@article{oai:repo.qst.go.jp:00080273, author = {Moon Jeong, Tae and Bulanov, Sergey and V. Sasorov, Pavel and Korn, Georg and Kevin Koga, James and S. Bulanov, Stepan and Bulanov, Sergey and Kevin Koga, James}, journal = {Physical Review A}, month = {Aug}, note = {The scattering of high-power probe laser pulses by tightly focused ultra-strong laser pulses has been investigated through a semi-classical approach using a perturbative method based on the Born approximation. Under a 4π-spherically-focused ultra-strong light field, the electric permittivity and magnetic permeability tensors for vacuum are calculated from the Euler-Heisenberg Lagrangian to show the nonlinear birefringent property of vacuum. And, from permittivity and permeability tensors, the scattering potential is derived for the Born approximation. The first-order solution of the Born approximation is taken as an electric field scattered from the 4π-spherically-focused laser pulse when a probe laser pulse propagates through the focused laser field. The differential cross section of the nonlinear birefringent vacuum is derived, and the number of photons scattered from the nonlinear birefringent vacuum is analyzed in the laser power range of 10 - 1000 PW.}, pages = {023504-1--023504-14}, title = {Photon scattering by a 4 π -spherically-focused ultrastrong electromagnetic wave}, volume = {102}, year = {2020} }