The Theoretic And Experimental Studies About The Diffraction And Talbot Effect Of Grating

Grating is used as one of the most important optical diffraction element which hasbeen widely used in many areas, such as information stored and encoded, the light wavemodulation and the high power laser pulses compression. As the new phenomenon ofgrating diffraction was found and the applications of grating continue to expand, thestudy of grating diffraction has been carried. The transmittance of the grating can beexpressed and the form of a spatial frequency spectrum, when all ingredients are met insome transmission distance,as a result of their superimposed, the self-imaging of thegrating appears, which is called the Talbot effect of the grating, the image of Talbot isfound after the grating with a distant of ZN=2Nd2/λ,(λ is the wavelength of the incidentlight, N is an integer, d is the grating cycle), these special distance ZNcalled Talbotdistance. This effect is used for interference measurement, laser array illumination andlaser phase lock. With the decrease of the grating period, the grating Taber distancedecreases. When the ZN(N is small) is in the deep Fresnel diffraction, the Talbot imageof the grating was called quasi-Talbot image. The grating theory and experimentalmeasurements of Talbot effect is study in this paper.This paper is mainly divided into the following five chapters.The first chapter introduces the definitions, some production methods and theclassification of the grating. The diffraction area of grating is divided in different fourpart. We derive the diffraction intensity formula in the deep Fresnel diffraction on basisof the scalar diffraction theory. But in near-field diffraction, we can not use the scalardiffraction theory, we can only use the vector diffraction theory for theoretical studies.This paper describes one of the vector diffraction theories--Finite Difference TimeDomain method. We also introduce the traditional Talbot effect phenomenon anddiscuss the formation of Talbot effect.The second chapter analyzes the diffraction in the deep Fresnel diffraction regionand derives the formular of the diffraction intensity distribution in this region. Theresults theoretically predicts the quasi-Talbot image of grating. In fact, the diffraction isnot the same to the grating structure in precise Taber distance. While the grating image clearly appears at a distance close to the exact Talbot distance of grating. Throughnumerical simulations, we know the causes for the formation of quasi-Talbot image andpresent the position of the quasi-Talbot image in this diffraction region.Chapter three analyzes the near-field diffraction of high-density grating with thefinite difference time domain method, and compare the diffraction of grating underdifferent polarization illuminations, and discuss the diffraction of grating with differentperiod. We find that the diffraction intensity in near field takes on the geometric effect,the combination of the geometric effect and the diffraction and the diffraction effect asthe propagation distance increases. The near-field diffraction under differentpolarization illumination is different. It indicates the polarization dependence ofnear-field diffraction of grating. The influence of grating period on the near-fielddiffraction is also discussed.Chapter four presents the experimental study about the diffraction of high-densitygrating in deep Fresnel diffraction,. The diffraction intensity of the grating in this regionare detected in experiment by use of the micro-magnify technique. The experimentalsetup is contact and flexible to obtain the magnified diffraction patterns. Theexperimental results verify the exact Talbot image of grating can not appear at the exactTalbot distance. Oppositely, the quasi-Talbot image appears at the nearer distance closeto the exact Talbot distance. These experimental results fit well with our theoreticalresults.Chapter five produce numerically the periodic structures with different shape coresthrough programming, and combine the liquid crystal spatial light modulator to obtainthe amplitude and phase gratings. According to the theoretical formulas, we produce thegrating with different shapes, such as ellipses, rectangles and squares. Adjusting thedirection and position of the polarization plate, the amplitude grating and the phasegrating can be chosen. Two complimentary diffraction of grating at the same positionare obtained. Furthermore, the Talbot image of two periodic structures combined intoone diffraction screen is measured in experiment.