The Physics of Laser Radiation–Matter Interaction : Fundamentals, and Selected Applications in Metrology

This textbook is intended for students of physics, physical or mechanical engineering, or natural sciences. The idea to start to write a book on the interaction of laser radiation with matter began to grow when I moved to Mittweida in 2013, tooling there a new professorship in physics and laser microtechnology. Textbooks on these topic exist for professionals, but my research on comprehensive books didn't get any valuable books on, in my opinion, very important derivations from equations and thoughts, describing such processes. So, I started to collect passages, generated topics, and finally finalized this book.These years of development were accompanied by numerous discussions with my team members, who in fact cleared my mind and allowed me to determine a red line on which a lecture on laser radiation-matter interaction should follow. My team colleagues were the "seeds and the plants" of most results described in this book. Especially, Markus Olbrich, M.Sc., being our fundamentalist in sense of the physical understanding, pitched this textbook on the right level. He was my first group member, and together we set up our lab at the laser institute in Mittweida. He introduced my group to the numerical techniques and taught all group members, and additionally also our students learning physical technology, to apply these wonderful techniques to many physical problems. The second key player in my group, Dr. rer. nat. Theo Pflug, was the experimenter, who developed many novel ultra-fast metrologies and who published in a very short time many wonderful articles on our group activities. Both supported me during my writing of this textbook with fruitful discussions and in setting up many diagrams and modeling plots. The last member who supported me is Philipp Lungwitz, M.Sc., who developed often very unorthodox physical techniques and opened some new research topics in my group. He is the perfectionist in our lab, who pushed some of our research to new levels. All of them I thank very much for the fruitful years and the friendship. The laser institute in Mittweida is a jewel, as there best-skilled scientists are working on different leading topics in laser technology. I thank all my colleagues for the strong collaboration. One great property is that many of them work together when help is needed, even not being in the same research group. Nothing would work in our labs at the institute without the strong support of Lars Hartwig, Sascha Klötzer, and Alexander Thurm. They were the first setting up vii viii Preface the illumination technology in my lab, making the room cleaner with flow boxes, and allowing us to start to work very quickly.This textbook is structured into four great parts, starting from the characterization of laser radiation. In my opinion, the most important topics deal little with "laser" radiation, but just on electromagnetic radiation. As this textbook does not deal with ultra-high-energy physics, also the topic laser will just deal with pulse duration down to the femtosecond regime. Just some insight on pulse shaping will enlarge the physics of laser radiation with matter.The second part of this textbook describes the processes for the generation of electromagnetic radiation, as firstly often radiation is generated during laser radiation/matter interaction, and secondly, every process of interaction features a kind of scattering of charges. Oscillating charges emit radiation, as will be shown by solving the Maxwell equations. In my opinion, even these derivations are somehow very theoretical, also an engineer should be able to follow the idea. This is important to understand physics!The third and largest part describes the interaction of radiation with matter. As a textbook, I decided to go step-wise from the simplest system, a free electron, to the most complex one, condensed matter, introducing semi-classical