Quantum Optics

In this chapter we discuss a variety of physical effects which primarily depend on the dispersive properties of the medium, i.e. how the real part of the refractive index depends on the frequency of light. For example, it is well known that the efficiency of nonlinear optical processes such as harmonic generation depends on the phase matching, which in turn depends on the refractive index at the fundamental and harmonic frequencies [1]. Thus a control of dispersion will enable us to obtain more efficient harmonic generation [2–5]. This in fact was the starting point of the work on control of dispersion [2]. Another subject where the dispersion is very important is in the propagation of the pulses which generally are distorted [6] by the dispersion of the medium and hence one needs to tailor the dispersion to obtain nearly distortionless propagation [7]. In Section 17.1, we have already shown how an appropriately chosen control field leads to a significant modification of the dispersion (Figure 17.4). We will now discuss some applications of this. We will also discuss how hole burning physics (Section 13.2) can be used to obtain very significant control of the dispersion.

Group velocity and propagation in a dispersive medium

Let us consider the one-dimensional propagation of an electromagnetic pulse in a dispersive medium characterized by susceptibility χ(ω) and refractive index n(ω).