The Kramers-Krδnig relationships provide fundamental rules for the relationships between the real and imaginary parts of the spectrum of any real physically realisable quantity when expressed as a complex function of frequency. One cannot, for example, design the optical gain spectrum to be any desired function of frequency without discovering that the phase spectrum is then closely prescribed. Frequently, such connections appear to be abstract and mathemat ically based. This appendix looks at three different ways of discovering these relationships which should help the reader to understand the fundamental nature and physics of the Kramers-Kronig relationships. The appendix includes at the end a collection of approximations for the real refractive indices of relevant laser materials.

Inspec keywords: Kramers-Kronig relations; refractive index; optical materials

Other keywords: laser materials; phase spectrum; real refractive indices; optical gain spectrum; Kramers-Kronig relationships

Subjects: Optical constants and parameters (condensed matter)