models for the interaction. In this textbook, no strong quantum mechanical derivations are given, as this is more adequate for the physicist, not for a user. Even though the semi-classical model is somehow crude, they describe the processes very well. Many examples are given. Getting an understanding of the interaction of simple systems, linear optics dealing with the interaction of radiation with the condensed matter without absorption is described. As ultra-fast laser metrology is in my opinion the metrology being able to investigate very fundamental processes, non-linear optics is then introduced, being the key process for ultra-fast physics. Up to now, no absorption is given, which is why in the following sections the absorption is introduced. To describe this properly in condensed matter, especially in this textbook solid state matter is discussed, and the name model for crystalline matter is introduced. Before that, clearly, the free electron gas is used as the simplest model to describe absorption and as a consequence, their optical properties. As now the inter-and intraband transitions are understood, many examples on the excitation of condensed matter are given, for metals, semiconductors, and as well dielectrics. Especially for dielectrics, as absorption can only take place when non-linear processes are given, a topic on non-linear absorption will describe the different channels enabling radiation to ionize matter.The fourth and last part deals with applications in metrology using laser radiation. I decided to describe some special metrologies, where ultra-fast laser radiation features the best properties to get some very deep insight. Also, I focused on pump-probe technologies only. I start with reflectometry, being the simplest metrology. There I describe the fundamentals of the pump-probe idea. A very impressive setup is then described allowing to detect space-and time-resolved reflectance change. The next chapter deals with ellipsometry, a fantastic metrology, allowing to determine the complex refractive index. After some fundamentals, I describe space-resolved and in the following space-and time-resolved ellipsometry. A more qualitative metrology, but quick in setting up, is Nomarski microscopy. It allows to determine space-and Preface ix time-resolved refractive index changes. Finally, I will describe in this part the whitelight interferometry. It is the royal league of interferometry, as using white-light a biunique detection of phase changes is possible, and combined with ultra-fast laser radiation, it becomes a very powerful metrology for the investigation of laser-induced processes.Many thanks to Prof. Sauerbrey for allowing me to use his very focused lecture notes on non-linear optics. I hope I got his message and could transpose it well. Also, I adopted some notes from the lectures on electrodynamics by S. Brandt and D. Dahmen I listened to as a student in physics at the University of Siegen in the year 1992. Finally, I want to thank many students, like Melwin Göse, B.Sc., Philipp Rebentrost M.Sc., Eric Syrbe M.Sc., Katrin Zerbe M.Sc., giving me a lot of helpful comments and revisions to the textbook. Oberschöna, Germany Preface Contents Acronyms Part I Electromagnetic Radiation 1 Properties of Electromagnetic Radiation 1.1 Fundamental Interactions 1.1.1 Nuclear Forces 1.1.2 Electromagnetic Force 1.1.3 Gravitational Force 1.2 Wave and Particle Description of Electromagnetic Radiation 1.3 Photon Description 1.4 Maxwell Equations 1.4.1 Maxwell Equations in Vacuum 1.4.2 Continuity Equation 1.4.3 Integral Description of Maxwell Equations 1.5 Electromagnetic Waves 1.5.1 Derivation of Wave Equations 1.5.2 Fundamentals on Waves 1.5.3 Orthogonality of the Vector Fields 1.5.4 Scalar and Vector Potential 1.6 Energy Density of Electromagnetic Wave 1.6.1 Electrostatic Approach 1.6.2 Generalization to Electromagnetic Fields 1.6.3 Planar Electromagnetic Waves 1.6.4 Phase and Group Velocity 1.7 Laser Radiation 1.7.1 