Techniques for steering of transient in Erbium-doped fiber laser; optimization of switch-on and switch-off.

Literature Review
The difficulty created by the oscillatory relaxation every time the laser power is changed was addressed very early on (1970's) in semiconductor lasers because of its implications in telecommunications. Consequently the optimization of the switch-on properties in semiconductor lasers, driven by the telecommunications market, has been a long-standing object of investigation. Over the decades, the only solution that was found was to make rectifications and modifications while producing the lasers and to fabricate them for telecommunications to make them less prone to oscillations. Many attempts were made at improving the laser’s performances under Direct Modulation either through changes in the structure of the semiconductor (e.g., by modifying the hetero-structures to reduce the ROs and improve the response [2]), by electric filtering, or by external means (e.g., through electric pulse shaping [2]), signal injection, optical feedback [2] technological solutions etc.). Most lasers used for technological applications belong to so-called Class B [3], which includes all solid-state, semiconductor, and CO2 lasers. All these devices have in common the long lifetime of the excited state (relative to both the medium polarization lifetime and to the photon lifetime in the cavity). All of them have the common unpleasant feature - the presence of Relaxation Oscillations (ROs) in every change in the laser operating state and also the system response has a significant amount of delay. Now, examining many different semiconductor and solid state lasers it has been confirmed that the main solution rests on an adequate modulation of the laser parameters during the transient evolution from the original state to the new one (e.g. switching between two different output power levels).

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Objective
In the last few years, revolutionary progress has been achieved in research and commercialization of erbium-doped fibre lasers (EDFLs). In particular, importance and use of optical amplifying devices based on rare earth doped fibre (REDF) have grown strongly [1]. The advantages of these lasers are the long interaction length of pumping light with the atoms, which leads to high gain and to single-transverse-mode operation produced by a suitable choice of fibre parameters. Meanwhile, these lasers are quite sensitive to any external perturbation that may destabilize their normal operation. Therefore, the study of the dynamic behaviour of these lasers under external modulation is of great importance.

Nowadays, the lasers used in different types of applications are based either on semiconductor technology, or on solid state devices. Both kinds of lasers have particularly favourable characteristics: very high optical efficiency, low consumption, robustness, versatility and ease to obtain high output power. These features made them more customary to be used in different applications and now cover the largest part of the market. However, both of them have a common disadvantage, their sensitivity to oscillations, in particular when their mode of operation is perturbed or, even more so, modified. Furthermore, any change in the operating point (output power) is accompanied by a sizeable time delay (which can reach several milliseconds in Er+doped fibre lasers) and an oscillatory decay towards the new state.

Generally, a remarkable output power peak appears when the laser power is turned up and followed by oscillations while the system relaxes to the final desired output power level. The peak intensity in some solid state lasers may amount to a few tens of times the CW level of operation. There is the additional disadvantage for these types of laser and that is the switch-offs are also comparatively slow. These stated features of the lasers are not brought about by technical design choices; instead they are intrinsic to their physical processes. Indeed, the high optical efficiency characteristic of these lasers comes from their deepest physical features. The lasing materials which are at the base of the devices possess internal relaxation constants for the main internal variable (population inversion) which are very long compared to the cavity parameters (i.e., relaxation constant for the electromagnetic field). As a result, the energy, supplied from the outside is stored into the material and very efficiently converted into radiation.
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This is not the case with most of the older kinds of lasers (e.g., gas lasers) whose performance is plug efficiency (≈10−4 ), remained for lack of viable alternatives the workhorse for over thirty very poor. This was notably the case of the Argon laser which, in spite of its abysmally low wall

years. In general the wall plug efficiency of semiconductor lasers is around 0.5 %.

Methodology
The project is mainly numerical and consists in finding the shape of the modulation to be applied to the laser pump (optical in this case) to obtain a smooth transition between two lasing states. A particular case, but an extremely interesting one, is the laser turn-on. Another one, even though less apparent, is the turn-off. The latter influences the ability to turn on and off the laser in “rapid” sequences and needs to be mastered. Thus, the quality of the laser turn-off affects the maximum speed at which the device can be cycled. Since the modulation parameters depend on the laser operating points (initial and final output power), an investigation of this dependence is important to successfully cover the different interesting regimes. Past work has shown that in some kinds of lasers the transient can not only be modified (removal of oscillations) but can also been shortened. The question has to be addressed directly for the fiber laser, since for the moment we do not have a general explanation for the reason why the time duration of the transient is reduced in some devices but not in others. At the present time, preliminary numerical results show that the pump modulation technique (described in the theory) works on fiber lasers, but only a few tests have been run. To find out the shape of the modulation to be applied to the laser pump (optical in this case) for a smooth transition between two lasing states a numerical analysis is carried on using Matlab. Since for the analysis of the modulation the major concerns are the two rate equations which are 1st order Ordinary differential equations (ODE), so the numerical method chosen is the Euler method. In mathematics and computational science, the Euler method, named after Leonhard Euler, is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic kind of explicit method for numerical integration of ordinary differential equations.
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Bibliography
1. Alexander N. Pisarchik, Alexander V. Kir’yanov, and Yuri O. Barmenkov, “Dynamics of an erbium-doped fiber laser with pump modulation: theory and experiment”, J. Opt. Soc. Am. B.22(2005) and the references therein.

2. N.Dokhane, G.L. Lippi, “Faster modulation of single-mode semiconductor lasers through patterned current switching:numerical investigation”, IEEE Proc Opto, Vol 151, pp 61-68 (2004) and the references therein. 3. J.-H.R. Kim, G.L. Lippi , H. Maurer, “Minimizing the transition time in lasers by optimal control methods Single-mode semiconductor laser with homogeneous transverse profile”.

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