Determination of Effective Photon Lifetime in Nitrogenic Laser in One and Two Dimension

Abstract

Abstract:Since one of the most valuable measurable parameters in laser, called effective cavity lifetime , gives useful information about laser, this paper aims to study the description of it dependency, , on geometrical characteristics of N 2 -laser, electrodes length and amplifier gap separation. First based on the studies carried out on it , an oscillator-amplifier laser is used which operates under moderate current density conditions; Then in order to obtain a theoretical relation for effective cavity lifetime and to demonstrate the mentioned dependency using rate equations, at first a one-dimensional method is used for the photon density. Since the answers of rate equations in an oscillator-amplifier laser are complicated, a single-oscillator based modelis offered to make rate equations simpler. In this model, at first it is supposed that the photon density of inner part of the amplifier could ben ph (z,t)= n ph (0,t) exp (g 0 (z)z), If n ph n ph (z,t), then rate equations are used for this density and since g 0 is a function of z or amplifier electrode length (Z l AMP ), the cavity effective life time is calculated for equivalent oscillator.Then ,Since most of studies carried out in one dimension , so for approaching to more actual system a two -dimensional method is used for the photon density. So, we consider Z andY, which Z is along amplifier electrodes length and Y is along gaps separation. Supposing that Z and Y are independent on the photon density, two independent relations can be considered for the photon density. In this step, 2-dimensional photon density could be regarded as:n ph (z,y,t) = n ph (z,t) n ph (y,t) . and then 2-dimensional effective cavity lifetime amount is obtained as:1 ‫ץ‬ ‫ץ‬ ‫ץ‬ ‫ץ‬ , This relation includes 2 independent values along the electrodes length (Z l AMP ) and gap separation (y d AMP ). It also demonstrates that the obtained 2-dimentional relation represents a perfect schema for lifetime behavior. The results of this calculation are consistent with other reported N2-laser effective cavity lifetime values measured under moderate current density conditions.