Spatial and Temporal Properties 1.7.2 Coherence 1.7.3 Spectral Modulation References 2 Generation of Electromagnetic Radiation 2.1 Discrete and Continuous Transitions 2.2 Spontaneous Emission 2.3 Acceleration of a Free Charge 2.3.1 General Aspects on the Retardation 2.3.2 General Solution of a Retarded Wave Equation 2.3.3 Maxwell Equations for a Moving Charge 2.4 Emission of Accelerated Charges 2.4.1 Collinear Velocity and Acceleration Vectors 2.4.2 Acceleration Perpendicular to the Velocity 2.4.3 Periodic Oscillation of a Charged Particle 2.5 Black-Body Radiation 2.5.1 One-Dimensional Hollow Black Body 2.5.2 Three-Dimensional Hollow Black Body 2.5.3 High- and Low Photon Energy Limits 2.5.4 The Stefan–Boltzmann Law 2.5.5 Wien's Displacement Law 2.5.6 Emitted Radiation Power 2.5.7 Real Thermal Emitter 2.6 Laser-Generated X-Rays 2.7 Concluding Remarks References Part II Interaction of Particles with Electromagnetic Radiation 3 Elastic Scattering at Charged Particles 3.1 Free Electron 3.1.1 Radiation Force 3.1.2 External Field 3.1.3 Dipole Moment and Differential Power per Solid Angle 3.2 Bounded Electron 3.2.1 Equation of Motion of a Weakly-Bounded Electron 3.2.2 Radiation Force 3.2.3 External Field 3.2.4 Dipole Moment and Differential Power per Solid Angle 3.3 Cross-Section 3.4 Polarization of Scattered Radiation 3.5 Photo-Excitation of Atoms 3.5.1 Linear Scattering 3.5.2 Non-linear Scattering 4 Inelastic Scattering and Absorption 4.1 Free Carrier Absorption—Inverse Bremsstrahlung 4.2 Raman Scattering 4.3 Photo-Ionization or Photo-Effect 4.4 Ponderomotive Energy and Force 4.5 Non-linear Photo-Ionization 4.5.1 Tunnel Ionization 4.5.2 Multi-photon Ionization 4.5.3 Keldysh Parameter for Atoms 4.5.4 Above-Threshold Multi-photon Ionization 4.6 Compton Scattering 4.7 Pair Production References 5 Scattering by Many Charges 5.1 Attenuation Coefficient 5.2 Coherent Scattering References Part III Interaction with Condensed Matter Without Absorption 6 Scattering in Matter 6.1 Reversible and Irreversible Interaction 6.2 Maxwell Equations in Matter 6.3 Lorentz Model 6.4 Refractive Index 6.5 Many Different Scatterers 6.6 Wave Equation in Matter 6.7 Straight Propagation in Condensed Matter 6.8 Speed of Light in Media References 7 Linear Optics 7.1 Steadiness of Fields 7.2 S-Polarized Radiation 7.3 P-Polarized Radiation 7.4 Boundary Conditions with Complex Refractive Index 7.5 Fresnel Equations for Transparent Dielectrics 7.6 Reflectance and Transmittance 7.7 Nearly Perpendicular Irradiation 7.8 Brewster Angle 7.9 Critical Angle for Total Reflection 7.10 Internal Reflection and Evanescent Waves 8 Non-linear Optics 8.1 Principal Equations of Non-linear Optics 8.2 Non-linear Repulsive Forces 8.3 Second-Order Processes 8.3.1 Equation of Motion with Non-centrosymmetric Media 8.3.2 Non-linear Polarization Density 8.3.3 Differential Equation for the Second Harmonic Field 8.3.4 Second Harmonic Generation 8.3.5 Three-Wave Mixing 8.3.6 Parametric Amplification 8.4 Third-Order Processes 8.4.1 Equation of Motion with Centrosymmetric Media 8.4.2 Four-Wave Mixing 8.4.3 Third-Harmonic Generation 8.4.4 Kerr Effect 8.4.5 Self-focusing 8.4.6 Catastrophic Self-focusing 8.4.7 Self-phase Modulation References Part IV Interaction with Absorption 9 Electron Gas in Condensed Matter 9.1 Periodic Potentials 9.2 Electronic Properties at Zero Temperature 9.2.1 Quantized Wave Number and Energy 9.2.2 Density of States 9.2.3 Fermi–Dirac Distribution at T=0 K 9.3 Electronic Properties at Higher Temperatures 9.3.1 Fermi–Dirac Distribution at Higher Temperatures 9.3.2 High Electron Density: Metals 9.3.3 Low Electron Density: Semiconductors References 10 Optical Properties of an Electron Gas 10.1 General Aspects—Lambert–Beer's Law 10.2 Electron Gas 10.2.1 Free Electron Gas 10.2.2 Quasi-free Electron Gas 11 Band Theory of Crystals 11.1 Electronic Band Formation 11.2 Valence and Conduction Bands 11.2.1 Crystals at Absolute Zero Temperature 11.2.2 Crystals at Higher Temperatures 