From Basics to Future Prospects

where ∆z denotes the distance traveled by a crest in the time interval t2 to t1 and c is the speed of light in a vacuum. The situation becomes more complicated when a pulse of light propagates through a dispersive optical medium. Via Fourier’s theorem, a pulse of duration τ comprises a range of frequencies. In a sense, a pulse can be thought of as resulting from constructive and destructive interference among various Fourier (frequency) components. At the peak of the pulse, the components tend to add up in phase and to interfere destructively in the temporal wings of the pulse (Figure 2). In a material with a refractive index that is frequency-dependent, each of these frequencies propagates with a different phase velocity, thereby disrupting the interference. If n(ω) varies linearly as a function of ω, the vp = ∆z t 2 – t 1 = c n(ω) How can the speed of light be reduced a millionfold, and why does this matter? The answers to these questions are intriguing and important.