Abstract
The causally interrelated effects of phase dispersion and absorption on the evolution of an electromagnetic pulse as it propagates through a homogeneous linear dielectric, particularly when the pulse is ultrawideband, developed originally by Sommerfeld [1] and Brillouin [2, 3, 4] in 1914 in support of Einstein’s 1905 special theory of relativity [5], Brillouin’s signal velocity description partially corrected by Baerwald [6] in 1930, and the theory finally completed in the 1970–1980’s by Oughstun [7] and Sherman [8, 9, 10, 11, 12] in a series of papers that forms the basis of the modern asymptotic theory have been described in detail in Chaps. 12–15 of this volume. The results show that after the pulse has propagated sufficiently far in the medium, its spatiotemporal dynamics settle into a relatively simple regime, known as the mature dispersion regime, for the remainder of the propagation. In this regime, the wavefield becomes locally quasimonochromatic with fixed local frequency and wavenumber in small regions of space–time which move with their own characteristic constant velocity. The theory provides accurate but approximate analytic expressions for the local wave properties at any given space–time point in the mature dispersion regime. The expressions are complicated, however, as is their derivation from a well-defined asymptotic theory (presented in Chap. 10), and neither do the results nor their derivations provide complete insight into the physical reasons for the wavefield having the particular local space–time properties it does have in the various subregions of space moving with specific velocities.
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Notes
- 1.
Remember that an ultrashort pulse is also ultrawideband, but that an ultrawideband signal need not be ultrashort.
- 2.
Notice that the variable notation ω′ = ℜ{ω} and ω′ = ℑ{ω} is still used here.
- 3.
The numerical algorithm used to evaluate the integral representation of the propagated pulse wavefield for this and subsequent examples in this section is described in [22]. As discussed in that reference, the algorithm begins to produce numerical artifacts in the results as θ approaches 1 from above for the delta function pulse. This is a consequence of the fact that the integral itself is ill behaved at θ = 1 (see Sect. 13.2.5).
- 4.
Notice that Stratton’s analysis is based on the Laplace transform with integration variable \(s = -\mathit{i}\omega \).
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Oughstun, K.E. (2009). Physical Interpretations of Dispersive Pulse Dynamics. In: Electromagnetic and Optical Pulse Propagation 2. Springer Series in Optical Sciences, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0149-1_8
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