Non-Linear Optical Response in Atoms, Molecules and Clusters (eBook)

Contents 6
Acronyms 8
Symbols 9
Greek Symbols 10
1 Introduction 11
1.1 The Need for Highly Nonlinear Optical Materials 11
1.2 Nonlinear Optical Phenomena in Terms of Response Functions 13
1.3 Brief Account of Nonlinear Optical Processes 15
1.3.1 Second Harmonic Generation 15
1.3.2 Optical Rectification 15
1.3.3 Electric Field Induced Second Harmonic 16
1.3.4 Self-focusing 16
1.3.5 Two Photon Absorption 16
1.3.6 Electro-Optic Kerr Effect 17
References 17
2 Response Functions 18
2.1 Causal Response 18
2.2 Kramers-Kronig 19
2.3 Symmetry Relations 20
2.3.1 Permutation Symmetries 20
2.3.2 Structural Symmetries 21
2.4 Quantum Field Theory Response Formalism 22
2.5 Diagrammatic Technique for Susceptibilities 25
References 28
3 Density Functional Perturbation Theory 29
3.1 The Original Sternheimer Method 29
3.2 Modified Sternheimer Method 30
3.3 Greens Function Approach to DFPT 31
3.4 Dyson Equation of DFPT 33
3.5 Dynamic Sternheimer Equation 34
3.6 Sternheimer Method for Nonlinear Response 35
3.7 Algorithm for Solving DFPT Equations 38
3.7.1 Sternheimer Equation Iteration 38
3.7.2 Self Consistent Iteration 39
3.7.3 Linear Polarizability 40
3.7.4 First Hyperpolarizability 40
3.8 Illustration of the Modified Sternheimer Method 42
References 42
4 Real Time Method 43
4.1 Adiabatic Local Density Approximation 43
4.2 Real-Time Evolution 44
4.3 Real-Space Implementation 45
4.4 The Real Time Algorithm 46
References 46
5 Response Functions from Real Time TDDFT 48
5.1 Method I: Reduction to a Linear System 48
5.1.1 Time Dependent Density 49
5.1.2 Extraction in Case of Isotropic Symmetry 51
5.1.3 Generalization 52
5.2 Locality of Nonlinear Response Under Monochromatic Excitation 54
5.3 Method II: Direct Evaluation 57
5.4 The Role of the Convolution Integral mathcalG(?) in Calculations of Response Functions 60
5.5 Method III: Differentiation in Frequency Domain 60
5.6 Conclusion 62
References 62
6 Nonlinear Response in Atoms, Molecules and Clusters 63
6.1 Numerical Considerations 63
6.2 Comparison to Experiment and DFPT Calculations 66
6.3 Silver Dimer 67
6.4 Summary 69
References 69
7 Extension to Condensed Matter and Outlook 70
7.1 Calculations in Dense Media 70
7.2 Calculations in Case of Periodic Solids 70
7.3 Future Directions 71
References 72
Index 73