11.2.3 Electrons and Holes in Semiconductors 11.2.4 Electrons in the Conduction Band of Metals 11.3 Band Structure and Dispersion Relation in Crystals 11.4 Non-crystalline Matter References 12 Linear Absorption 12.1 Absorption in Condensed Matter 12.2 Interband Excitation 12.2.1 Reduced Band Structure Plot 12.2.2 Dielectrics and Semiconductors 12.2.3 Transition Metals 12.3 Intraband Excitation 12.4 Non-crystalline Matter—Disordered Matter 12.5 Excited State Transitions 12.5.1 Dielectrics and Semiconductors 12.5.2 Recombination and Meta-Stable States 12.5.3 Excited Transition Metals 12.6 Optical Properties of Metals 12.6.1 Non-excited Metals 12.6.2 Excited Dielectrics References 13 Non-linear Absorption 13.1 Excitation Pathways 13.2 Electron Rate Equation 13.3 Non-linear Photo-Excitation 13.3.1 Keldysh Parameter for Crystals 13.3.2 Tunnel Excitation 13.3.3 Multi-photon Excitation 13.3.4 Non-linear Photo-Excitation 13.3.5 Two-Photon Absorption 13.3.6 Three-Photon Absorption 13.4 Impact Ionization 13.5 Channeling and Filamentation 13.5.1 Channeling 13.5.2 Filamentation References 14 Heating 14.1 Process Steps of Heating 14.2 Two-Temperature Model 14.3 Derivation of the Heat Equation 14.4 Heating of Metals 14.5 Thermophysical Properties of the Electron System 14.5.1 Heat Capacity of the Electron System 14.5.2 Thermal Conductivity of the Electron System 14.5.3 Electron-Phonon Coupling Parameter 14.6 Thermodynamic Properties of the Phonon System 14.6.1 Heat Capacity of the Phonon System 14.6.2 Thermal Conductivity of the Phonon System 14.7 Numerical Approach 14.8 Examples for Laser-Heated Metals 14.8.1 Nanosecond Laser Radiation 14.8.2 Femtosecond Laser Radiation References 15 Phase Transitions 15.1 Laser-Induced Phase Changes 15.1.1 Slow Heat Transfer 15.1.2 Fast Heat Transfer 15.2 Heating with Phase Transitions—Modeling 15.3 Thermo-physical Equations References Part V Selected Applications in Metrology 16 Reflectometry 16.1 Measurement Methods 16.2 Pump and Probe Metrology 16.3 Time-Resolved Reflectometry 16.3.1 Principle and Set-Up 16.3.2 Examples References 17 Ellipsometry 17.1 Fundamentals on Polarization States 17.2 Principles of Ellipsometry 17.3 Experimental Approach 17.4 Reflection at One Interface 17.5 Reflection at Many Interfaces for Thin Layers 17.6 Layer- and Dispersion-Models 17.7 Imaging Ellipsometry 17.7.1 Principle Set-Up 17.7.2 Spatial-Resolved Measurement 17.8 Space- and Time-Resolved Ellipsometry 17.8.1 Principle Set-Up 17.8.2 Examples References 18 Nomarski Microscopy 18.1 Principle of Nomarski Microscopy 18.2 Time-Resolved Nomarski Microscopy 18.3 Examples Reference 19 White-Light Interferometry 19.1 Principle of Mach-Zehnder Interferometry 19.2 White-Light Interferometry 19.3 Pump-Probe White-Light Interferometry 19.4 Super-Continuum Source 19.5 Interferogram Analysis 19.6 Examples 19.7 Conclusion Reference Appendix Bibliography Index This textbook explains the fundamental processes involved in the interaction of electromagnetic radiation with matter. It leads students from a general discussion of electrodynamics, forming the mathematical foundation for the Maxwell equations, to key results such as the Fresnel equations, Snell’s law, and the Brewster angle, deriving along the way the equations for accelerated charges and discussing dipole radiation, Bremsstrahlung and synchrotron radiation. By considering more and more interacting particles, the book advances its treatment of the subject, approaching the solid-state regime using both classical and quantum mechanical approaches to describe interaction paths with electromagnetic radiation. Finally, specific interactions of laser radiation with matter are explained such as ultrafast, coherent, and selective interaction. With an emphasis on achieving an intuitive grasp of the basic physics underlying common laser technology, this textbook is ideal for graduate students seeking both a better fundamental and applied understanding of laser–matter interaction.