Chapter 7 Lasers After having derived the quan tu m m echan ically correct suszeptibility for an in ver ted atomic system that can pro vid e gain, w e can use the t wo-level model to study the laser and its dynamics. After discussing the laser concept briefly we will investigate various ty pes of gain media, gas, liquid and solid-state, that can be used to construct lasers and amplifiers. Then the dynam ics of lasers, threshold beha vio r, steady state beha vior and relaxation oscillations are discussed. A short in troduction in the generation of high energy and ultrashort laser pulses using Q-switching a n d mode lock in g will be giv en at the end. 7.1 The Laser (Oscillator) Concept Since the inv ention of the vacuum amplifier tube by Robert von Lieben and Lee de Forest in 1905/06 it was known how to amp lify electrom ag netic waves o v er a broad wavelength range and how to build oscillator with whic h suc h waves could be generated. This was extended in to the millime ter wave re-gion with advances in amplifier tubes and later solid-state devices suc h as transistors. Until the 1950’s thermal ra dia tion sources were mostly used to generate electromagnetic wa ves in the optical frequency range. The gener-ation of coherent optical wa ves was only made possible by the Laser. The first amplifier based on discrete energy levels (quantum amplifier) w as the MASER (Microw a v e Amplification by Stimulated Emission of Radiation), which was in vented by Gordon, To wnes and Zeiger 1954. In 1958 Scha w lo w and Townes proposed to extend the MA SE R principle to the optical regime. 293294 CHAPTER 7. LASERS The amplification should arise from stimulated emission bet ween discrete en-ergy levels that must be inverted , as discussed in the last section. Am pli fiers and oscillators ba sed on th is principle are calle d LA SER (Light A m p lification b y Stim ulated Emission of Radiation). Maiman w as the first to demonstrate a laser based on the solid-sta te laser material Ruby. Figure 7.1: Theodore Maiman with the first Ruby Laser in 19 60 and a cross sectional view of the first device [4]. The first HeNe-L a ser, a gas laser follo wed in 1961. I t is a gas laser built by A li Ja van at M IT , with a w av elength of 63 2.8 nm and a linewidth of only 10kHz. The basic principle of an oscillator is a feedback circuit that is unstable, i.e. there is positive feedb ack at certain frequencies o r certain frequ ency ranges, see Figure 7.2. It is th e feedback circuit that deter m ines the frequ ency of oscillation. Once the oscillation starts, the optical field will build up to an in tensity approaching, or even surpassing, the saturation in tensity of the amplifier medium b y man y times, un til the amplifier gain is reduced to a value equal to the losses that the signal experiences after one roundtrip in the feedbac k loop, see Figure 7.3295 7.1. THE LASER (OSCILLATO R) CONCEPT Image removed for copyright purposes. Figure 7.2: Pr in cip le o f an oscillator circuit : an amp li fier with positiv e feed-bac k [6] p. 495. Image removed for copyright purposes. Figure 7.3: Saturation of amplification with increasing sign al power leads to a stable oscillation [6], p. 496 . In the radio frequency range the feedback circuit can be an electronic feedback circuit. A t optical frequen cies we use an optical resonator, which is in most cases w ell modeled as a one-dim en siona l Fabry-Perot resonator, which we analysed in depth in section 7.4. We already found bac k then that the transfer chara cterisitcs of a Fab ry-Perot resonator can be understood as a feedbac k structure. All we need to do to construct an oscillator is pro v ide amplification in the feedback loop, i.e. to compensate in the resonator for eventual internal losses or the losses due to the output coupling via the mir-rors of the Fabry-Perot, see Figure 7.4.We have already discussed in section296 CHAPTER 7. LASERS 2.6.2 various optical resonators, which ha ve Gaussian beams as the funda-men tal resonator modes. One can also use w aveguides or fibers that have semitransparent mirrors at its ends or form rings as laser resonators. In the latter ones output coupling of ra dia tion is achieved with wa veguide or fiber couplers in the rings. Today lasers generating light contin uosly or in the form of long, nanosec-ond, or very short, fem toseco n d pulses can be built. T y pically these lasers are Q-switched or mode-locked, respectiv ely. T he average power lev el can vary from microwatt to kilowatts. Image removed for copyright purposes. Figure 7.4: A laser consists of an optical resonator where the internal losses and/or the losses due to partially reflecting mirrors are compensated by a gain medium inside the resonator [6], p. 496. 7.2 Laser Gain Me dia Importan t chara cteristics of laser gain media are whether it is a solid, a gase or liquid, how inv er sion can be ac hieved and what the spectroscopic paratmeters are, i.e. upperstate lifetime, τL = T1,linewdith ∆fFWHM = T2 2 and the crosssection for stimulated emission . 7.2.1 Three and Four Level Laser Media As we discussed before inversion can not be ac hieved in a two level system b y optical pumping. The coherent regime is typically inaccesible b y typcial optical pump sources. In version by optical pump ing can only be ac hieved when using a three or four-lev el system, see Figures 7.5 and 7.6297 7.2. LASE R G AIN MEDIA a) b)N2 22 N2 γ21 γ21Rp Rp N1 1 N11 γ γ10 10N00 N00 Figure 7.5: Three-level laser medium. 3 N3 γ32 2 N2 Rp γ21 1 N1 γ100 N0 Figure 7.6: Fou r-level laser medium. If the mediu m is in thermal equilibrium, typ ically only the ground state is occupied. By optical pumping with an intense lamp (flash lamp) or another laser one can pum p a significant fraction of the atoms from the ground state with population N0 into the excited state N3 both for the three level laser operating according to schem e shown in figure 297 (a) or N4 in the case298 CHAPTER 7. LASERS of the four lev el laser, see Figure 7.6. If the relaxatio n ra te γ10 is v e ry fast comp ared to γ21, where the laser action should occur in version can be ac hieved, i.e. N2 >N1. For the four leve l laser the relax ation rate γ32 should also be fast in comparison to γ21. These systems are easy to