Ultrashort Laser Pulse Phenomena, 2nd Edition

410 Femtosecond Pulse Amplification

Values of ¯n

2

are listed for various transparent materials in Table 7.2.

2

To a

typical value of ¯n

2

≈ 5×10

−16

cm

2

/W at 0.6 µm corresponds a critical power of

P

cr

≈ 700 kW, or only 70 nJ for a 100 fs pulse. Much higher energies are readily

obtained in fs amplifiers. To estimate the self-focusing length, let us consider a

saturated amplifier. The pulse energy W = Pτ

p

is of the order of the saturation

energy density ω



/2σ

01

times the beam area S ≈ 0. 5πw

2

0

. For a dye amplifier

operating around 600 nm (σ

01

≈ 10

−16

cm

2

), the saturation energy density is of

the order of 3 mJ/cm

2

; hence the peak power for a 100 fs pulse in a beam