for the shape and the number of vortex spiral. Upon the number density, it is found a more sensitive to the cycle number, in particularly, it is enhanced by more than one order of magnitude for small cycle pulse, while it is increased about few times when the time delay is small. These results provide an abundant theoretical testbed for the possible experimental observation on the multiphoton pair production in future. Meanwhile, it is applicable to regard the particles momentum signatures as a new probing to the laser field information with it from the vacuum.