ايجاد قيم بعض معاملات معادلات المعدل لليزرات العاملة بالنمط المفتاحي السلبي باستخدام تقنية الامثلية

Finding Some Rate Equations Parameters for Passively Q- Switched Lasers Using Optimization Technology

Abstract
This study, aims to find the optimal values of some coefficients of the rate equations for a Cr : LiSAF laser Q-switched by Cr: YSO saturable absorber.
The mathematical model used is based on four first-order nonlinear differential equations that represent the evolution of the temporal behavior of the system components, as follows.
The first equation represents the rate equation for the cavity photon number (n). The second stands for the rate equation for the gain medium with population inversion (Ng). The third serves the rate equation for saturable absorber molecule at the ground state (Na). The fourth represents the rate equation for saturable absorber molecule at the first excited state (Nau). It was solved numerically using Runge – kutta – fehlberge method to determine the characteristics of the laser-generated giant pulse.
After that the optimization technique was utilized to determine the following parameters, the excited state absorption cross-section to the ground state absorption cross-section of the saturable absorber molecules (β), the saturable absorber decay rate 〖(γ〗_a), photons losses inside the laser cavity〖(γ〗_c), using constrained Rosenbrock optimization technique. Where it was found that the value of (β )increases with increasing the number of Cr: YSO molecules number, but values of both Cr: YSO relaxation rate (γ_a) and photons losses rate (γ_c) decrease with increasing number of Cr: YSO saturable absorber molecules number until reaching a certain value, at which point the variation becomes negligible. Optimal solutions were reached with accuracy and balance that achieve the best operating conditions for the laser system. The absolute error ratio between the theoretically calculated and the practically calculated parameters was (0.0299, 0.000009, 0.0000032), respectively.