Phase Singularities Of Speckle Fields Produced By The Scattering From Gaussian Correlation Random Surfaces

When the coherent light waves are scattered from the random surfaces or the random media, speckles are formed in the diffraction regions. Measurements and computer simulations have shown that the speckle grains and phase singularities have the same density in the random fields, so there are as many phase singularities as speckle grains in speckle field. The zeros of light intensity are the phase singularities at which the phase of is undefined. Around each singularity the current circulates and then the zeros are also called optical vortices. It exists in various linear and nonlinear physical systems, such as the angular momentum eigenstates of the hydrogen atom, the Meissner state of type-II superconductors, vortex states of superfluids, Bose-Einstein condensates, and optical vortex solitons. Phase singularities are very important and widely used in the optical microcontroller, quantum entanglement, information transmission. Phase singularities in optical fields owing to potential applications have driven a surge of interest in recent years. However, the existing literatures on the zero-contour of the real and imaginary parts of speckle field are intersection situation. As we all know, in fact, due to the complexity of the speckle field, the zero-contour of the real and imaginary parts can be in tangential or superposition situation. Study the characters of phase singularities in random speckle field have leading significance, not only a new task for speckle phase singularities but also for the phenomenon of optical vortex in other areas of physics, and have important applications in related frontier areas of optics and physics.This thesis combining methodologies and the theories in the achievements in such frontier areas of physics as the speckle fields generated by the Gaussian correlation random scattering screen and their phase singularities properties under the illumination of continuous lasers. The phase singularities of speckle fields produced by the scattering from square aperture Gaussian correlation random surfaces in the Fraunhofer plane, the zero-contour of the real and imaginary parts of complex amplitude of speckle fields are tangent and coincidence, at the tangential points and the superposition-lines can also form phase singularities, the speckle fields produced by the square loop aperture and circular ring aperture and their phase singularities, the intensity distribution and phase singularities of speckle fields generated by multi-aperture random scattering screens and the intensity distribution and topological charge singularity of special phase singularities generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region.The results presented in this thesis offer us a better understanding of phase singularities which may result in applications in optical switching, optical data storage, manipulation of micro-particles and optical limiting for eye protection, and the results could help researchers in geology, engineering, and medicine learn about the internal makeup of materials and tissues by studying the so-called speckle pattern in waves that pass through them. The major achievements are summarized as follows:1. The two-dimensional speckle fields and the phase produced by the Gaussian correlation random surfaces on the Fraunhofer plane were simulated. It was found that the zero-contour of the real and imaginary parts can be in the tangent and superposition situations besides the traditional intersection situation. The tangential points and the superposition-lines can also form phase singularities, around which the phase distribution shows the characteristics of discontinuity and symmetry and differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. With the propagation of the optical wave, the relative positions of the zero-contour of the real and imaginary parts change from tangent to superposition, and then to intersection on the different observation plane with the simultaneously changes of the the phase singularities.This result provides an important means to different application requirements in speckle simulation, and provides experimental observation to accurately understand and analyze the reasons of formation of the phase vortex phenomenon.2. The speckle fields and their phase singularities produced respectively by the square loop aperture and circular ring aperture are studied. It is found that the zero-contour of the real and imaginary parts can be in the complex tangent and intersection situations. The complex tangent and intersection points can also form phase singularities, around which the phase distribution shows the characteristics of symmetry and discontinuity, it differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. The speckle particles distribution in the speckle fields produced by the square loop aperture and circular ring aperture differ from those by the traditional square aperture: the speckle particles distribution is modulated by the scattering aperture, respectively in stripes of level or vertical outlines and circular outlines. In addition, an interesting phenomenon occurs: a lot of circle-like dark regions appear in the intensity pattern of the speckle fields, it is called"light intensity dark nucleus", whose center corresponds to a vortex, with homogeneous phase distribution.We study the properties of particular phase vortices of random speckle field is important not only for research on speckle phase vortices but also plays an important role in the frontier area of singular phenomenon in