Book contents
- Frontmatter
- Contents
- Preface
- List of symbols
- List of abbreviations
- 15 Hilbert transforms in En
- 16 Some further extensions of the classical Hilbert transform
- 17 Linear systems and causality
- 18 The Hilbert transform of waveforms and signal processing
- 19 Kramers–Kronig relations
- 20 Dispersion relations for some linear optical properties
- 21 Dispersion relations for magneto-optical and natural optical activity
- 22 Dispersion relations for nonlinear optical properties
- 23 Some further applications of Hilbert transforms
- Appendix 1 Table of selected Hilbert transforms
- Appendix 2 Atlas of selected Hilbert transform pairs
- References
- Author index
- Subject index
21 - Dispersion relations for magneto-optical and natural optical activity
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- List of symbols
- List of abbreviations
- 15 Hilbert transforms in En
- 16 Some further extensions of the classical Hilbert transform
- 17 Linear systems and causality
- 18 The Hilbert transform of waveforms and signal processing
- 19 Kramers–Kronig relations
- 20 Dispersion relations for some linear optical properties
- 21 Dispersion relations for magneto-optical and natural optical activity
- 22 Dispersion relations for nonlinear optical properties
- 23 Some further applications of Hilbert transforms
- Appendix 1 Table of selected Hilbert transforms
- Appendix 2 Atlas of selected Hilbert transform pairs
- References
- Author index
- Subject index
Summary
Introduction
The focus of this chapter is the derivation of dispersion relations arising in magnetooptical applications and for natural optical activity. A further topic considered is the development of sum rules for some of the quantities that are experimentally accessible. These include the optical rotatory dispersion (commonly abbreviated as ORD in the literature), circular dichroism (CD), the magnetic analogs, the Faraday dispersion, and magnetic circular dichroism (MCD). These terms will be defined shortly.
A number of the ideas that are employed are very similar to those developed in the preceding two chapters. There are, however, some major differences that arise for the cases of magneto-optical and natural optical activity. The dispersion relations for magneto-optical and natural optical activity have a different structure compared with what was found for the typical case of other optical properties discussed in Chapters 19 and 20. The difference arises primarily from the form of the crossing symmetry relations for the refractive indices and absorption coefficients for left and right circularly polarized light. The reason for the absence of simple dispersion relations for the individual modes corresponding to the refractive indices for left and right polarization, and the corresponding absorption coefficients for right and left circularly polarized light, is also discussed.
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- Hilbert Transforms , pp. 306 - 350Publisher: Cambridge University PressPrint publication year: 2009
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