Studies on Resonator Dependent Dynamical Behavior of Solid-State Lasers by the Iterative Maps of Gaussian Beam Propagation

• Main Authors: Ming-Dar Wei, 魏明達
• Other Authors: Wen-Feng Hsieh
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/81983550317645665885

博士 === 國立交通大學 === 光電工程所 === 87 === In a general optical resonator without gain or loss, Gaussian beam dynamics can be studied by using the residue of the conservative iterative map, which is a function of resonator G-parameters'' product. We found, for the first time to our knowledge, there exist new singularity configurations within the geometrically stable regions if the system persists to nonlinear effect. These specific configurations correspond to G-parameters'' product equals 1/2, 1/4 or 3/4, and  as a result of low order resonances. Numerical simulation further show that the dynamics of a dissipative resonator with loss optical elements is equivalent to a damping oscillatory motion and can be determined by the corresponding conservative resonator without those loss elements. In an end-pumped solid-state laser, we experimentally observed a fundamental mode power dip when the cavity length was adjusted approaching these configurations under pumping spot size less than that of the cavity mode. We found the laser exhibits a relatively low threshold together with shrinking beam waist and unexpected far-field beam profile. Within the dip a specific region has irregular behavior of which noise fluctuation is about 21 times of that outside this region. We apply the map method for the unresolved self-starting issue of the Kerr-lens mode-locking (KLM) lasers. Since a physical system tends to stay at lower energy state, by minimizing Hamiltonian between KLM and cw operations we obtained the preferable Kerr-lens mode-locking regions agree with the experimental self-starting ones. Again, the same conclusion can be made by considering the system having dissipative elements, in which the modulus of eigenvalue of the Jacobian matrix represents the convergent rate of the system against a small perturbation and can be defined as the stability factor of the physical system. Further discussing the nonlinear behavior of KLM optical resonator in specific configurations without dissipative elements, we found due to residue equal to zero more than one spatial fundamental Gaussian modes may happen in the concentric and confocal resonators. The pitchfork bifurcation results in more symmetrical configurations and saddle-node bifurcation appears as the symmetry being broken. From the properties of bifurcation, we suggest that the equal-arm and near-confocal resonator is suitable for the emergence of bistability in KLM lasers. In addition, period doubling, tripling and quadrupling can occur at the configurations with cavity generalized G-parameters'' product equals 1/2, 1/4 or 3/4, and , respectively. The systems will result in irregular behavior if one further increases the nonlinear effect. Even though we just considered the conservative system in previous discussions, the predicted results agree with the experimental ones that are dissipative. Thus, the nonlinear behavior of KLM laser may be observed in experiments.