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William H. Hayt and John. A. Buck, Engineering Electromagnetics. McGraw-Hill, ver 7, 2006.

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William H. Hayt and John. A. Buck, Engineering Electromagnetics. McGraw-Hill, ver 7, 2006.

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CHAPTER 13

Having β2 change sign at the midpoint, yields a zero ∆τ , and so the pulse emerges from the
output unchanged! Physically, the pulse acquires a positive linear chirp (frequency increases
with time over the pulse envelope) during the first half of the channel. When β2 switches sign,
the pulse begins to acquire a negative chirp in the second half, which, over an equal distance,
will completely eliminate the chirp acquired during the first half. The pulse, if originally
transform-limited at input, will emerge, again transform-limited, at its original width. More
generally, complete dispersion compensation is achieved using a two-segment channel when
β2L = −β2 L, assuming dispersion terms of higher order than β2 do not exist.
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