Nonlinear Focusing Of Weak Beam By Another High Power Laser

The nonlinear propagation of an ultra-short pulse through a transparent medium can result in dramatic changes to its temporal, spatial and spectral properties. It has become an indispensable tool both in the laboratory and over a wider range of applications in the medical, industrial and telecommunication sectors. Particularly, the development of all-optical network aroused interest in the all-optical switching. Compared with the traditional optical switch controlled by electronic, all-optical switch has the advantages of faster response time and lower switching power. Therefore, it is certainly worth investigating how to harness the propagation of coupling beams.Firstly, we have been theoretically analyzed the propagation of coupling beam in the self-focusing media, and acquired the formula of beam width and the focal distance to the probe beam. Based on the theory of self-focusing and cross-phase modulation, we have been obtained an exact analytical solution under the approximate condition. It finds that the width and the focal distance of the probe beam affected by incident power, initial waist, and wavelength of pump beam. The length of focusing is inversely proportional to the incident power, directly proportional to initial beam waist of the pump beam.Secondly, we have been analyzed that the focal distance, the efficiency of focusing and beam width of probe laser varied with incident power, initial waist and wavelength of bump laser, respectively, and obtained the principle of controlling of induced focusing. Based on the nonlinear propagation equation, which accounts for diffraction, self-focusing and dispersion affections and split-step Fourier method, we have been Theoretically and experimentally researched how did the width and the focal spot of probe laser affected by incident power, initial waist and wavelength of bump laser, respectively. It shows that the length of focusing decreased with incident power and wavelength of bump laser, increased with the initial waist. The principle of controlling focal distance could be summarized that controlling the relationship between incident power, initial waist and wavelength of bump beam, to make the defocusing and focusing balance.Finally, we have been investigated beam width and the efficiency varied with incident power, initial waist and pulse delay of bump laser in spatiotemporal coupling dimensions, and ensured the efficiency of induced-focusing when the focal distance is controlled. According to the theory of transfer equations, it has been shown that the efficiency of induced-focusing decreased with initial waist, increased with the incident power and pulse delay. The numerically simulations in spatiotemporal coupling dimensions are well consistent with theoretical analysis. At last, it finds that the profile of probe laser can be controlled induced by bump laser beam.