Paper C2: Laser Science and Quantum Information Processing - Laser Physics Prof. Simon Hooker Michaelmas Term 2011 ii Contents 1 Basic Laser Physics 1 1.1 Introduction . .1 1.2 Recommended texts . .1 1.3 Lineshapes . .1 1.3.1 Homogeneous broadening . .2 1.3.2 Inhomogeneous broadening . .2 1.3.3 Comparison of homogeneous and inhomogeneous transitions . .4 1.4 The optical gain cross-section . .6 1.4.1 Laser rate equations . .7 1.5 Gain saturation . .7 1.5.1 homogeneous broadening . .7 1.5.2 Inhomogeneously broadened transitions . 10 1.5.3 Summary . 11 1.6 Threshold behaviour . 11 1.6.1 Homogeneously broadened laser transitions . 12 1.6.2 Inhomogeneously broadened systems . 13 2 Solid State Laser Materials 15 2.1 General considerations . 15 2.1.1 Radiative transitions . 17 2.1.2 Non-radiative transitions . 17 2.1.3 Line broadening . 18 2.2 Trivalent rare earths, 4fn − 4fn transitions . 19 2.2.1 Energy level structure . 19 2.2.2 Transition linewidth . 19 2.2.3 Nd:YAG laser . 19 2.2.4 Other crystalline hosts . 24 2.2.5 Nd:Glass laser . 24 2.2.6 Erbium lasers . 24 2.3 Trivalent iron group, 3dn − 3dn transitions . 27 2.3.1 Energy level structure . 27 2.3.2 The ruby laser . 33 2.3.3 Alexandrite laser . 36 2.3.4 Ti:sapphire . 37 2.3.5 Host materials . 41 iii iv CONTENTS 3 Q-Switching 43 3.1 Laser Spiking and relaxation oscillations . 43 3.1.1 Rate equations . 44 3.1.2 Cavity lifetime . 45 3.1.3 Numerical analysis of laser spiking . 46 3.1.4 Analysis of relaxation oscillations . 47 3.2 Q-switching . 49 3.2.1 Techniques for Q-switching . 49 3.2.2 Analysis of Q-switching . 52 4 Modelocking 57 4.1 Introduction . 57 4.2 General ideas . 57 4.2.1 Simple analysis . 59 4.2.2 Further general comments . 60 4.3 Active modelocking techniques . 60 4.3.1 AM modelocking . 60 4.3.2 Synchronous pumping . 65 4.3.3 Pulse duration of actively modelocked, homogeneously broadened lasers . 66 4.4 Passive modelocking techniques . 66 4.4.1 Saturable absorbers . 67 4.4.2 Kerr lens modelocking . 69 4.5 Examples of modelocked lasers . 69 4.5.1 CW modelocking . 69 4.5.2 Pulsed modelocking . 70 5 Ultrafast Lasers 71 5.1 Propagation in dispersive media . 71 5.1.1 Propagation through an arbitrary system . 72 5.1.2 Propagation of Gaussian pulses . 73 5.1.3 Nonlinear effects: self-phase-modulation and the B-integral . 76 5.2 Dispersion control . 77 5.2.1 The grating pair . 79 5.2.2 The prism pair . 80 5.2.3 Introduction of positive GDD . 81 5.2.4 Chirped mirrors . 81 5.3 TW and PW laser systems . 82 5.3.1 Regenerative and multipass amplifiers . 83 5.3.2 Multipass amplifiers . 85 5.3.3 Low-energy, TW laser systems . 85 5.3.4 High-energy, PW laser system . 86 5.4 Applications of ultrafast lasers . 87 6 Semiconductor & Fibre lasers 89 6.1 Review of semiconductor physics . 89 6.1.1 Distribution over energy levels . 91 6.1.2 Doped semiconductors . 92 6.2 Radiative transitions in semiconductors . 93 6.2.1 Joint density of states . 95 CONTENTS v 6.2.2 Density of possible transitions . 95 6.2.3 The gain coefficient . 96 6.2.4 Condition for gain . 96 6.2.5 Generating gain: the injection density . 97 6.3 Homojunction diode lasers . 98 6.3.1 Structure of homojunction diode lasers . 100 6.4 Double heterostructure lasers . 100 6.4.1 Forming heterostructures: Material properties . 101 6.5 Geometries of heterostructure diode lasers . 102 6.6 Output characteristics of diode lasers . 103 6.7 Fibre lasers . ..