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Part 2: Laser in Pulsed Operation

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Part 2: Laser in Pulsed Operation Part 2: Laser in pulsed operation 1 Theoretical principles 1.1 Generation of short laser pulses The output power of existing continuous wave laser systems is between a few milliwatts (He-Ne lasers) and a few hundred watts (Nd or CO2 lasers). However, there is a possibility to increase the output power of the laser for a small period of time by pulsed laser operation. Solid-state lasers are particularly suitable for this purpose, as they can achieve pulse peak output powers of up to 1012 W. This value corresponds approximately to the average electrical energy generation of the entire world. The difference, however, lies in the period in which this performance is achieved. While all the power plants together reach this value continuously, a single laser produces this high output power only for a duration of 10−13 s. In this case, the extremely short pulse duration appears to be disadvantageous, but there are also applications which exactly require this. One example is laser ablation, which is a method in material processing. Here, a small volume of material at the surface of a work piece can be evaporated if it is heated high enough in a very short amount of time. On the other hand, supplying the energy gradually would allow the heat to be absorbed into the bulk of the piece, never attaining a sufficiently high temperature above the evaporation point of the material. Other applications rely on the very high peak pulse power to obtain strong non-linear optical effects, like it is necessary for efficient second-harmonic generation or for optical parametric oscillators (OPO) which converts an input laser wave into two output waves of lower frequencies. Finally, ultra-fast laser spectroscopy techniques use laser pulses for the study of dynamics on extremely short time scales (attoseconds to nanoseconds). Different methods are used to examine dynamics of e.g. charge carriers, spin polarizations, or the motions of atoms and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges. One example is the so-called pump-probe experiment, where a first laser pulse creates some kind of imbalance in the investigated sample (e.g. photo-excited charge carriers or a spin polarization) and a second laser pulse, which has a variable time delay to the first one, probes the time evolution of this imbalance. In principal, there are three possibilities for generating short laser pulses: 1. Using a pulsed pump source, 2. temporarily changing the quality factor of the optical resonator (Q-switching), 3. and the so-called mode coupling. 1.2 Short revision To better understand the methods of pulsed pump sources and the quality modulation of a laser system, it is advisable to once again look at the processes in a four-level laser system (see Fig. 1(a), the following is a short revision of the far more detailed explanations in the first part of the introduction - equations and definitions of the physical quantities can be found there). By optical pumping, electrons are excited from level N0 to level N3. The latter state has a very short lifetime, so that it remains almost unoccupied even under heavy pump powers. Because of non-radiative transitions, electrons go from level N3 to the metastable level N2. The transition of an electron from level N2 to level N1 creates a photon of E2−E1 the laser frequency n = h . Since the level N1 also has a very short lifetime, like N3, the electron now quickly returns to the ground level N0. Since the respective lifetimes of the levels N3 and N1 are very short, these states remain almost unoccupied. Once optically pumped, inversion occurs between levels N2 and N1. When the laser starts up, the active medium spontaneously emits photons in all directions. However, a small part of the emission occurs along the axis of the resonator. These spontaneous photons can travel back and forth through the resonator and hence the active medium. As the laser medium posses a finite size and the probability for the induced 1 (a) (b) (c) E N3 N3 non-radiative non-radiative n transition transition nmax N2 N2 pump pump laser induced spontaneous nth photon photon emission photon emission N1 N1 W = const non-radiative non-radiative p transition transition t N0 N0 Figure 1: Schematic diagram of a four-level laser system with (a) and without (b) optical resonator. (c) Population inversion with an optical resonator under ideal conditions (gray solid line), with an optical resonator with transient effects (green dotted line) and without an optical resonator (red dashed line) as a function of time at a constant pumping power. emission is also finite, this optical feedback is a necessary requirement for a photon to create several replicas before it is coupled out of the resonator (as the actual laser beam) or is lost due to absorption or diffraction processes. The increase in the photon field r over times then triggers more and more induced emission events from laser level N2 to laser level N1. Finally, a steady case condition with a positive photon density (r > 0) is reached. In this case no inversion beyond the threshold inversion value can be generated even with the strongest pumping mechanisms. Instead of the population inversion, the photon density increases with increasing pumping power (see Fig. 1(c)), which thus limits the inversion at the threshold value because of an increased probability of induced emission. If this equilibrium has been established, the number of electrons at the excited level N2 can be considered constant. The light inside the resonator is now amplified by the amplification factor G as much as it is attenuated by the losses L (scattering, reflection and transmission) during a passage through the laser medium. Thus, for stationary operation follows: G·L = 1. 1.3 Pulsed pumping and spiking So far only the steady state solution of the rate equations was discussed. However, in practice, conditions of perturbed equilibrium occur (amongst other things, due to slight mechanical disturbances of the laser resonator or fluctuations in the pump light intensity). Small deviations of the population inversion or of the photon density from the equilibrium lead to damped harmonic oscillations of n and r, respectively. However, larger deviations from the equilibrium may also lead to undamped, non-harmonic oscillations of the output power, which make the occurrence of large power spikes possible. In this case, the first power peak (“initial spike”) can exceed the steady-state value of the output power by magnitudes. A deviation from the steady state condition undoubtedly occurs when the pump-light source is switched on. In this case the rate equations are only solvable numerically and hence only a qualitative view of the so-called spiking will be discussed in the following. Figure 2: Spiking Until the threshold pump power Pth is reached, there are practically no photons present in the resonator. When the population inversion reaches the threshold, a photon field is formed. However, due to the resonator propagation 2 time, it takes a while until the photon density reaches the steady state value. During this period the inversion, which rises linearly with time, increases above the value of the threshold inversion (see green dotted line in Fig. 1(c)). This in turn means a more rapid increase in the photon density and hence a temporarily higher output power compared to the steady state condition (see Fig. 2). Due to induced emissions, the population inversion is then reduced so quickly that it drops to a value below the threshold and the laser oscillation stops. In this way, the radiation field collapses, the laser intensity decreases. The laser goes off until enough atoms have been excited by the pumping process and the intensity can rise again. The process starts again, but this time the laser is only slightly below the threshold and the expected inversion overshoot is not so large as before. In this manner the system approaches the steady state condition. This kind of pulsed laser pumping can yield laser pulse lengths down to 10−6 s. 1.4 Q-switching In case of the pulsed pumping method, there is still a functional optical resonator present all the time. For the Q-switch method this is not the case anymore. Rather, the optical resonator is temporarily “switched off” by an optical element, which covers one mirror (see Fig. 3). optical switch active laser medium mirror 1 mirror 2 (highly reective) pump source (semi-transparent) Figure 3: Schematic of a laser system with an optical switch for pulse generation. A Q-switch is achieved by putting some type of variable and controllable attenuator inside the optical resonator. When the attenuator is switched off, the laser beam can pass it without significant loss. Therefore, the photons inside the optical resonator can travel forth and back between the two mirrors and laser operation is possible. But when the attenuator is switched on, light which leaves the active medium along the optical axis cannot experience the feedback effect but is rather coupled out of the system at mirror 2 or reflected/absorbed at the optical switch. This attenuation inside the cavity corresponds to a decrease in the quality factor (Q-factor) of the optical resonator. Now the active laser medium is pumped while the Q-switch is set to prevent the feedback of light. Hence, there is no significant photon field r inside the resonator and accordingly no induced emission processes (see Fig. 1(b)). As a result the population of level N2 and therefore the population inversion can now grow above its steady state laser threshold nth (see Fig.
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