Ultrashort Laser Pulse Phenomena, 2nd Edition

632 Slowly Evolving Wave Approximation

So far the propagation equation is still exact, and no approximations have been

made. The terms on the right-hand side are small compared to those on the left-

hand side and can be neglected if Eqs. (3.94)–(3.96) are satisfied. In this case we

obtain Eq. (3.97). One should exercise caution in the application of Eq. (3.97)

up to an arbitrary order in the expansion of

ˆ

D. Depending on the particular pulse

duration, the higher order terms in the expansion of

ˆ

D on the right-hand side of

Eq. (C.13) may not be negligible as compared to the highest-order term of the

left-hand side of that expression.

Note, in the main text we frequently used t,z as local coordinates in a frame

moving with the group velocity.

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