Page 465 - Engineering Electromagnetics, 8th Edition

CHAPTER 12 Plane Wave Reflection and Dispersion 447

Figure 12.15 Gaussian pulse intensities as functions of
time (smooth curves) before and after propagation through
a dispersive medium, as exemplified by the ω-β diagram of
Figure 12.14b. The electric field oscillations are shown
under the second trace to demonstrate the chirping effect
as the pulse broadens. Note the reduced amplitude of the
broadened pulse, which occurs because the pulse energy
(the area under the intensity envelope) is constant.

pulse, whose frequency spectrum is obtained only from the pulse envelope, is known
as transform-limited.In general, however, additional frequency bandwidth may be
present since E 0 may vary with time for one reason or another (such as phase noise
that could be present on the carrier). In these cases, pulse broadening is found from
the more general expression

τ = ωβ 2 z (96)

where ω is the net spectral bandwidth arising from all sources. Clearly, transform-
limited pulses are preferred in order to minimize broadening because these will have
the smallest spectral width for a given pulse width.

REFERENCES
1. DuBroff, R. E., S. V. Marshall, and G. G. Skitek. Electromagnetic Concepts and
Applications. 4th ed. Englewood Cliffs, N. J.: Prentice-Hall, 1996. Chapter 9 of this text
develops the concepts presented here, with additional examples and applications.
2. Iskander, M. F. Electromagnetic Fields and Waves. Englewood Cliffs, N. J.: Prentice-Hall,
1992. The multiple interface treatment in Chapter 5 of this text is particularly good.
3. Harrington, R. F. Time-Harmonic Electromagnetic Fields.New York: McGraw-Hill,
1961. This advanced text provides a good overview of general wave reflection concepts
in Chapter 2.
4. Marcuse, D. Light Transmission Optics.New York: Van Nostrand Reinhold, 1982. This
intermediate-level text provides detailed coverage of optical waveguides and pulse
propagation in dispersive media.