other physical fields.3. The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase patterns produced by the two-pinhole aperture, whose phase distributions appear striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.This result has an important significance in the studies of the essential structures, the new characteristics and new laws of phase vortices, and the new singularity phenomena in the speckle fields. This might also be used in such field as multi-hole interferometer design.4. The diffraction theory of Kirchhoff is applied to the four-pinhole aperture diffraction screens, the intensity, the zero-contour of the real and imaginary parts of complex amplitude and the phase distribution in deep Fresnel diffraction region are simulated, and it is found that the bright spots in interference field show central symmetry distribution. When the observation plane close to the diffraction screen, the zero-value points of light intensity can form line segment, on which the eccentricities of the light intensity isoline are close or equal to 1, the intensity changes very fast on both sides of the zero-line of light intensity. The zero-contours of the real and imaginary parts of complex amplitude are closed curves. The number of intersection points of the zero-contour of the real and imaginary parts is even, and positive and negative singularities are equal. Not only the phase around special phase singularities appears symmetry distribution, but also the topological charges of special phase singularities show singularity phenomena. With the propagation of the optical wave, the line segment of zero-value intensity change shorter and shorter, final to a point.This has an important significance in the studies of the essential structures, the new characteristics and new laws of phase singularities, and the new singularity phenomena. This would be a better understanding of the characteristics of phase singularities in other physical fields.5. The phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by multi-aperture diffraction screens are simulated, and it is found that: when the orbital angular momentum quantum number of incident beam is equal to zero, at the center of interference field zero-lines can not intersect with each other, therefore, where can not form the phase vortices; when the orbital angular momentum quantum number of incident beam are opposite, namely, -1and+1, at the center of interference field zero-lines perpendicular and intersect to each other, the signs of the phase vortices at the corresponding positions in interference fields are opposite too; when the orbital angular momentum quantum number of incident beam is equal to±2 or±3 , there are four zero-lines intersect with alternating distribution at the center of interference fields, where the topological charge values of phase vortices are just equal to the orbital angular momentum quantum number of the Laguerre-Gaussian beams. This method, based on a multipoint interferometer, has its most important application in measuring the orbital angular momentum of light from astronomical sources and vortex laser beams.This paper is divided into six chapters. In first chapter, we propose the first time the theory methods of phase singularities of the random speckle field and description of the phase singularity phenomenon. The history, current status and main developments of phase singularities, the basic concept of the phase singularities in scalar wave field, a number of generating methods about scalar phase singularities in optical fields and the application of phase singularities are summarized. At the same time, we give the concept of phase singularities----phase vortices, the computational method of topological charge and the sign principle of phase singularity of wave field, and the eccentricities of intensity-contours. In chapter 2, by computer simulation, we study the properties of phase singularities at the tangential points and the superposition-lines of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields on the Fraunhofer plane, verify those two types of phase singular phenomenon are not caused by surface roughness, and analyze the mechanism of their formation. In chapter 3, by theory and experiment, we study the properties of phase singularities at the complex tangential intersection situation of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields produced respectively by square loop aperture and circular ring aperture on the Fraunhofer plane, and analyze the mechanism of their formation. At last, we give the causes of"light intensity dark nucleus"and regular arrays of speckle particles distribution. In Chapter 4, we study distribution characteristics of optical intensity and phase vortices of the speckle fields produced by multi-aperture random scattering screens on Fraunhofer plane in detail. In Chapter 5, Based on the diffraction theory of Kirchhoff, the intensity, the special phase singularities and the zero-contour generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region are studied in detail, and we find that the bright spots in diffractive field show central symmetry distribution. The eccentricities of the zero-line of light intensity are rather large, showing that the typical phase structure is strongly anisotropic. The phase around special phase singularities is symmetrical distribution, whose topological charges may appear singularity phenomena. In Chapter 6, Based on numerical calculation, we study the distribution properties of phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by Laguerre-Gaussian beams through multi-aperture diffraction screens.