Study About The Fresnel Diffraction Of Aperture And Grating With Modulated Edges

As the basic problems of the diffraction optics, more than two hundred years of aperture diffraction studies have never stopped. Up to now, the diffraction by aperture is still as important means to explore the extraordinary phenomena physical mechanisms in optics attract much attention. Through the limit of aperture and diffraction, the energy of the beam can be realized distribution again in space. For this purpose, through design the shape and structure of aperture so as to realize the artificial control of the energy of the beam, this promote the aperture and its diffraction are widely used in the studies of beam shaping, beam coupling and wave-front transformation, etc, becoming the important basis of design and manufacture of the micro-nano device.The grating is the seam or aperture structure of periodic distribution in space, The special periodic array structure presents particular diffraction characteristics, its application appear in various fields, such as, laser pulse compression, optical wave modulation, information coding and information storage, etc, become the important means in pulse compression, wave-front modulation, frequency spectrum analysis, etc. The Talbot effect of grating is the self-imaging phenomenon in the process of diffraction, this diffraction optical phenomenon is applied to the array of lighting, phase locking, optical storage, at the same time, turn into important optical technology methods also in laymen measurement of beam and optical wave-front, the detection of temperature and displacement, etc. With the deepening of the research, the Talbot effect of grating this tradition of diffraction optical phenomenon is extended to the different scientific fields, such as nonlinear optics, atomic optics and quantum optics, etc, promote the development of the cross of different subjects vigorously.Design the structure of aperture to adjust and control the energy of diffraction on the spatial distribution is the primary task in diffraction optical device function design, is the main purpose of the research of optical diffraction also. In the processing of diffraction studies, the diffraction unit edge of aperture and grating is smooth, but in fact, any production technology is difficult to do this. The edge of the actual manufacturing of the aperture and grating is rough in most cases. In view of this, this paper around the aperture and grating of modulated and its Fresnel diffraction to carry out the research, the modulated edges quantitative description are given, the diffraction distribution of aperture and grating with modulated edges have been deduced in theoretical, measured the diffraction pattern of aperture and grating with modulated edges in experiment, explores the evolution rule of the Fresnel diffraction of the aperture and grating with modulated edges. The specific contents are arranged as following:The first chapter is the introduction of this paper, first introduced the basic theory of scalar diffraction, including Huygens principle, Huygens-Fresnel principle, Kirchhoff diffraction theory, Rayleigh-Sommerfeld theory, Fresnel diffraction and Fraunhofer diffraction theory, etc, at the same time, the applicable conditions of these basic diffraction theories are given clear definition. Then, analyzed the research status of aperture and grating diffraction based on these theories, points out the necessity of the research about the diffraction of aperture and grating with modulated edges.Chapter two mainly introduced the generate method of aperture and grating with modulated edges. For the shape of the diffraction aperture is circular and elliptical aperture two types, the modulated edges have sine edges and random edges. The rough edges of aperture of the experiment made satisfy the Gaussian statistical distribution, so, by using the roughness w and the transverse correlation length ? these two parameters to describe in the model of Gaussian statistical. While, the grating edges by using the model of the self-affine fractal statistical distribution by S. K. Sinha puts forward, when the ? is equal to 1, this model is degrade into the model of Gaussian statistical naturally. At this time, by using the roughness w ?the transverse correlation length ? and the roughness exponent ? these three parameters to describe the rough edges of grating. In addition, with the aid of computer programming simulation produced the corresponding edges, obtained the aperture and grating with modulated edges, lay the foundation for the later work to carry out.Chapter three investigates the Fresnel diffraction of aperture with modulated edges by the theoretical calculation, numerical simulation and experimental measurement. In the theoretical, according to the theory of scalar diffraction and the principle of statistical optical deduced the analytic expression of the Fresnel diffraction by circular and elliptical aperture. The numerical simulation of diffraction pattern of aperture with different edges of modulated parameters at different propagation distances are given, compared with the diffraction of circular and elliptical aperture with smooth edges, analyzed the influence of the shape of aperture and edges modulated parameters for the diffraction. With the aid of spatial light modulator to obtain samples of aperture, set up light path, complete the diffraction experimental measurement of aperture with modulated edges. The experiment verified the results of the theoretical calculation and numerical simulation. This research are not only helpful for deepen understanding the diffraction, but also the obtained characteristics of the diffraction pattern can promote its applications in the optical beam shaping and micro manipulation, etc.Chapter four mainly carry out the research of the Fresnel diffraction of grating with modulated edges, based on the second chapter theory, simulation generated the grating with modulated edges, the numerical simulation of diffraction intensity distributions of grating with modulated edges are given, analyzed the rule of evolution of the Talbot imaging of grating with the edges of modulated parameters of grating. In order to explain these phenomenons, with the aid of scalar diffraction and the principle of statistical optical deduced the Fresnel diffraction of grating in theoretical, the diffraction intensity analytic expression of the Fresnel diffraction of grating with modulated edges are given. In experiments, with the aid of liquid crystal light modulator obtain the grating sample, measured the diffraction intensity of grating at different Talbot distances of grating with modulated edges, showing the influence of modulated parameters for the diffraction of grating intuitive. These results for the evaluation of self-imaging of the actual grating diffraction and promoting its application research have certain guiding significance.Chapter five gives the summary of this paper and shows the following work plan combined with the research progress of the current diffraction optics.