Ultrashort Laser Pulse Phenomena, 2nd Edition

6 Fundamentals

From Eq. (1.10) it is obvious that the decomposition of (t)intoω and ϕ(t)

is not unique. The most useful decomposition is one that ensures the smallest

dϕ/dt during the intense portion of the pulse. A common practice is to identify

ω



with the carrier frequency at the pulse peak. A better definition—which is

consistent in the time and frequency domains—is to use the intensity weighted

average frequency:

ω=



∞

−∞

|

˜

E(t)|

2

ω(t)dt



∞

−∞

|

˜

E(t)|

2

dt

=



∞

−∞

|

˜

E

+

()|

2

d



∞

−∞

|

˜

E

+

()|

2

d

(1.18)

The various notations are illustrated in Figure 1.2 where a linearly up-chirped

pulse is taken as an example. The temporal dependence of the real electric field