Accelerating superluminal laser focus generated by a long-focal-depth mirror with high numerical aperture

The long-focal-depth mirror is a novel reflective element proposed in recent years. Due to the advantages of negligible dependence on wavelength and high damage threshold, it is suitable to focus ultra-short laser pulses with broadband spectra and high intensity with a focal depth of centimeter scale. To the best of our knowledge, the focusing properties of this mirror has been only studied under low numerical aperture (NA). In this paper, we extend it to the case of high NA and it is proved that an accelerating superluminal laser focus can be always generated by this extension, in which the degree of acceleration increases with the increase of NA. And the velocity of laser focus increases approximately linearly from c to 1.6c for NA=0.707. Due to its properties of tight focusing, the Richards-Wolf integrals have been used to study the intensity distribution of each polarization component for different kinds of incident light. And these are linearly polarized light, radially polarized light, azimuthally polarized light, linearly polarized light with spiral phase, and linearly polarized light with ultrashort pulses. From comparisons of numerical results, the intensity distributions are obviously different for different kind of incident light, and accelerating superluminal laser focus with special structure (such as the hollow conical beam) can be produced under appropriate condition. We believe this study can expand the fields of application for the long-focal-depth mirror