Study On Light Scattering Of X-ray Laser And Ultra-intensive Laser

In classical vacuum,photons cannot interact with each other as Maxwell's equation is linear,which means different beam propagates independently and couldn't interact with each other.However,according to the theory of quantum electrodynamics(QED),vacuum is full of quantum fluctuation,giving rise to a large amount of non-linear processes,and photons can scatter with each other through the interchange of virtual particles.When the strength of electromagnetic field is much smaller than Schwinger critical field,effective field theory allows for a semi-classical treatment of photon-photon scattering,with the nonlinear correction to Maxwell's equations in vacuum,.Photon-photon scattering is an important phenomena for QED.However,it hasn't been observed directly in laboratory,because the cross section of this process is very small.Here we investigate the scenario of head-on colliding between an optical laser pump and a x-ray free electron laser(XFEL)probe,where the effects of spatial-temporal envelops,polarization state and incident angle of two beams are considered.To detect the signal,we investigate vacuum diffraction,vacuum birefringence and four-wave mixing,corresponding to the effect on probe photon's wavevector,polarization and frequency.In vacuum diffraction effect,when the optical laser has larger waist than XFEL probe,scattering photon could have the wider angular distribution than XFEL probe.In this way,the polarized vacuum could be viewed as diffracting the probe.In previous study,the spatial envelop of probe is usually ignored.Here,we consider its effect and find that the scattering photon number can be greatly enhanced when the XFEL is composed of different Laguerre-Gaussian modes.As an example,with SHINE's setup there will be 185 photons separable from the XFEL background for each shot,which is 2.5 times of the case with usual Gaussian profile.Furthermore,we consider the orthogonal relation of different mode basis,including the effect of incident angle and off-axis parameter.Vacuum birefringence refers to the change of beam's polarization state after passing through a strong and slow-varying background field.Here we recalculate this process with the startpoint of scattering wave.With this method we can get 190 photons with different polarization direction from XFEL probe,which is similar with the result from the startpoint of refractive index.On the photon lever,four-wave mixing can be understood as two photons being scattered into two photons,one being back to the background field and the other corresponding to scattering wave with different frequency and propagation direction can be generated.Usually,the phase match condition can't be satisfied for the case of just two beams,where two photons are provided by the same pump.Here,we show that detectable number of scattering photon could still be generated based on the uncertainty relationship of the interaction region.For the scattering process of the absorption accompanied by the emission(and vice versa)of pump photons for a probe photon,scattering wave's frequency could vary in the range of optical laser's temporal length and Rayleigh length,which could be separated from the probe if the latter is monochromatic enough.For the scattering process of the absorption two pump photons for a probe photon,it can be realized with the uncertainty relationship of interaction region.When using XFEL with quasi-plane envelop we can get 5 photons in the oblique direction.The advantage of this method is the signal can be separated from XFEL probe both in frequency and scattering angle.Finally,we propose the method of enhancing vacuum polarization signal with the flying focus pump laser.For vacuum diffraction and birefringence effect,flying focus with phase velocity-c greatly increase the interaction length and we can get thousands of scattering photons for large enough optical laser's temporal length.For four-wave mixing,the bandwidth of signal generated by flying focus pump laser with phase velocity-c could be much wider than the case of traditional Gaussian beam,not limited by the temporal length of pump laser.Furthermore,the scattering process of the absorption or emission two pump photons for a probe photon can be realized by flying focus pump laser with phase velocity close to c.