Propagation Characteristics For The Broadband Laser Beams Through The Complex Optical Systems

Optical researchers have found that the broadband laser has many advantages over the narrowband laser in the high-power laser driven optical system. The interference and diffraction can be restrained and the output power can be obviously improved and so on. With the development of laser technology and the appearance of new material, the spectrum of the laser becomes more and more broad. The propagation characteristic for the monochromatic laser beam is well known for us, but we lack the knowledge about the broadband laser. So it is necessary and valuable for us to do some research works on the propagation of broadband laser. The broadband laser beam propagating through complex optical systems is studied in this dissertation. The spatial and spectral distribution for the input broadband laser beam is supposed to be separated. For the convenient of numerical calculation, the spectral distribution function is assumed to be a rectangular function. The research result in this dissertation provides us with a theoretical basis for its application in many field, it also enriches the theory of the propagation of laser beams.In Chapter 1, we have introduced the research background. The research work done in this dissertation has been briefly introduced. Some theories and methods used are detailedly given, including the matrix optics, the generalized diffraction theory, the partially coherent optics, the fractional Fourier transformation, the beam propagation factor and the kurtosis parameter.In Chapter 2, the broadband Gaussian beam and the broadband Gaussian Schell-model beam in free space are analyzed with the help of the second-order intensity moment and fourth-order intensity moment, respectively. It has proved that the intensity of the broadband laser beam is equal to the sum of the intensity of each frequency component. The propagation theory of the monochromatic laser beam is generalized to the case of the broadband laser beam, and the intensity moments are also given for the broadband laser beam. It is very difficult for us to obtain analytical expressions for the propagation equation and the intensity moments when the broadband laser beams propagate in free space. Numerical calculations are done. It is shown that the beam width, the divergence angle, the beam propagation factor and the kurtosis parameter enlarge with the increasing of the bandwidth. In Chapter 3, the broadband partially coherent flat-topped laser beam propagating through the atmospheric turbulance is analyzed. Suppose the broadband laser beam is stationary, the cross-spectral density function for the broadband partially coherent flat-topped laser beam propagating through the atmospheric turbulance is obtained and the second-order intensity moments for the broadband partially coherent laser beam are given. The simulation results show that the divergence angle and the beam propagation factor for the broadband partially coherent flat-topped laser beam in the free space maintain unchanged. The second-order intensity moments for the broadband partially coherent flat-topped laser beam in the atmospheric turbulance are less affected by the bandwidth compared with those in free space. The second-order intensity moments for the broadband fully coherent flat-topped laser beam are less influenced by the bandwidth than those for the broadband partially coherent flat-topped laser beam.In Chapter 4, we have firstly proposed the matrix for the hard-edged aperture. The hard-edged aperture is described by finite Gaussian aperture with different weighing coefficients. The matrix for the apertured fractional Fourier transforma optical system is obtained. This method is convenient and efficient for us to deal with the propagation problem of laser beams in the apertured optical system. Results show that the intensity distribution for the broadband Gaussian Schell-model beam in the plane of small fractional order is more obviously affected by the bandwidth. The modulation in the intensity distribution for the broadband Gaussian Schell-model beam is more prominent than that for the broadband fully coherent Gaussian beam when they propagate through the apertured fractional Fourier transforming optical system. The intensity distribution for the broadband Gaussian Schell-model beam through the ideal fractional Fourier transforming optical system is rarely influenced by the bandwidth.In Chapter 5, intensity distribution and the equal-time complex degree of coherence are studied when the broadband Gaussian Schell-model array beams pass through a free space. It is shown that the effect of the bandwidth on the intensity and equal-time complex degree of coherence in the near field is weak. In the case of coherent superposition, the effect of the bandwidth on the intensity in the far field is obvious. In the far field, the bandwidth can restrain the modulation in the intensity. With the increasing of the propagation distance, the difference in the equal-time complex degree of coherence turns out to be obvious.Finally, in Chapter 6, a summary is outlined and the future work is considered.