Ultrashort Laser Pulse Phenomena, 2nd Edition

Evolution of the Pulse Energy 303

be taken into account by using the operator defined in Eq. (3.79) for the media

instead of Eq. (5.29) derived from the rate equations.

The operator describing the pulse change at each round-trip is obtained by

multiplying the transfer functions of all elements of the cavity, neglecting prod-

ucts of small quantities. To evaluate the steady state (5.28),

˜

E(t + h ) can be

conveniently written as (1 + h

d

dt

+ …)

˜

E(t), leading to an integro-differential

steady-state equation for the complex pulse envelope. The type of laser to be

modeled determines the actual elements (operators) that need to be included.

A parametric approach ...