Oscillator Model of Strong Light-Matter Coupling

Abstract

The optical properties of matter are determined by the coupling of various types of “oscillators” in matter to the electromagnetic radiation field. In other words, an incident electromagnetic field will cause these oscillators to perform driven oscillations. In this strong coupling approach we find a typical resonance behavior where the amplitude of the driven oscillations depends on the angular frequency $\omega$ of the incident field, on the eigenfrequency $\omega _{0}$ of the oscillators, on the coupling strength f between electromagnetic field and oscillator, and on its damping $\gamma$. In semiconductors the main intrinsic oscillators or optical excitations are optical phonons, excitons including their ionization continuum and higher band-to-band transitions or plasmons. Actually, we can anticipate that many basic features of the optical properties related to these oscillators are similar. Therefore it is reasonable to discuss first, in a general way, the optical properties of an ensemble of model oscillators. These model oscillators are known as Lorentz oscillators. By using the results of this treatment we find a quite simple and intuitive access to the optical properties of semiconductors which is in many respects very close to reality. This is obvious when comparing the calculated optical spectra and the dielectric function in the vicinity of the resonances of optical excitation to the experimental results reviewed in the remaining chapters of this book. We will thus follow this classical approach for some while, and explain at the appropriate places which modifications appear if quantum-mechanical properties are included. We begin with the simplest case of uncoupled oscillators and refine the concept in various steps in the course of this chapter.

Problems

7.1

Study for the case of weak damping some reflection spectra in the infrared (optical phonons) of at least partly ionic bound semiconductors, and compare with the data for $\omega _{0}$ and $\omega _{\text {L}}$ given there.

7.2

Calculate the spectra of reflection for a single surface for weak and for strong damping with otherwise constant parameters. Compare the shift of the reflection maxima and minima with respect to the transverse and longitudinal eigenenergies $\omega _{0}$ and $\omega _{\text {L}}$, respectively. Which quantity can be deduced with reasonable accuracy from a first inspection of the reflection spectra?

7.3

Make a qualitative sketch of the electric fields for normal incidence of light on a medium with higher or lower index of refraction and weak or vanishing absorption, for strong absorption and for frequency $\omega _{0}<\omega <\omega _{\text {L}}$ and vanishing damping.

7.4

Compare the experimental preparation of the Reststrahlen band in Fig. 7.7a to the functional principle of a so-called Lummer–Gehrcke device. The latter is a plane-parallel slab of transparent matter that was formerly used as an optical filter. Explain the differences of the two devices.