Propagation Properties Of Beams With Random Modulation

The unavoidable defects existing in optical components will influence the beampropagation in the optical system. The research of the effect of the amplitudemodulated defects and phase modulated defects on the intensity distribution of theGaussion beam in the free space and nonlinear medium would has some referencevalue on the avoiding of defects induced damage in the ICF. And the research of thescintillation index properties of the double vortex beams propagating in the turbulenceatmosphere has some value in the development of the optical communication.In this dissertation, the intensity distribution of the Gaussion beam modulated bythe multitude modulated defects and phase modulated defects in the free space，in thenonlinear medium are studied in detail. We also studied the scintillation indexproperties of the double vortex beams propagating in the turbulence atmosphere. Themain research contents are listed as follows:1. The effect of the amplitude modulated defects on the intensity distribution andthe angular spectrum of a Gaussion beam are studied. Based on the Fresnel diffractionintegral and the definition of angular spectrum, we derive the analytical expressionsfor the intensity distribution and angular spectrum of a Gaussian beam modulated byfinite amplitude modulated defects. The influence of the size and the modulationamplitude of the defects on the intensity distribution and angular spectrum of thebeam are also studied. It is shown that the intensity distribution will recover toGaussian distribution after propagating a certain distance. The larger size of defects is,the longer propagation distance for the beam recovering to Gaussian distribution.Furthermore, the angular spectrum of the modulated beam in the low frequency areabecomes smaller and the angular spectrum in the high frequency area becomes greaterwith the increase of the size and the modulation amplitude of the defects.2. We studied the properties of the intensity distribution and the angular spectrumof a Gaussion beam with local phase modulation Based on the generalizedHuygens–Fresnel diffraction integral, the propagation mode of the Gaussion beammodulated by the local phase is built and the analytical expressions for the intensitydistribution and angular spectrum of a Gaussion beam modulated by finite phase modulated defects has been derived. The impact of the modulation by phasemodulated defects is studied. It shows that in the process of transmission theevolution of the light intensity is the same for different modulation depths and sizesof the defects. The deeper of the modulation depth of the defects that modulated thebeam, the higher of the intensity produced along the propagation process. The largerof the defect, the nearer of the proposition where produced the highest intensity fromthe defects location. The angular spectrum in the low frequency area become smallerwhile the angular spectrum in the high frequency area become greater with theincrease of modulation depth and the size of the defect as well as the defect gettingcloser to the middle of the beam.3. Studying the modulation of the amplitude modulated defect on the nonlinearmedium for the beam. Based on the Fresnel diffraction integral and Taylor seriesexpansion, built the model of the beam propagate through the nonlinear mediumwith defect on it, and derive the analytical expressions for the intensity distribution atdifferent distance of a Gaussian beam get through the defective nonlinear medium.The impact of the size of the defect and the additional phase shift in the medium onthe intensity distribution of the beam propagating through the medium is studied. It isshown that the larger of the defect and the more of the additional phase shift in themedium, the deeper the beam been modulated. With the modulation of the defect andthe nonlinear effect in the medium, there would generate a strong intensity near therear surface of the nonlinear medium before the beam covergence or diffusion afterthe beam propagating through the medium with positive and negative nonlinear indexof refraction respectively, and the lager of the phase shift the beam generate in themedium, the stronger the intensity emerge.4. Based on the Fresnel diffraction and split-step Fourier method, has analog studythe two dimensional intensity distribution of the Gaussion beam propagation in thenonlinear medium and the free space. And the intensity distribution of the beampropagation in the medium with defect on it and the free space is also scrutiny studied.It shows that the longer of the medium’s thickness and the lager of the nonlinearindex of refraction, the more of the beam focus and the shorter of the focal positionpart from the medium. The defects on the medium would lead to a strong intensity generate near the rear surface of the medium. And the intensity generated by thephase modulated defects is stronger than the intensity generated by the amplitudemodulated defect.5. We study the scintillation index of a double vortex beam propagating in strongturbulent atmosphere by numerical simulation. It is found that the on-axis scintillationindex of double vortex beams is smaller than that of single vortex beams propagatingin the atmospheric turbulence. Moreover, when the beam propagation distanceexceeds a certain value, the on-axis scintillation indices of double vortex beams aresmaller than that of the Gaussion beam.