Study On Self-image Effect Of Bionic Fractal Grating

Grating is a general term for a periodic structure,and Talbot effect of grating refers to the self imaging effect appearing at the specific distance from the grating illuminated by a monochromatic plane wave.Since Talbot first proposed the Talbot effect more than one hundred years ago,as an important optical diffraction phenomenon,Talbot effect has been widely studied in many fields,such as phase holography,spatial filtering and Talbot array illumination,nonlinear optics,information coding,and so on.With respect to the periodic structure,fractal refers to the structure of long-term order and short-range disorder.The fractal structure has the special properties of self-similarity and scale-invariance,and the fractal also extends into many different fields,such as architecture,materials,statistics and physics.Recently,combining the grating and the fractal,fractal gratings has become one of the hot spot of the optical information processing because they have both the properties of grating and fractal.It is well known that the fractal structure is common around us.For example,the eye of an insect is characterized by a fractal structure,which shows the optical laws of parallel imaging,precise positioning and polarization sensitivity in the imaging process.In this thesis,based on the bionic fractal grating structure,the imaging effect of curved grating,fractal grating and curved fractal grating is studied.The similarities and differences between the Talbot imaging rules of bionic fractal grating and traditional grating Talbot effect are explored through systematic research.In view of the complexity of fractal representation,the design method of bionic fractal grating is put forward,and then the general law of diffraction of bionic fractal grating is analyzed by using diffraction theory.The fractal grating is designed and fabricated smartly,and the physical theory of its self imaging effect is explored.The content of this paper is arranged as follows:The first chapter is the introduction of this thesis.In this section,the optical diffraction,periodic grating and the diffraction characteristics of periodic grating are introduced,especially,the diffraction self-imaging effect of periodic grating is analyzed in detail.The concept of fractal,the common fractal structure and the mathematical description of fractal are also presented.In recent years,the studies about the fractal grating and its diffraction self-image are summarized.Finally,the exploration about the insect's eyes predicts the importance of the diffraction of the bionic fractal grating,and this is the reason for proposing the study of this thesis about the self-imaging effect of bionic fractal grating.In the second chapter of this thesis,the diffraction theory used in the study about the Talbot effect of grating is analyzed.According to the propagation distance from the observation plane to the grating plane,the diffraction can be divided into near-field diffraction,deep Fresnel diffraction,Fresnel diffraction and Fraunhofer diffraction.The last three diffractions are the scalar diffraction.The common Talbot effect of grating appears in the Fresnel diffraction region,so the scalar diffraction theory can be used to analyze it.Because of the periodic characteristic of grating,its mathematical expression can be expressed as a Fourier series,which provides the convenience for analyzing Talbot effect of grating.Based on these theoretical bases,Talbot effect of common periodic grating is derived,which lays a good foundation for exploring the Talbot effect of bionic fractal gratings.In the third chapter of this thesis,the self-imaging of two-dimensional grating with controllable size is studied.In view of the traditional self-imaging of grating can only obtain equivalent and reduced image.The way to get a magnified image is the utilization of a point light source or a curved grating.In this thesis,we propose a size adjustable Talbot image of grating based on the combination of a lens and a curved grating.In the experiment,the lens and the grating are inserted in the curved groove to form the magnified,equivalent and reduced Talbot image at different propagation distances.In order to verify the experimental results more intuitively,the same grating parameters are chosen to simulate,and the simulated results verify the experiment.Moreover,Fraunhofer diffraction of the curved grating with different opening ratios obtained on the focal plane of the lens is simulated,and the distribution of the diffracted Talbot carpet is obtained,and magnified,equivalent and reduced Talbot image of the grating are also generated in this far-field region.The size controllableself imaging of grating is helpful for the applications of the Talbot image in optical interconnection and optical lithography.In the fourth chapter of this thesis,the size controlled Talbot image of the bionic fractal grating is studied.The bionic fractal grating refers to the fractal grating on the curved surface.Based on the research foundation of the third chapter,the fractal grating is inserted into the curved surface groove to form a bionic fractal grating structure.The bionic fractal grating and the lens are combined to obtain the size controllable self-imaging of the grating.Theoretically,based on Fresnel diffraction theory,Fresnel diffraction field of the bionic fractal grating is derived,and the mathematical expression gives the dependence of the Talbot image with the curvature of grating,the focal length of lens,the distance between grating and lens.It provides a theoretical basis for obtaining the size controllable self-image of the grating.The results of numerical simulation confirm the existence of the bionic fractal grating Talbot image.The magnification,equivalent and reduced self imaging of fractal grating presented in Fresnel diffraction region provides favorable conditions for the wide applications of grating Talbot effect.The fifth chapter of this thesis gives a summary.In this section,we not only expound the innovation,but also explain the shortcomings of this thesis.Meanwhile,we look forward to the future work based on the present research situation.