| The coherence properties of the optical source determine the behaviors of the radiation field including propagating,scattering and focusing.Since it is possible to actively control the coherent state,it provides a powerful tool for optical field manipulations.This has extremely important applications in the fields of optical imaging,optical trapping and optical communication,as partially coherent fields with structured complex coherence states can meet the needs of different applications.Previous research on complex coherent states has mainly focused on the magnitude of the complex degree of coherence and its conventional phase structure,and the lack of unconventional complex coherent states limits further research.On the other hand,one of the most intriguing concepts in the coherence theory is the twist phase,which cannot exist in the limit of full coherence and is served as a unique concept in coherence theory.Yet,we still know very little about the twist phase,further investigation into the unconventional structure of the complex coherence state and the physical mechanism of its optical field can,therefore,deepen our understanding of the complex coherence state.In the context of the above research,this dissertation focuses on optical fields with unconventional complex coherence states.First,we investigate the propagation properties of Gaussian array structure carrying twist phase.This is followed by a study of unconventional complex coherent states carrying astigmatism phase and generalized nonseparable phase,the physical properties of these beams and the orbital angular momentum of the light are discussed in detail.Finally,the concept of a class of optically coherent lattices is proposed,which can generate a perfect optical lattice structure in the far-field.The chapters of the dissertation are arranged as follows:Chapter 1 introduces the research background,history and recent progress of the complex coherence state of light.Then,the fundamental knowledge involved in this dissertation is introduced,which includes six aspects:the theoretical description of the coherence theory of the optical field in the space-time and spatial-frequency domains,the coherent modes decomposition,the generalized diffraction integral,the twisted Gaussian Schell mode correlation structure,the orbital angular momentum of the light and the experimental generation of partially coherent beams with unconventional complex coherence state.In Chapter 2,a new class of twisted partially coherent beams,called twisted Gaussian-Schell model array beams,is proposed and their physical realizability is demonstrated.General analytical expressions for the propagation of such beams are derived,which allows us to study the statistical properties of the new class of twisted partially coherent beams in detail.Further,we quantify the twist effect of such beams.Chapter 3 studies the existence of a class of partially coherent light fields with controllable rotating properties,whose complex coherence states are introduced from the nonnegative definition.The underlying physics of these beams and the unique rotating effects they exhibit are investigated in detail.Our findings are further compared to those of twisted Gaussian Schell mode beams,the nature of these beams with a strong and a weak twist as well as anomalous twist effects are also discussed.Chapter 4 studies a general class of partially coherent beams and brings into evidence the countless nonseparable phases.These beams carry high-order nonseparable phase with respect to two spatial positions and exist only in the case of partial coherence due to the nonnegative definition.This distinguishes them from the conventional concept of phase terms.We discuss and reveal the physical properties of beams carrying generalized nonseparable phases,including the specular symmetry as well as the orbital angular momentum of light.Further,we highlight our general results with a specific example:a non-uniformly correlated partially coherent beam carrying quartic nonseparable phase.We illustrate in detail the underlying physics and propagation dynamics of such beam and discuss the interplay between the magnitude and the phase of the source complex coherence state.Chapter 5 investigates the coherence state structure of a partially coherent light field that produces a stable optical grid in the far-field,the analytical expressions for the beam condition,the beam quality factor and the propagating cross-spectral density function are derived.Further,in order to achieve a fully controllable periodic structure of the optical field,we present the concept of perfect optical coherence grids by the use of convolution operations.Chapter 6 is a concluding section,which outlines the main work and innovations of this dissertation,this is followed by a discussion of the outlook for future work. |
