Ultrashort Laser Pulse Phenomena, 2nd Edition

26 Fundamentals

If the propagation of short pulses is computed over long distances, the cumu-

lative error introduced by neglecting the right-hand side of Eq. (1.88) may be

significant. In those cases, a direct numerical treatment of the second-order wave

equation is required.

Further simplifications are possible for a broad class of problems of practical

interest, where the dielectric constant changes slowly over frequencies within the

pulse spectrum. In those cases, terms with n ≥ 3 can be omitted too (D = 0),

leading to a greatly simplified reduced wave equation:

∂

∂ξ

˜

E(η, ξ) −

i

2

k





∂

2

∂η

2

˜

E(η, ξ) = 0,

(1.93)

which describes the evolution of the complex ...