A Study On Propagation Properties Of Partially Coherent Beams

Recently, the 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. A typical example of the partially coherent beams is Gaussian Schell-model(GSM) beam, which has been studied extensively. Both the intensity distribution and the complex degree of coherence of the GSM beam are Gaussian distribution. This thesis introduces additional partially coherent beam models, which are partially coherent modified Bessel-Gaussian beams(MBGB) and J₀ -correlated Schell-model (JSM) beams. The basic theories and analytical methods for the beam transformation are also introduced. In practical applications, the effect of aperture diffraction on beams is not able to neglected because the aperture confines the propagation of laser beams, the study of propagation and transformation of partially coherent MBGB and JSM beams with an aperture is necessary. However, it is well known that the paraxial approximation is no longer valid for the beams with large divergence angle or small spot size comparable with the wavelength. With the advent of diode lasers, photonic crystal, micro-apparatus and micro-cavities etc., considerable interest has been paid to the propagation of the partially coherent beams in nonparaxial domain. It would be of important significance to study nonparaxial properties of partially coherent MBGB and JSM beams. The main works of the thesis are as follows:1. The propagation properties of partially coherent MBGB and JSM beams passing through a paraxial ABCD optical system with hard-edge aperture are studied. By means of expanding a hard-edged aperture function into a finite sum of complex Gaussian functions, the approximate analytical formulas are derived. As an application example, numerical calculations are performed for partially coherent MBGB propagating in free space with hard-edge aperture. The computation errors and application ranges of those analytical formulas are discussed. It is shown that the method provides the advantage of reduction of computing time and analyzing the propagation properties of partially coherent MBGB through the apertured optical systems. The influences of Fressnel number and truncation parameter on the intensity distributions are investigated. In addition, the focusing properties of JSM beams through a thin lens system with circle-aperture are analyzed and discussed. Numerical calculation results show that the relative focal shifts of focused JSM beams depend on Fressnel number and truncation parameter.2. By using the generalized Rayleigh diffraction integral formulation and theory of partially coherent light, the analytical propagation equations for nonparaxial partially coherent MBGB of any order and nonparaxial JSM beams in free space are derived. The far-field expression of nonparaxial partially coherent MBGB and the propagation equation of paraxial partially coherent MBGB are presented as special cases of nonparaxial partially coherent MBGB. Numerical calculations and analysis show that, the f parameter plays an important role in determining the beam nonparaxiality, whereas the spectral degree of coherence additionally affects the nonparaxial behavior of partially coherent MBGB. For nonparaxial JSM beams, the analytical propagation equations under the far-field and paraxial approximation, as well as the closed-form expression of the phase are presented as special cases. It is found that the f parameter and the f_βparameter play important roles in determining the nonparaxial behavior of JSM beams. Besides, the f parameter also affects the phase distribution of nonparaxial JSM beams.3. Usually, the focal point of focused beam is determined by the axial maximum irradiance. When the on-axis irradiance is zero, an encircle-power criterion is introduced to define the focal plane. Furthermore, owing to non-planar waveguide, the focal point is not located at the position of the focal plane. Starting from practical applications and the concentrative degree of energy, the real focal plane is equal to the plane of beam waist(the minimum plane of beam width). As an application example, the focal plane and the position of the plane in cosine-Gaussian beams are analyzed and discussed. Based on the field distributing expression for cosine-Gaussian beams passing through a thin lens system, the analytical formula for the beam width of the focused cosine-Gaussian beam is derived using the second-order moment definition. Both waist width and the position of the waist are obtained. The closed-form expression for the relative focal shift of the focused cosine-Gaussian beam is presented. The dependence of the real focal plane position for the focused cosine-Gaussian beam on optical system parameters and beam parameters are analyzed and illustrated with numerical examples.