Pulsed lasers have many applications such as material processing, aerial or space communications, remote sensing or medicine. Most often such lasers are based on either amplifying bulk crystals or optical fibers and use active Q-switching or mode locking by mean of an intra-cavity bulk modulator driven by an external energy source. As the integration of pulsed lasers into more compact and reliable systems is highly desirable, passive modulation is investigated. In the case of fiber lasers, this has been implemented using bulk saturable absorbers (SA), such as transition-metal doped crystals [l]. However, insertion losses remain high and alignement critical, due to coupling optics. Therefore using an etYicient fiberized saturable absorber would offer an interesting alternative because of the well known inherent efficiency, reliability, ruggedness, simplicity and low cost of totally fusion spliced fiber systems. Passive Q-switching (PQS) results mainly from the non linear response of a transition-metal doped saturable absorber (SA) or a semiconductor mirror to incident laser beam. In a PQS laser a pulse is generated when the gain in the amplifying medium overcomes the total losses of the cavity whereas the absorption of the SA drops. Recently new optical fibers doped with transition elements have been realized, allowing the demonstration of an all-fiber passively Qswitched laser [2]. As an example, Figure 1 shows a setup based on the Er3+:Co2+ system in a linear cavity composed of two fusion-spliced doped fibers. However, the present study could be applied to many other systems, such as Yb3+: Cr4, in any laser configuration. amplifier saturable A (Er3+) SA (Co2+) 14s) pump absorberI signal 3SA) kL I [A I SA I *I2 :f-r 13S) I P L A2s) R mirrors R is) Fig. 1: Schematic laser setup. Ri and Ro are the input and output mirror Fig. 2: Energy level diagram of the amplifying and absorbing reflectivities, respectively. media, respectively. Solid arrows: optical transitions, dotted arrows: non-radiative decays.In this paper, we present a model describing the time dependent characteristics of a PQS laser composed of amplifying and saturable absorber fibers, specially taking into account the transverse singlemode intensity distribution, long interaction length, high gain and absorption coefficients, and including the effects of amplified spontaneous emission. The model is described by three coupled differential equations connecting the saturable absorption, the gain and the optical power, all directly measurable macroscopic variables. These are preferred to the usual variables such as ion populations and photon flux, because they help showing the influence of the overlapping between gain/absorption and mode in the active fibers. They also allow us to easily introduce the excited state absorption in the SA and the signal absorption in the amplifier. The model uses the opto-geometric parameters associated to each fiber (core radius, numerical aperture, radial distribution of dopants) and to the cavity (mirror reflectivity, fiber...
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