Determination of effective photon lifetime in nitrogenic laser in one and two dimension

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 N2-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 benph (z,t)= nph (0,t) exp (g0(z)z), If nph nph (z,t), then rate equations are used for this density and since g0 is a function of z or amplifier electrode length (Z lAMP), 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:nph (z,y,t) = nph (z,t) nph (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 lAMP) and gap separation (y dAMP). 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.