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Published online by Cambridge University Press: 05 June 2012
Introduction and preview
While everything in Chapter 6 came under the umbrella of linear optics, in this chapter we will be looking at a range of nonlinear phenomena associated with optical pulses. We will consider the process of self-phase modulation in considerable detail, and see how it can be used, in combination with dispersion, to stretch and compress optical pulses, and to generate optical solitons. We will examine the adverse effects of group velocity dispersion on second harmonic generation, and examine various ways of optimising the bandwidth in optical parametric chirped pulse amplification. Finally, we will discover how nonlinear optical techniques can be used in the diagnosis of ultrashort pulses and for the stabilisation of the carrier-envelope phase.
Wave equation for short pulses
A detailed derivation of the differential equation governing the propagation of short optical pulses under nonlinear conditions is long and intricate; see for example [59]. To avoid this, we will take a series of reasonable steps that lead to the correct conclusion.
We start, as in Section 2.2, by substituting Eqs (2.4) and (2.5) into Eq. (2.3), but we now retain three time-dependent terms that were previously discarded.
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