Research About The Intensity And Spectrum Property Of Laser Beams In Fractional Fourier Transform Systems

Fractional Fourier Transform is regarded as the development and extension of traditional Fourier transform, except for the characteristic of traditional Fourier transforms, it also has its own advantages. It provides a more convenient tool to study the characteristic of propagation and transformation for beams. Researches on the transmission of beam in fractional Fourier transform system have important significance in beam sharping and beam quality control. And the study on the spectrum property of beam in chromatics aberrated fractional Fourier transform system has important reference value in experimental observation of fractional Fourier transform for beams, spectral switch and it application in optics interconnect and optics communication. This thesis mainly studies the intensity and spectrum property of beams in fractional Fourier transform system.The mainly work of this thesis are arranged as follows:1. Analyzed the intensity characteristic of Hermite-Laguerre-Gaussian beam in fractional Fourier transform system based on Collins integral formula. It is shown that the intensity distribution on output plane changed with fractional Fourier transform order, the beam modulus index and the beam parameterα, the variation period of intensity distribution with fractional Fourier order is 2.2. Based on Collins integral formula and the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of Cosh-squared-Gaussian beam passing through ideal and apertured fractional Fourier transform systems have been studied. It is shown that the simulation results obtained by using the approximate analytical formula are coincide with those by using the numerical integral calculation quite well. Further, the variations of normalized intensity distributions with fractional Fourier transform order is periodic: while the impact of aperture can not be ignored, the variation period is 4; while the impact of aperture can be ignored, the variation period is 2.3. Discussed the spectrum property of partially coherent Gaussian beam in chromatics aberrated fractional Fourier transform system. The researches explicit indicate that the fractional Fourier transform order has great effect on the normalized spectrum and relative spectral shift. The relative spectral shift changed with the fractional Fourier transform order, and the chromatic aberration coefficient affect the critical fractional Fourier transform order (at which the spectral switch taking place) and the magnitude of the spectral jump. The relative spectral shift changed with chromatics aberration as well, and the variation changed with fractional Fourier transform order as well. Furthermore, in chromatic aberrated fractional Fourier transform systems, whether Lohmann I system equivalent to Lohmann II system or not depending a lot on the fractional Fourier transform order.4. The spectrum of partially coherent Hermite-Gaussian beam in fractional Fourier transform system with chromatics aberration has been studied. It is shown that the fractional Fourier transform order, chromatics aberration coefficient and beam order has significance influence on the normalized on-axis and off-axis spectrum. The relative off-axis spectral shift changed with fractional Fourier transform order, and the chromatics coefficient and beam order affect the variation. The relative off-axis spectral shift changed with the chromatics aberration coefficient as well and the variation curves are different when the fractional Fourier transforms order or beam order vary.