The Researches On The Talbot Effect Of High-density Gratings

A periodical reappearance of the gratings distribution occurs when the gratings is illuminated by cohenrence source.For a traditional grating with less grooves per mm,the amplitude distribution of the observed plane on the Talbot distance is totally same with that behind the gratings.The scalar diffraction theory gives a perfect interpretation about the phenomenon and the position of those self-imaging plane.For a grating with 2000 grooves per mm,the period of the grating close to the wavelength of incident wave,the scalar diffraction theory does not work efficiently.A rigorous vector diffraction theory need to be applied to solve those problem.The reason why the self-imaging occur and the position of the self-imaging plane was retrieved by the analysis from space domain,frequency domain and space-frequency domain.It's concluded that the wave behind the grating can be seen as a set of plane wave with special frequency,and the transform function has a quadratic complex exponential function form.A rigorous analysis on the high-density gratings applying FDTD method with a CPML boundary condition has been took.It's found that the self-imaging disappear when the period of the gratings less than 2 times wavelength and still remain when more than 2 times wavelength.Another vector diffraction theory applying vector-potential method gives a similar conclusion about the distribution in the diffraction zone.Measurement and array illumination based on the Talbot effct may benefit from this conclusion.A probe wave with a shorter wavelength can measure a more exquisite structure.