Theoretical application of z-dependent gain coefficient to describe amplified spontaneous emission

Abstract

Based on the geometrical modeling of the unified gain coefficient and the reported amplified spontaneous emission (ASE) output energy measurement ε(ASE) versus amplifying excitation length, l(AMP) in a KrF laser oscillator, we managed, as an example, to explain the ASE output energy behavior both numerically and analytically. In this approach, introducing the ASE gain-coefficient profile for the KrF laser, g(0,KrF)(ASE), was not avoidable. It was found that while the g(0,KrF)(ASE) profile follows the introduced gain-modeling formulation, it is, however, slightly lower than the KrF laser gain profile, g(0,KrF)(exp), deduced from the measurements reported by different researchers. The present approach, up to the present time, is able to explain all of the existing ambiguities on understanding the ASE behavior.

Study of the amplified spontaneous emission spectral width and gain coefficient for a KrF laser in unsaturated and saturated conditions

“…In our previous report we showed that by using the photon density rate equation it is possible to predict the ASE output energy ε ASE versus medium excitation length, l AMP , for KrF lasers [14,15]. Consequently, we managed to explain the reported experimental measurements that appeared in [16].…”

“…, where g ν 0 0 is given by equation ( 2), and x = 2(ν − ν 0 )/ ν 0 is the normalized frequency offset [21,22]. For µ = 0 and ν = ν 0 the ASE intensity was calculated numerically, as in [14,15], where we obtained accordingly that m 1 = 0.001 cm −1 and γ max L = 4.5. In the present work for µ = 1, and by considering again that ν = ν 0 , we performed the numerical calculation and the results are given in figure 1, where in contrast to the case for [14,15], the ASE output energy, ε ASE , is given on a logarithmic scale for a better visualization of the fitting of the experimental data to the proposed model of the geometrically dependent gain coefficient (GDGC).…”

Theoretical study of amplified spontaneous emission intensity and bandwidth reduction in polymer

“…The analytical approach to explain the ASE behavior, using a four level system for a homogeneously broadened transition, has led to an analytical expression for the ASE output energy or intensity, and has been introduced in Refs. [22] and [23]. Thus, the details of this part of the calculation are not given here, except some relevant parts for better understanding of the proposed method.…”

“…( 4) is γ(z)g ν 0 (z)hν/σ ν stim τ sp , and the solution of Eq. ( 4) for I ν (z) is given by the following expression: [22,23]…”

“…(3). With the available experimental measurements, as specific examples, equation (3) was used to predict the ASE output behavior in KrF [22][23][24][25] and N 2 [26,27] lasers, and we found that the corresponding ASE gain profiles, denoted by g ASE 0,KrF and g ASE 0,N 2 , obey Eq. ( 3) with slightly different gain parameters, compared with those obtained by direct gain measurements.…”