Partially Coherent Beam Focusing Characteristics Of The Study

Since the invention of laser, the property of transmission and focusing of spatially completely coherent beam has extensively been studied. Recently, many investigators turn to study the characteristics of focusing of the partially coherent beams, because high power laser beam with the multi-transverse mode can theoretically be described by partially coherent beams. Moreover, the partially coherent beams are superior to spatially completely coherent beams in practical applications. For example, partially coherent beams are not sensitive to speckle and they are less influenced by turbulence than the spatially completely coherent beams when they are propagating in the atmosphere. Recently, partially coherent vortex beams as a new family of laser beams with many predominant properties have triggered a lot of interests. This kind of beams does not only possess the properties of general partially coherent light but also have its own capability. It has been shown that the beams with vortices can be used to, e.g., trap and rotate particles, for sensitive detection of light and create optical waveguides in nonlinear media. In addition, the orbital angular momentum (OAM) of optical vortex beams states can be used to construct a high-dimensional Hilbert space, which implies higher data density in applying in data storage. Consequently, we can find that it is meaningful for us to investigate such kind of laser beams for their propagation and focusing characteristics. According to above statement, this dissertation can be organized by three parts: In detail, my research work is listed as follows:1. Base on the propagation equation of partially coherent beams, the focusing properties of partially coherent beams, whose intensity distribution is Gaussian, and spatial coherence function is of Bessel function of order zero have been investigated. The research results show that,the intensity distribution in the neighborhood of the geometrical focus is not only dependent on the intensity distribution of the incident partially coherent beam, but also on its spatial coherence. Moreover, we achieve flattened intensity profile or bottle beams near geometrical focus by adjusting the value of focal length and coherent length of the incident light beams2. Based on Huygens-Fresnel principle, we derive the propagation expressions of a lens axicon illuminated by polychromatic Gaussian beams. A numerical calculation and physical analysis is performed to investigate the axial and lateral intensity distribution of the focal segment. In comparison with the monochromatic Gaussian beam, how does the half-with value of the polychromatic Gaussian beams affect the distribution of the axial intensity and the lateral intensity is also discussed in detail.3. According to cross-spectral density function of the partially coherent beam, both backward-type and forward-type lens axicons illuminated by a Gaussian Schell- Model (GSM) beam are studied. We study the influence of the spatial coherence and beam radii of incident GSM beam and aberration of the focusing lens on the axial intensity distribution in diffraction field.4. Based on the generalized Huygens-Fresnel diffraction integral (Collins formula), we study the intensity distribution of the Gaussian Schell-model (GSM) beam diffracted by a spiral phase plate (SPP) with arbitrary integer singularity of order n. The free space propagation properties of such partially coherent optical vortex beam are investigated theoretically.5. By using of the classical Debye theory and Debye approximation, we derive the expressions of the field distribution in focusing of high numerical aperture cylindrical vector beams with optical vortices. The effects of topological charge n and numerical aperture (NA) on the intensity distribution of the focal region in the systems of high numerical-aperture are discussed in detail.6. According to the classical Debye theory and Debye approximation, we study the partially coherent vortex beam focused by a high numerical aperture objective. A lot of attentions are paid to discuss how the topological charge n and the spatial coherence of incident partially coherent vortex beam affect the intensity distribution and the coherence distribution of the focal region.