Kramers-Kronig Relations in Optical Materials Research

1. Front Matter

   Pages I-IX

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2. Introduction

   Pages 1-3

3. Electrodynamic Properties of a General Physical System

   Pages 5-10

4. General Properties of the Linear Optical Response

   Pages 11-26

5. Kramers-Kronig Relations and Sum Rules in Linear Optics

   Pages 27-48

6. General Properties of the Nonlinear Optical Response

   Pages 49-69

7. Kramers-Kronig Relations and Sum Rules in Nonlinear Optics

   Pages 71-81

8. Kramers-Kronig Relations and Sum Rules for Harmonic-Generation Processes

   Pages 83-92

9. Kramers-Kronig Relations and Sum Rules for Data Analysis: Examples

   Pages 93-107

10. Modified Kramers-Kronig Relations in Nonlinear Optics

    Pages 109-114

11. The Maximum Entropy Method: Theory and Applications

    Pages 115-131

12. Conclusions

    Pages 133-135

13. Back Matter

    Pages 137-162

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TheKramers-Kronigrelationsconstitutethemathematicalformulationofthe fundamental connection between the in-phase to the out-of-phase response of a system to a sinusoidal time-varying external perturbation. Such connection exists in both classical and quantum physical systems and derives directly from the principle of causality. Apart from being of great importance in high energy physics, statistical physics, and acoustics, at present the Kramers-Kronig relations are basic and widely-accepted tools for the investigation of the linear optical properties of materials, since they allow performing the so-called inversion of optical data, i.e. acquiring knowledge on dispersive phenomena by measurements of absorptive phenomena over the whole energy spectrum or vice versa. Since the late ’80s, a growing body of theoretical results as well as of experimental evidences has shown that the Kramers-Kronig relations can be adopted for e?ciently acquiring knowledge on nonlinear optical phenomena. These results suggest that the Kramers-Kronig relations may become in a near future standard techniques in the context of nonlinear spectroscopy. Thisbookisthe?rstcomprehensivetreatisedevotedtoprovidingauni- ing picture of the physical backgrounds, of the rigorous mathematical theory, and of the applications of the Kramers-Kronig relations in both ?elds of l- ear and nonlinear optical spectroscopy. Some basic programs written for the 1 MATLAB environment are also included. This book is organized as an argumentative discourse, progressing from the linear to the nonlinear phenomena, from the general to the speci?c s- tems, and from the theoretical to the experimental results.

• Linear optics
• Nonlinear optics
• Optical materials research and development
• Optical spectroscopy
• Physical chemistry
• entropy
• optics
• spectroscopy

• Department of Mathematics and Computer Science, University of Camerino, Camerino (MC, Italy

  Valerio Lucarini

• Department of Physics, University of Joensuu, Joensuu, Finland

  Kai-Erik Peiponen

• Department of Physics, University of Toronto, Toronto, Canada

  Jarkko J. Saarinen

• Department of Electrical Engineering, Lappeenranta University of Technology, Lappeenranta, Finland

  Erik M. Vartiainen