A Study On Modal Decomposition And Propagation Properties Of Partially Coherent Beams

Recently,the modal decomposition,characterization and propagation of partially coherent beams are topics of considerable interest.The partially coherent sources could produce the same far-field intensity distribution as a laser.Moreover,the partially coherent beams are demonstrated to have advantage over the spatially completely coherent beams.Two typical examples of the partially coherent beams are Gaussian Schell-model(GSM)beams and partially coherent modified Bessel-Gauss beams.Laser beams generated from high-power lasers usually result in a complex mufti-mode structure and possess partial coherence because of the high gain,large aperture,amplification of spontaneous emission,nonlinear optical effects,diffraction of cavity mirror,as well as the variation of laser control parameters.It would be of important significance to study the laser mode decomposition,beam characterization, beam propagation and beam quality control.The goal of this thesis is to study the mode decomposition,the propagation properties,and the M² factor of the partially coherent beams.The main results obtained in this thesis can be summarized as follow:1.By using the Fouriert tansform method,the cosh-Gaussian beam has been coherent and incoherent decomposed,the weight factor of cosh-Gaussian beam has been derived and calculated.The results show:(1)When the modulation parametersδis small,the interference of adjacent modes is not significant,we can have a relatively easy non-coherent decomposition by ignoring the interference between adjacent modes.(2)When the modulation parametersδis gradually increasing,the interference between adjacent lower-order modes is become significant,the results of non-coherent decomposition have a greater deviation with the actual situation.(3)When the modulation parametersδis larger,the curve of the weight factor C_2m,2m+2with m has a peak,the interference of the lower-order modes is start smaller and several higher-order modes is become significant.2.With Hermite-Gaussian modes as a normalized orthogonal system,the sinh-Gaussian beam,the sine-Gaussian beam and the cosine-Gaussian beam have been coherent decomposited.By using the Fouriert tansform,the weight factors and M² factors of those beams have been derived and calculated.The results show:(1)sinh-Gaussian beam and the sine-Gaussian beam are composed of odd order Hermite-Gaussian modes,cosh-Gaussian beam and cosine-Gaussian beam are composed of even order Hermite-Gaussian modes. (2)When the modulation parametersδis smaller,cosine and sine type Gaussian beams can mainly been composed of lower-order Hermite-Gaussian modes.(3)When the modulation parametersδis larger,the weight factor of the lower-order modes is starting smaller,at the same time,the weight factor of several higher-order modes is become significant.(4)With increasing of the modulation parameters,the number of Hermite-Gaussian modes has also increased.(5)The M² factor is the non-linear growth function of the modulation parameters,the quality of the beam is decided by the modulation parameters.3.Based on the modular decomposition theory of partially coherent light,a new class of partially coherent Gauss beams has a variable parameter of the spatial coherence degree is introduced.By using the propagation law of partially coherent beams,the analytical propagation equation of the partially coherent Gauss beams through a paraxial optical ABCD system is derived. Furthermore,by using the intensity moments method,the important characteristic parameters,including the beam width,far-field divergence angle, M² factor of partially coherent beams,are expressed in a simple form.Finally a new class of partially coherent elliptic Gauss beams is introduced.By using the propagation law of partially coherent beams,the analytical propagation equation of the partially coherent elliptic Gauss beams through a paraxial optical ABCD system is derived.Results show that the shape of such partially coherent beams is not changed.Furthermore,the intensity distribution and the important characteristic parameters have been analysised extensively.